Tabu Search with both short-term memory

AN ABSTRACT OF THE DISSERTATION OF

Kevin Donald Boston for the degree of Doctor of Philosophy in Forest Engineering presented on June 27, 1996 Title: Using Tabu Search to Solve Tactical Forest Planning Problems with Spatial Wildlife Habitat Goals and Constraints

Abstract approved: John Sessions

A method was developed to formulate and solve a fifty-year tactical harvest scheduling problem that included spatial wildlife habitat goals and constraints for a 4800-acre watershed in Northwestern Oregon under four scenarios. Three goals and two habitat constraints were included in each scenario. The first goal was a volume goal. The second goal was a landscape aggregation goal measured with

the contagion index. The third goal was a shape goal using the ratio of the existing perimeter of closed-canopy stands with that of a circle with equivalent area. The first constraint required a minimum cluster of connected closed-canopy stands that spanned opposite edges of a map. The second constraint limited the maximum opening created in

any period. The algorithm included both fixed and variable cost components for the transportation network.

Tabu Search with both short-term memory restriction and a long-term diversification strategy was used to solve this ten-period problem. The performance of the

heuristic was measured by comparing the results with an estimate of the optimal value obtained from extreme value theory using a three-parameter Weibull distribution.

In scenario one, the shape goal was reached in most periods and the average contagion index was 0.35. The volume goal was met or exceeded in all periods. The

heuristic found one solution within 2 percent of the estimated optimal value, while

75

percent of the solutions were within 80 percent of the estimated optimal value.

In scenario two, the average contagion index was 0.40. The goal was met in over 50 percent of the periods.

The volume and shape goals were met or exceeded in all

periods. The heuristic found one solution within 6 percent of the estimated optimal value, while the remaining solutions were within 83 percent of the estimated optimal value.

Two additional scenarios were developed to create specific wildlife habitat. Scenario three developed high quality habitat for pine marten containing a connected

landscape of closed-canopy stands with minimum edge habitat.

Scenario four was

developed for elk. This analysis produced habitat with a mixture of open and closedcanopy stands in a dispersed pattern.

USING TABU SEARCH TO SOLVE TACTICAL FOREST PLANNING PROBLEMS WITH SPATIAL WILDLIFE HABITAT GOALS AND CONS TRATNTS

by

Kevin Donald Boston

A DISSERTATION submitted to

Oregon State University

in partial fulfillment of

the requirements for the

degree of Doctor of Philosophy

Completed June 27, 1996 Commencement June 1997

Doctor of Philosophy Dissertation of Kevin Donald Boston Presented on June 27, 1996 Approved:

Major Professor Representing Forest Engineering

Head of the Department of Forest Engineering

Dean of the Graduate School

I understand that my dissertation will become part of the permanent collection of Oregon State University libraries. My signature below authorizes release of the thesis to any reader upon request.

Kevin Donald Boston, Author

TABLE OF CONTENTS

Page

INTRODUCTION

1

LITERATURE REVIEW Landscape Ecology Forested Landscape Studies Landscape Indices Percolation Models Harvest Scheduling Mixed-Integer Techniques Lagrangean Relaxation Techniques Dynamic Programming Techniques Decomposition Techniques Random Search Techniques Directed Search Techniques Tabu Search Genetic Algorithms Extreme Value Theory and Heuristic Performance

42

JUSTIFICATION

46

OBJECTWES

48

DATA COLLECTION AND CALCULATION OF VARIABLES Inventory Data Growth and Yield Log Values Discount Rate Logging Cost Transportation Cost Riparian Areas Seral Stages

50 50 52 52 53 53 54 54 59

METHODS MsD PROCEDURES Site Selection Procedures Problem Formulation The Objective Function The Constraints The Search Procedure Evaluation of the Heuristic

61 61 61 63 66

4 4 8 11

14 15

21 26

27 27 29 34 36 41

68 70 78

TABLE OF CONTENTS (Continued)

Page

RESULTS Results for Scenario One Results for Scenario Two Results for Wildlife Scenarios Three and Four Evaluation of the Heuristic Discussion of Results

101 101

CONCLUSION Recommendations for Data Preparation Recommendations for Analysis

110 111 111

BIBLIOGRAPHY

113

APPENDICES Appendix 1 - Inventory Data Appendix 2 - Silvicultural Yields Appendix 3 - Transportation Network Appendix 4 - Solutions for Scenario One Appendix 5 - Solutions for Scenario Two

121 122 126

80 80 82 93

237 246 256

LIST OF FIGURES

Figure

Page

Generalized Tabu Search Algorithm

39

Generalized Weibull Distribution with Shape> 0

44

Existing Stand Map for the Horse Creek Drainage

51

Transportation Network and Logging Units for Horse Creek Drainage

55

Yarding Costs for Various Distances and Tree Sizes

56

Stream Systems for Horse Creek Drainage

58

Existing Seral Stages for Horse Creek Drainage

60

Vicinity Map for Horse Creek Drainage

62

Master Planning Coverage for Horse Creek Drainage

67

Unit Neighborhood Procedures

76

Road Neighborhood Procedures

77

Volume Harvested by Period for the Best Five Solutions - Scenario One

81

Area Perimeter Ratio for the Best Five Solutions - Scenario One

83

Contagion Index by Period for the Best Five Solutions - Scenario One

84

Location of Silvicultural Treatments in Period 0 for Scenario One

85


85


86


86

Location of Silviculturãl Treatments in Period 4 for Scenario One

87

LIST OF FIGURES (Continued)

Figure

Page


87


88


88


89


89

Volume Harvested by Period for the Five Best Solutions - Scenario Two

90

Area Perimeter Ratio for the Five Best Solutions - Scenario Two

91

Contagion Index by Period for the Five Best Solutions - Scenario Two

92

Location of Silvicultural Treatments in Period 0 for Scenario Two

94


94


95


95


96


96


97


97


98


98

Results for Pine Marten Analysis - Scenario Three

99

LIST OF FIGURES (Continued)

Figure

Page

Percolation Network for Pine Marten Analysis - Scenario Three

100

Results for Elk Analysis - Scenario Four

102

Percolation Network for Elk Analysis - Scenario Four

103

Weibull Distribution and Solutions for Scenario One

104

Weibull Distribution and Solutions for Scenario Two

105

LIST OF APPENDIX FIGURES

Figure

Page

Harvested Volume for Solutions 6 - 10 Scenario One

247


248


249

Area-Perimeter Ratio for Solutions 6 - 10 Scenario One

250


251


252

Contagion Index for Solutions 6 - 10 Scenario One

253

Contagion Index for Solutions 11 - 15 Scenario One

254

Contagion Index for Solutions 16 -20 Scenario One

255

Harvested Volume for Solutions 6 - 10 Scenario Two

257


258


259

Area-Perimeter Ratio for Solutions 6 - 10 Scenario Two

260


261


262

Contagion Index for Solutions 6 - 10 Scenario Two

263


264


265

LIST OF TABLES

Table,

Page

Summary of Spatial Harvest Scheduling Techniques

37

Log Prices by Grade for Planning Area

53

Riparian Area Classification and Stream Buffers, Distances in Feet

57

Residual Basal Area for Streams in the Oregon Forest Practice Rules Using Even-aged and Uneven-aged Silvicultural Systems

57

Seral Stage Classification

59

LIST OF APPENDIX TABLES

Table

Page

Existing Inventoiy Data: BA = Basal Area ft A2; TPA = Trees Per Acre

123

Yields for Even-Aged Prescriptions in Mbf per Unit

127

Yields for Uneven-Aged Prescriptions in Mbf per Unit

182

Road Network

238

© Copyright by Kevin Donald Boston June 27, 1996 All Rights Reserved

IJSIIG TABIJ SEARCH TO SOLVE TACTICAL FOREST PLANNING PROBLEMS WITH SPATIAL WILDLWE HABITAT GOALS AN]) CONSTRAIITS

INTRODUCTION

Increased public pressures now require that industrial forest land owners manage their

timber resources with increased concern for wildlife habitat. Several states have forest

practice rules mandating industrial timberland owners account for wildlife habitat requirements on their property. The California Forest Practices Act in 14 CCR 919.16, for example, currently requires mitigating measures be implemented by the forest land owners

to offset the impacts of harvesting timber in old growth and late seral forest stands on

private forest lands.

These measures must include a discussion of the anticipated

recruitment of functional wildlife habitat and the long-term anticipated landscape patterns.

Besides the mitigating measures for individual timber harvest plans, each large landowner in California is required to develop a sustained yield plan to determine the allowable harvest

levels for their property. These sustained yield plans are for a minimum planning horizon of one hundred years. The plan must address threatened, endangered, and sensitive plants and wildlife species. The assessment will describe a species' habitat needs, including patch type, patch shape, and distribution of habitat in relation to growth and yield projections and harvest schedules 14 CCR 913.11. The sustained yield plan will describe feasible measures

to avoid or mitigate adverse environmental impacts on wildlife habitat. With the listing of

the marbled murrelet, Branchyramphus marmoratus, and the northern spotted owl, Strix occidentalis caurina, as threatened species, many large timberland owners in the Pacific

2

Northwest are developing habitat conservation plans that include spatial arrangement of their harvesting units to promote the development of desirable wildlife habitat to mitigate the impacts of harvesting on wildlife habitat as part of their habitat conservation plans.

California is not the only western state with spatial harvesting restrictions.

In

Washington State, the Forest Practices Rules require harvesting patterns on big game winter ranges be designed to increase edge habitat. The Washington State Forest Practices

Rules have a complex adjacency requirement. These rules require that the perimeter of a proposed clearcut area meet one of the following criteria (WAC 222.30-025): At least 30 percent of the adjacent stands greater than 30 years. Sixty percent of the adjacent stands be fifteen years or older.

Ninety percent of the adjacent stands be five years or older.

The goal for this complex adjacency requirement is an attempt to reduce the cumulative impacts of timber harvesting on the environment.

The increased regulation has raised the importance for tactical forest planning on industrial timberlands. The high degree of regulation has made piecemeal harvest planning impractical and financially risky. Improper planning can result in large areas of timberland

being unavailable to harvest due to the spatial constraints imposed by forest regulations.

Foresters must consider two scales when applying management activities to a forest. The first scale is within the stand. It includes stand characteristics such as tree size, quantity

and quality of snags, and amount of down woody debris. The second scale is the landscape

scale, the arrangement and quantity of various patches in a forest. This is a landscape study; it will describe a methodology to assist industrial forest land managers in tactical harvest planning. A tactical plan will be developed that will maximize present net revenue

3

less the penalties for deviating from the wildlife and timber goals. The system will include

constraints limiting the size of the opening that can be created and will require the maintenance of a minimum cluster to connect opposite edges of the planning area. There will be three goals for this tactical plan. The first goal is a landscape aggregation goal. The

second goal is a shape goal for the closed-canopy stands. The final goal is an even-flow harvest goal.

4

LITERATURE REVIEW

One goal for this project is to develop a methodology to incorporate spatial wildlife constraints and goals into a tactical forest planning model. The literature review will begin

by describing the importance of spatial arrangement on wildlife populations. These measures of spatial arrangements have been incorporated in many forest management simulators developed to study of impacts of management activities on forested landscapes. Following the documentation of the importance of landscape structure, the literature review

will describe two methods that can quantify landscape structure. The remaining section will be devoted to mathematical optimization techniques. It will

begin by documenting the analytical methods used to solve resource planning problems.

The next section will review the use of Tabu Search and genetic algorithms to solve combinatorial problems. The last section will describe how extreme value theory can be applied to measure the performance of heuristics by estimating the optimal value.

Landscape Ecology

Landscape ecology has emerged as a cornerstone in ecosystems sciences since the 1960's. Forman and Gordon (1986) describe three main elements in landscape ecology. They are:

The importance of the pattern on the landscape function. The flow of biotic and abiotic elements throughout the landscape. The change in landscape pattern and flow with time.

5

These elements have applications in forestry and wildlife management. Forest management

activities change the composition, structure, and arrangement of patches in a forest. This influences the quality and quantity of wildlife habitat. Any conservation strategy involving

the spatial arrangement of patches must consider these concepts from landscape ecology. One of the major impacts of forest management activities has been the fragmentation of late seral forest habitat. The cutting pattern and cutting unit size determined the rate of fragmentation. Spies et al. (1994) used satellite imagery to calculate the structural change in forested landscapes between 1972 and 1988 on private and publicly managed forest lands

in Western Oregon. Private timberlands had larger units, and a higher cutting rate. This resulted in a rapid reduction of interior forest habitat, and provided minimal edge habitat.

The public lands were managed using a staggered setting policy. This harvesting pattern has smaller units located in a dispersed pattern. One result was more late seral forest habitat

but this habitat is highly fragmented (Spies et al., 1994).

Some studies have documented the impact of fragmentation on animal populations.

Mader (1984) studied the impact of isolation caused by roads on small mammals and arthropods in Europe. Animals were trapped, marked and released for a five-year period.

None of the forest dwelling rodents were caught in a patch that required them to cross a permanent road. The reluctance to cross roads was observed for forest roads that have low

traffic levels and are closed to public travel (Mader, 1984).

Many studies concerning the impact of forest fragmentation on wildlife habitat have been accomplished with simulation models. Fabrig and Merriam (1985) developed a patch

dynamics model for the white-footed mouse, Peromyscus leucopus, that inhabits forest patches in an agricultural landscape. Their results showed that isolated patches had a high

6

probability of extinction for the white-footed mouse. The results from the simulation model

are supported by a field study with the white-footed mouse in Ottawa. A significant difference in the population growth rates occurred for the white-footed mouse in the isolated woodlots (Fahrig and Merriam, 1985).

Lamberson et al. (1993) have developed a model that investigates the relationships

between the degree of aggregation in the landscape and the level of occupancy of the northern spotted owl. Their analysis showed that the greater the degree of aggregation of

the habitat patches in the landscape, the greater the occupancy of owls. Areas with the ability to maintain twenty or more nest sites can maintain populations when there is a moderate degree of connectivity among these areas (Lamberson et al., 1993). Beier (1993) simulated the population dynamics of cougars, Felis concolor, in Southern

California. His results showed that an inter-range corridor between the Palomar Range and

the Santa Ana Mountains could supply the immigration needed to maintain the likelihood

of persistence of cougars in the Santa Ana Mountains. Without this connection between the two areas, the Santa Ana Mountains are unable to maintain a genetically diverse cougar

population. This resulted in low probability of persistence for the mountain lion (Beier, 1993).

These studies show the consequences of isolation on wildlife populations. There is a reduction in immigration to these patches, a loss of genetic diversity within the patches. These factors lead to a high probability of local extinction in the isolated patches. Corridors

are often considered as a mitigating measure to reduce the likelihood of isolating the renmant patches, but corridors are not without criticism (Noss, 1991).

7

Noss and Hanis (1986) developed a conceptual scheme for preserving diversity. Their approach utilizes a system of nodes connected by conidors. Noss and Harris (1986) believe

that this arrangement of the landscape can maintain native biodiversity. The nodes are

subsets of the high diversity areas in the landscapes. The corridors will allow for the movement among nodes. By maintaining a larger genetic base, a specie's ability to adapt

will be enhanced. They urge a cautious approach to the use of corridors; corridors may allow for harmfhl agents to rapidly move through the corridors to the nodes (Moss, 1991). There are others who recommend the use of corridors to maintain species conservation.

Lindenmayer and Nix (1993) provided guidelines for the effective use of corridors to prevent isolation. Their criteria require incorporating the social and feeding characteristics

of the animals along with the characteristics of the sites when designing the corridor. Harrison (1992) adds other criteria for corridor design. Corridors must contain enough

suitable habitats for a species to permanently occupy the corridor. The width of the corridor must be determined by the length of the corridor. Longer corridors should be wider than short corridors.

The previous studies have documented the impacts of fragmentation on a species survival. Many warn against the use of corridors to offset the impacts of fragmentation. They feel that corridors are often improperly designed and do not promote the movement

of desired species. Many corridors become avenues for less desirable species to expand their ranges into the scarce habitats (Moss, 1991).

Forested Landscape Studies

These studies have dealt with small patches or single species within a landscape. The next section will review papers describing the potential impacts of management activities

on the forested landscape. Franklin and Forman (1987) investigated the consequences of various cutting patterns

on landscape structure. They represented their landscape as a grid with ten cells on each side. Each cell represented a ten-hectare unit. The model assumed that each cell could be harvested once during the analysis period and the only prescription allowed was the clearcut

prescription. The five harvesting patterns used in their analysis are the checkerboard, strip cutting, four nuclei, single nucleus, and progressive parallel strips. Landscape structure was

measured using average cut-over patch size and the length of edge. The results show that the checkerboard pattern produced the most edge habitat. The maximum edge occurs when

half of the area has been treated. The progressive parallel strips produced the least amount

of edge habitat. The single nucleus had the largest average cut-over patch size until 70 percent of the landscape was treated, then the checkerboard had the largest average patch size (Franidin and Forman, 1987). Although these models are a simplified representation of forest management, they acknowledge the influence of cutting-unit pattern on landscape

structure.

Li et al. (1993) continued to study the impacts of harvesting pattern on landscape structure. They developed a simulation model with more detailed cutting prescriptions to

investigate the landscape impacts from five cutting scenarios. The first was a random cutting strategy that selects a pixel at random and then assigns adjacent pixels to that unit

9

randomly until the maximum size is reached. The second scenario used a maximum dispersion pattern. The goal of this pattern is to locate units as far as possible from each other. The third approach is a staggered setting approach with small units that cannot be

adjacent to each other. The fourth scenario divides the landscape into four equal size blocks. A block is selected randomly, then all units within that block are selected randomly

for harvest. The final harvest pattern is a progressive cutting model that begins to cut in a random direction at each move from an existing unit. The model does not consider the spatial arrangement of existing vegetation, nor the location of streams, roads, and logical cutting unit boundaries. Li et al. (1993) used five measures of landscape structure; edge density, area-weighted

shape index, relative patchiness, and interior area fragmentation index. The maximum dispersion, staggered settings, and random cutting patterns produced the highest values for

fragmentation measures. The speed that the forest was fragmented is due to the level of aggregation of the cutting units. The greater the level of aggregation, the less fragmented the landscapes. Hansen et al. (1993) used the simulation model developed by Li et al. (1993) to develop

an approach to manage wildlife habitat on forest lands. They assumed that animal communities respond to landscape change. Changes in these animal communities can be

explained by the life histories of the animals and the changing landscapes' trajectories (Hansen et al., 1993). Four cutting patterns on the forest were used, staggered settings with a seventy-year rotation, a multiple use prescription with long rotations, an aggregate

harvesting technique, and a no cutting prescription. Their results show that the seventy-

year rotations produced the lowest habitat diversity of all of the prescriptions. This was

10

primarily due to the loss of micro features such as snags and down woody debris. The multiple use prescription maintained habitat for all of the late seral species, but reduced the

commodity outputs (Hansen et al., 1993).

Wallin et al. (1994) developed the CASCADE simulation model to investigate how forest management activities influence landscape pattern. It was one of the first landscape simulation models to incorporate logical logging units, and existing vegetation patterns into

the analysis.

The model investigated dispersed versus aggregate cutting patterns on

landscape structure. The cutting pattern was allowed to change from a dispersed pattern to an aggregate pattern during the analysis. Their results showed that the dispersed cutting method fragmented the forest in the least

amount of time. After twenty years of dispersed cutting, switching to an aggregate cutting pattern did little to reduce the fragmentation of the forest.

The landscape pattern becomes

somewhat rigid after a small portion of the entire landscape has been treated with the staggered setting approach (Wallin et al., 1994). The results agree with the other landscape

studies that the staggered setting cutting pattern fragments the forest in the least amount of time.

Liu (1993) created ECOLECON to simulate animal population dynamics and economic

revenues in response to different timber management objectives. Two types of cutting

prescriptions are allowed in this model. The first is a fixed rotation length; the other prescription allows for random cutting patterns once a stand reaches a minimum age. ECOLECON randomly assigns treatments to stands that are older than a minimum age. The model calculates the average population for a user-defined species during each period

in the simulation. Besides the population parameters, the model calculates the economic

11

returns from each treatment. This allows the analyst the opportunity to investigate different

management activities on species viability and on economic returns. These landscape simulation models do not allow a mixture of prescriptions in a single

analysis. Most do not use actual settings boundaries, but limit the polygons to simple geometric figures such as squares. They base their cutting pattern on a random number generator and measure the resulting landscape pattern following the treatments. They do

not provide a harvest schedule that can promote a desired landscape structure or meet volume targets.

Landscape Indices

In order to develop a desired landscape, the first step is to quantif,' landscape structure.

Two techniques for quantifying landscape structure will be reviewed in this section; they are landscape indices and percolation models.

Numerous landscape indices have been developed. Some are based on information theory such as the Shannon diversity index (Morganti, 1993). The Shannon diversity index

has two components. The first is the landscape richness which measures the number of

patch types on a landscape. The second component is the evenness component which measures the number of patches within each patch group. Another index often used in landscape ecology is the contagion index. The contagion index was developed by O'Neill et al. (1988) to measure the degree of aggregation within

the landscape. Li and Reynolds (1994) modified O'Neill et al.'s original formulation to increase the contagion index sensitivity to landscape change.

12

LaGro (1991) described patch shape using a relationship between the area and the perimeter. By combining the area-perimeter for all patches in the landscape a regression equation is used to calculate the fractal dimension for the landscape. LaGro calculated the

fractal dimension for a forested landscape from 1938 and 1988. The indices showed the increase in forest cover and the decrease in forest fragmentation between the periods. Bowen and Burgess (1981) collected many landscape indices and used them to measure

landscape pattern in the central hardwood forests of Ohio. One of the indices they described is the diversity index. It compares the perimeter of a patch with the perimeter of

a circle with equivalent area.

Other indices used were measures of isolation and

connectivity of the various patch types. These describe the potential movement of plants and animals across the landscape.

McGarigal and Marks (1993) developed FRAGSTATS, a comprehensive program to quantiI,r the landscape structure. FRAGSTATS provides numerous indices that can be used

to measure the landscape structure over time. It contains over fifty landscape indices grouped into eight categories. The first category contains the area metrics including total area and area by patch type. These measures do not describe the spatial arrangement of the

landscape. The second category includes the patch metrics. Examples of patch metrics are

the average patch size and the number of patches. Variance for these measures are also calculated. The third category contains the edge metrics. This category includes the total

edge and the amount of edge contrast that exist within a landscape. The fourth category

contains the shape metrics. They are based on the area-perimeter relationships for each patch. The fifth category includes the core area metrics. These are computed for patches

by eliminating the area influenced by the edge for each patch type. The sixth category

13

incorporates spatial arrangement into metrics. These include the nearest neighbor distance and the proximity index that include the size of the patch and the distance to other patches

within a specified range (McGarigal and Marks, 1993). The seventh category is the

diversity index that has been described by Morganti (1993). The last category is the contagion describe by Li and Reynolds (1993), and interspersion metrics. The interspersion

index measures the level of aggregation of the patches on the landscape.

These indices have been used in a number of studies. Recently, Schumaker (1994) related nine landscape indices with results from a computer dispersion model. The area-

perimeter ratio was one of the better performing indices for correlating the successful dispersion of the northern spotted owl. Schumaker felt that a new index, patch cohesion,

would be a better predictor of dispersion success. The patch cohesion index is the perimeter-area ratio divided by a shape index. Schumaker felt this index adequately predicted successful dispersal rates for the northern spotted owl. Hulshoff (1995) used a suite of indices to describe the Dutch landscape. These include the dominance index, two shape indices, and one change index. These indices were applied

independently and in combination for maps from 1845 to 1982. Hulshoff felt that the area metrics combined with the mean patch size adequately described the changes that occurred

in the Dutch landscape. The combinations of indices provided the best set of information for describing the landscape structure.

14

Percolation Models

Another technique used to quantify the landscape structure is derived from percolation theory.

Percolation models were used to predict the potential movement of animal

populations (Gardner et al, 1992). The key component in percolation theory is the critical

value. It occurs when the landscape's largest cluster spans one side of the map to other side. For random maps with square pixels this experimentally derived average critical value

is 0.592 (Gardner et al., 1992), or when approximately 60 percent of the landscape is contained in the largest cluster it will span the edges of the map.

There are two types of potential movement in percolation theory. One is bond percolation; it simulates the movement to the nearest neighbor.

The other type of

movement is site percolation; movement occurs to all neighboring sites.

O'Neill et al. (1992) used a percolation model to simulate the interaction of a disturbance with the spatial pattern of a landscape that contained habitat susceptible a disturbance that moves through a landscape. When the quantity of habitat was below the

critical value, disturbances have a low rate of spread. The landscape had become too fragmented to spread the disturbance to neighboring patches. In landscapes with the largest cluster greater than the critical value, the disturbance spreads rapidly until the critical value

is reached. Below the critical value the rate of spread decreases. (O'Neill et al., 1992). Percolation models have primarily been used with randomly generated landscapes; however, most natural landscapes are not random. They have a hierarchical structure. A

hierarchical structure is one that has distinct subsystems. These subsystems can have various degrees of connectivity between levels (O'Neill et al., 1986). Percolation theory is

15

still useful for modeling potential movement. The ability for a landscape to percolate can vary in nonrandom landscapes from 54 percent to 72 percent of the landscape occupied by

the largest cluster (O'Neill et al, 1992).

Harvest Scheduling

This section will the review development of mathematical techniques that incorporate

wildlife habitat constraints or solve spatially constrained harvest scheduling problems. It will begin by describing a linear programming approach for incorporating wildlife habitat requirements. The second part will describe multiple objective harvest scheduling problems.

The final section will describe techniques to solve spatially constrained problems. Linear programming is a common technique used to solve strategic harvest scheduling problems. There have been a number of strategic scheduling models developed using linear

programming (Dykstra, 1984). Some strategic planning models using linear programming

are FORPLAN (Johnson and Scheurman, 1977), Timber RAM (Navon, 1971), and MAX

MILLION (Clutter et al., 1968).

Sessions and Crim (1995) have incorporated habitat suitability indices into a linear programming model. Many habitat suitability models are the geometric mean of several habitat variables; thus, they are nonlinear. Sessions and Crim used a log transformation and a series of lower bound constraints to allow the analyst to include a habitat suitability index

in the linear programming formulation.

Each habitat suitability constraint can be

approximated by one log transformation of the original habitat suitability constraint and a lower bound constraint for each variable for each period in the planning horizon. This will

16

allow for these types of wildlife habitat constraints to be included in a linear programming

model, but it lacks any spatial arrangement.

Forestiy problems are complex. Many forestiy problems have conflicting goals such as producing timber and wildlife habitat. Several multiobjective programming techniques have been applied to solve these problems.

One technique for solving multiple attribute problems based upon the utility theoiy developed by Keeny and Raiffa (Canada and Sullivan, 1989). Hyberg (1987) developed a multiple attribute utility function for nonindustrial forest owners. The attributes used in this

model were forest aesthetics and forest revenues. Utility functions were created through

a series of lotteries. The forester's goal is to select the treatment that yields the highest utility value.

Mendoza et al. (1987) and Mendoza and Sprouse (1989) have developed an approach to generate alternatives for forest management problems. Their goal is to generate a set of

maximally different alternatives. This will provide the decision maker with a real choice

among the alternatives. The hop-skip-jump method generates maximally different alternatives. The algorithm begins by solving either a linear programming or a goal

programming problem. This becomes the starting point for the hop-skip-jump algorithm. A new alternative is found by solving the following linear program.

J Min

1.

j Subject to:

Z(x)

Tk

2.

17

Where J is the set of indices for the decision variables, x(j) in the original solution. This will

change the set of the basic variables, but the set of constraints will remain satisfied. Once these alternatives are created, Mendoza and Sprouse (1989) used the Analytical Hierarchy

Process (AHP) developed by Saty, 1980 to select the preferred alternative. AHP ranks

alternatives based on a series of pairwise comparisons. Mendoza and Sprouse (1989)

applied this system to a 23,000-acre forest. Three goals were incorporated in their problem. The first goal is to maximize economic returns; the second goal is to maximize the area of suitable wildlife habitat. The final goal is to maximize the area for recreation. They conclude that the combination of significantly different alternatives and AHP was a useful process for solving difficult multiple-use forest management problems.

Multiple objective techniques have not been commonly applied to tactical forest planning problems. One of the first examples was developed by Kangas and Pukkala (1996). They developed a multiattribute additive utility model to represent biodiverisity. Three categories are included in the utility function. They are mean volume of deciduous

trees, percentage of old forest, and mean volume of deadwood. Treatments are assigned to discrete units to maximize the sum of the utility functions.

There have been several attempts to disaggregate solutions from strata-based models to achieve spatially feasible plans. Jamnick and Walters (1992) developed CRYSTAL; a mle-based approach to allocate the results of strata-based planning to the landscape. These mles include restrictions on the maximum opening size. This technique is useful for many

problems that do not have complex spatial goals and constraints that must be included in the formulation when calculating the sustainable harvest levels.

18

Nelson and Enrico (1993) developed another approach to incorporated adjacency constraints into a strategic plan. Their approach requires three parameters be specified. They are: the number of passes to be made through the forest before all stands are treated,

the volume to be harvested in each pass, and the time between passes. The solution strategy utilizes the four-color theorem. By assigning adjacent blocks different colors, they

represented adjacency constraints by the chromatic number of the map. For the problems

Nelson and Enrico solved, they were able to easily generate a solution to the five-color

problem, but not for the four-color problem. The next step was to meet the even-flow volume harvest constraint. Their algorithm assigned stands for harvest in the first two periods to the last two periods until approximately 20 percent of the available volume is harvested in each period. This is to overcome the difficulty of obtaining even flow resulting

from the large difference in the number of stands assigned to each color.

Nelson and Enrico (1993) stated that the spatial strata-based models suitably approximated the area-based plans. They state that it may be more appropriate to develop prescriptions that describe the desired remaining forest cover in terms of species, age, and

spatial arrangement of forest cover that must always exist to meet integrated resource objectives.

Davis and Martell (1992) developed a decision support system called SILVIPLAN. This tool is used to evaluate short-term operational plans that are linked to a strategic plan. The results from the strategic plan provides targets for harvest volumes and treatment areas.

The solution strategy involves solving a series of linear programming problems for ten one-

year periods after it has solved a larger strategic plan with linear programming.

19

Manley (1993) created a short-term feasible harvest planning model linked to a long

term forest scheduling system. Stands within five years of the rotation age were not

aggregated. The younger stands were aggregated. The model was tested against more detailed planning models and has produced similar results to the more detailed area planning

models without the computational burden of solving large spatial problems.

The disaggregating approaches have attempted to find an implementable solution by relaxing the integer constraints. As the problems become more complex, the relaxing of the

integer constraints and applying a set of rules to allocate units for a spatial harvesting plan

may become too difficult to implement because the actual problem is significantly more constraining than the relaxed linear problem, or the plans developed from these rules may result in economically inefficient schedules.

Jones et al. (1986) investigated four planning techniques for three planning areas to determine the potential efficiency gains from integrated tactical forest planning models. The

four methods included in their study were (Jones et al., 1986): Fixed Access - managers decide how to access each unit before scheduling the unit for harvesting.

Variable Access- Managers choose the units, and the routes can be changed by analyzing alternatives with simulation.

Simulation - Managers can choose the units and the route is optimized. Optimization - Both units and routes are optimized simultaneously. The authors selected discounted net revenue as the efficiency measure. In all cases, the

highest discounted net revenue occurred when both the transportation and unit selection

were optimized simultaneously. There were small differences between the other three

20

methods. The authors hypothesized that the more complex the planning problem, the greater the benefit would be derived from combined optimization approaches (Jones et al. 1986).

Brodie and Sessions (1991) described three analytical approaches to solving tactical

harvest scheduling problems. The first approach is the random search technique. This approach includes Monte-Carlo integer programming, bill climbing techniques with random starting solutions. These techniques are suitable for finding solutions to adjacency problems

for two or three periods. The second approach discussed in their paper are Lagrangean relaxation techniques. By developing a Lagrangean relaxation constraint, one is able to

solve large mixed-integer programming problems. The final approach uses combined heuristics. These include random search techniques used to find bounds for mathematical

optimization techniques such as branch and bound or cutting plane algorithms. Sessions and Brodie (1991) felt that these combined approaches have the potential to solve a variety of spatial problems.

There have been many different techniques applied to tactical harvest scheduling problems. These can be divided into six categories. The first category contains the mathematical techniques commonly used to solve mixed-integer programming problems.

The second category contains the Lagrangean relaxation techniques. The tbird category describes dynamic programming approaches for tactical harvest scheduling problems. The fourth category contains decomposition techniques. The fifth category contains the random

search techniques. The sixth category are the gradient search techniques. Literature on these six approaches follows.

21

Mixed-Integer Techniques

One of the first attempts to solve the spatial harvest scheduling problem was developed

by Weintraub and Navon (1976). They believed that substantial savings could be obtained by imultaneously solving the harvest scheduling and transportation planning problem. The objective ftinction is to maximize the net revenue subject to constraints on available capital,

harvest volume, and adjacency constraints. The transportation network is included in the

problem. Existing road costs includes maintenance and variable hauling costs; new road

segments include construction costs. Weintraub and Navon (1976) used the Steiner Problem to aid in solving the transportation problem. They computed the shortest variable

cost path from each sale to the existing transportation network.

Navon and Weintraub (1976) formulated the problem as a zero-one mixed-integer programming problem. For a hypothetical example, the authors have shown a total in net

revenue of 12.08 million dollars from simultaneous planning compared to 11.31 million

dollars in net revenue for plans where the units and transportation system were independently scheduled.

Another early attempts to solve this problem was made by Kirby et al. (1980).. They developed the Integrated Resource Planning Model (1RPM). 1RPM used zero-one integer

programming techniques to solve the selection of logging units and the transportation system simultaneously. It was soon discovered that these zero-one integer programming problems became computationally large very quickly. It became impractical to solve these

problems with the current computer hardware and software algorithms. The size of the

22

tactical forest scheduling problems has limited traditional integer programming methodology as a solution technique.

Hof and Joyce (1993) developed another mixed-integer formulation to solve tactical harvest scheduling problem. It includes the spatial layout of the harvesting units and the shape of the units. They have selected circles as the basic shape, the size of each circle is the decision variable. The goal is to maximize the cardinal weight of the three targets; edge

habitat, interior habitat and volume targets. By shifting the radius of the circle, the model will simultaneously change the amount of edge habitat and interior habitat that is available in each period.

The authors admit that their examples are unrealistic. Their formulation provides a different methodology for solving spatial wildlife habitat problems. More recently, Hof and

Joyce (1993) continued their work with mixed-integer programming formulations for spatially optimizing wildlife habitat and timber management goals. They have included

habitat fragmentation, habitat connectivity and edge effect into their model. They have continued their multiple objective function containing the cardinal weights for timber and the wildlife goals. They developed a fragmentation model based on the random movements

of animals. If two cells are adjacent to each other, there is a 50 percent chance of the

animal moving from one cell to the other. If the cells are separated by one full cell then there is a 15 percent chance of an animal moving from one cell to the other cell (Hof and Joyce, 1993). The probability of a cell being connected is:

pr= 1- [fJ(1_pr*C1]

3.

23

They have developed a linear approximation for this probability function. They assume that

the equation is an effective representation of the probability function (Hof and Joyce, 1993). It is:

pr

4.

This equation is incorporated into a problem with twenty-five grid cells and a single

period.

The problem includes minimum area constraints by habitat type, volume

constraints, and edge constraints. This formulation was solved on a personal computer with

a commercial linear programming solving package in approximately two hours. Hofet al. (1994) enhanced their mixed-integer programming approach for optimization of harvest schedules for wildlife habitat and timber output. Their habitat constraints include

edge effect and minimum interior habitat requirements. Other constraints include a piecewise linear representation of the logistic viability regression function. This formulation

includes four possible silvicultural treatments for each cell. Hofet al. (1994) have solved a vaiiety of objective functions using a common data set. The first two objectives maximizes the young forest and old forest separately. The objective

function maximizes the young forest species habitat and harvests all of the units in period

two or period three. The second objective function maximizes the old-forest species. As expected, this formulation produced no timber outputs. The third objective goal is to maximize both the early seral forest habitat and the late seral forest habitat. The result is to cluster the harvesting to maintain large interior forest habitat.

24 The fourth objective solved assigns twice the cardinal weight to the early seral species

as the late seral species. It produces a pattern similar to the first objective and harvests all of the volume in the middle periods.

The fifth the objective function uses a maxmin operator for both early and a late seral

forest species. It allows for more harvesting in period two and period four increasing the dispersal population for young seral forest species. The sixth objective function solves a maxmin problem for both the young and old seral forest species' logistic viability function. The seventh objective function maximizes the joint

probability of the piecewise logistic viability function. Both alternatives six and seven produced similar results to objective function five, the maxmin alternative.

Guignard and Wang (1994) have formulated the habitat corridor problem along with adjacency constraints and even-flow constraints as a zero-one mixed-integer programming

problem. Their first attempt to incorporate all paths into the model was unsuccessful (Guignard and Wang, 1994). To reduce the computational burden of solving for all paths,

some assumptions were made. They were (Guignard and Wang, 1994): Wildlife move towards their destination only. Only polygons that are linked will be included in the trigger relationships

If a line is drawn between the two points, it must cross any path at least once. These relationships were used to develop a set of trigger constraints. If a unit contains

suitable habitat and is connected by other units with suitable habitat, then a trigger relationship is established. A layer is created from a set of linked units. These layers are formed in a series of concentric circles around critical sites. Wildlife may move within a circle or to an outer circle, but cannot move backwards. The triggers are defined as zero-

25

one variables linked to assignment of the units. The formulations was applied to a three hundred polygon problem. A corridor was found in each period; but the solution time is strongly affected by the type of formulation used.

Weintraub et al. (1994) have developed a heuristic to solve zero-one mixed-integer

progranmiing problems. Their technique is a cutting plane algorithm using linear programming to generate the cutting planes. After the polygons and transportation network

have been generated, the algorithm begins by solving the relaxed linear programming problem. The next step in the algorithm is to reduce the variable transportation cost by dividing it by 100. This emphasizes the fixed cost component in the analysis. The second

iteration modifies the capacity constraints on the transportation network. It encourages traffic on links with high use. Once the capacities have been changed, the linear program

is resolved. The third iteration assigns zero or one to the new road links with a ranking scheme that uses a combination of the slack variables from the side constraints, and the amount of traffic flowing across that link. Those arcs with the highest rankings are assigned

a value of one. The other arcs are assigned a value of zero. The linear program is analyzed again with the new road assignments. The fourth iteration continues adjusting the capacity

assignments to determine if a better solution can be found. The fifth iteration insures that the links have the correct timing. A connection between each sale and mill is available in

each period. These iterations continue until all roads receive a zero or one variable. This usually requires between six and twelve iterations with each iteration requiring the solution

of a linear program.

26

The results from their heuristic are within 10 percent of the optimal value obtained by branch and bound algorithm, with a fraction of the solution time for the branch and bound algorithm. A similar heuristic was developed by Jones et al. (1991) to solve zero-one mixed-integer

programming problems. Their heuristic solves a series of linear programming problems adjusting the traffic capacities until all values are assigned a value of zero or one. Their heuristic can solve problems with four thousand constraints and three hundred zero-one variables.

Lagrangean Relaxation Techniques

Torres-Rojo et al. (1991) used Lagrangean relaxation techniques to solve the even-flow

harvest scheduling problem with area constraints. This technique can converge on a solution quickly and can solve large problems. A key element to solving these problems is

finding values for the set of multipliers (Torres-Rojo et al., 1991). They used a gradient method to solve the problem of calculating the Lagrangean multipliers. The solution strategy is to solve the dual of the relaxed linear programming model. This

solution to the dual will provide an upper bound for the primal problem. The gradient method is then used to find the weights for the multipliers. This strategy provides a nearly integer solution.

27

Dynamic Programming Techniques

Hoganson et al. (1995) formulated the adjacency problem as a dynamic programming

problem. One problem with dynamic programming is the difficulty in solving large problems. The authors formulated the problem in a manner to reduce the dimensionality

of the tactical problem. They have defined the state variable as the edge that separates scheduled stands from unscheduled stands. Each stage has its own front (Hoganson et al., 1995).

With their definition of the state variables, they have developed a procedure to solve

large problems. The first step generates a strip along the outside edge of forest and running along the long axis of the forest. The next step is to formulate and solve the dynamic program for this strip. After solving the dynamic program, the scheduled stands are eliminated from the strip and a new strip is created parallel to the first strip. Additional

strips are added until the forest has been traversed. The authors applied their algorithm to a hypothetical one thousand unit forest for five

periods. Solution time was influenced by the order in which the strips were generated.

Decomposition Techniques

Forest planning problems are hierarchical; they can be divided in logical subunits that

are interconnected. Many of these goods produced from these subunits have spatial and non-spatial constraints that conflict with each other. Some small basins can supply some of the goods, but may not be able to provide all the goods desired from the forest. Hof et

al. (1992) developed a linear decomposition algorithm for solving the hierarchical forest

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planning problem. The master problem assigns targets for the district problems. The district problems return whether it has remained feasible and value of the shadow prices for

the resource constraints. The master problem incorporates this information and reallocates

targets to those districts that have the lowest shadow price for the desired resources from the forest. Yoshimoto et al. (1994) developed a heuristic to solve present net worth maximization problems. The heuristic utilized a partitioning technique that has been successfully applied

to stand optimization problems. The PATH algorithm eliminates inferior alternatives and

reduces the computational tasks (Yoshimoto et al., 1994). This requires a two-phase approach to problem solving. Phase one is a global optimization phase; it selects the best

solution from a set of feasible alternatives. The second phase generates these feasible alternatives with a regional optimization model. The regional optimization model utilizes a one-stage-look-ahead technique to maintain feasibility. A random order heuristic varies

the unit's selection order.

This allows the algorithm to take a fine-scale look at

combinations of feasible solutions in order to create a better solution. The model produced

values that were within 1 percent of the optimal answer. Weintraub et al. (1994), Barahona et al. (1992) have developed another decomposition technique to solve the spatial harvest scheduling problem. The goal of the master problem

is to maximize the present net benefit subject to the land allocation constraints and the

minimum timber production requirements. A column generating algorithm calculates variables for the master problem. To maintain feasible solutions within each region, the spatial harvest scheduling problem was formulated as a stable set problem. The stable set

problem has no known polynomial time solution algorithm. It attempts to find a set of

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nodes on a graph such that no two nodes selected are joined by one edge. The edge represent either an adjacency constraint or a trigger relationship where only one decision variable can be assigned a value of one. To generate these variables for the master problem,

a two-phase solution strategy is used. The first phase is a greedy algorithm. It attempts to

select the node that produces the highest value while maintaining feasibility. If there is a dilliculty in finding a feasible solution, phase two begins. Phase two is a linear program and

it is used to solve the stable set problem as a maximum clique problem.

Once the sub-regional problems are solved, the solution to the master problem is calculated.

This often results in fractional estimates for each column, violating the

feasibility to the sub-regional problem. The fractional solutions are eliminated in a two-step

procedure. The first step is to select the area with all integer solutions. These areas will

keep their current values. The second step is to select the sub-basins with the highest fractional value while insuring that the deviations from the regional goals are minimized.

This algorithm produced results within 1 percent of the relaxed linear programming problem. This method can solve medium-sized problems in a reasonable time frame.

Random Search Techniques

A popular technique for solving spatial harvest scheduling problems are the random search techniques, Monte Carlo integer programming being the most common. Nelson et al. (1991) and Nelson and Brodie (1990) were the first to use this technique to solve spatial

harvest scheduling problems. Nelson and Brodie (1990) developed a three-step procedure

to integrate the area-based plans with strata-based plans. The first step is to solve the

30

strata-based plan with linear programming. This generates the strata-based harvest levels

that will guide the area plan. The second step is to solve a three-period area plan that includes the spatial constraints. The final step is to incorporate the solution from the areabased plan for the first three periods into the strata-based plan, and resolve the strata-based plan. The technique used in the second step involves generating a list of binary variables for

all eligible stands, and assigning them a value of one. Once a stand is selected for harvest,

the binary variables of the adjacent stands are assigned a value of zero. The unit volume is added to the total volume and the net present revenue is calculated for that period. The total volume is compared with the tolerance from the strata-based plan, if the total volume

is within the desired tolerance the analysis will begin to select stands for the next period. This process is repeated until the desired volume is reached in all periods or fifty attempts

to add another unit have failed. The algorithm terminates when two hundred feasible patterns are generated. Clements et al. (1990) modified Nelson's Monte Carlo integer programming algorithm

to solve three spatially constrained harvest schedules. The degree to which the problem is

spatially constrained is modeled by the length of time that adjacent units cannot be harvested. Different levels of wildlife habitat requirements are represented by different

levels of adjacency restrictions. The objective function's goal is to maximize the total harvest volume with even-flow, adjacency, and maximum forest opening constraints. Clements et al. (1990) have incorporated a biased sampling procedure developed by O'Hara

et al. (1989) to improve the solution in the model. Clements et al. (1990) applied their algorithm to a 1154 hectare area for twenty-five periods. They generated one thousand feasible solutions for each problem. The more restrictive the constraints, the greater the

31

reduction in volume harvested. There was a drop of 9 percent for the highest spatially constrained problem and a 4 percent drop for the least spatially constrained problem when

compared to the unconstrained problem. OHara et al. (1989) developed another stochastic technique for solving spatial harvest scheduling problems. Their approach used four sampling techniques for selecting candidate

units. The first sampling technique was based on equal probability for selecting each unit.

They also developed three biased sampling techniques to improve the results from their model. The first bias sampling technique preferred to select those stands with the highest volume per area. The second sampling method selected stands that have the least number of adjacent units. The final sampling technique was a combination of the volume and the adjacency sampling techniques. For each of these sampling methods, one hundred feasible solutions are generated. The objective thnction's goal is to maximize the sum of the volume

harvested in each period. The constraints are minimum and maximum volume harvested in

each period, and adjacency constraints. OHara et al. (1989) solved a 242-unit problem for five ten-year periods. The only prescription allowed is a clearcut prescription. Results from

the four sampling procedures were always within 5 percent of the estimate of the optimal answer using a confidence interval from extreme value theory.

Sessions and Sessions (1991) developed a heuristic, SNAP II, as a tool to implement strategic plans. SNAP II contains many types of spatial constraints such as the maximum opening size and habitat connections. SNAP H can limit the area in a given seral stage in

any period. Besides these vegetation management constraints, SNAP II can incorporate both the new construction cost and variable hauling cost when optimizing the transportation

network for the scheduled units.

32

Sessions and Sessions (1991) summarized their solution strategy in five steps. The first

step evaluates the area potential for timber production by relaxing the multiple-use constraints. This generates an upper bound for the second step, where spatially feasible

random harvesting patterns are generated for each period. The final step prepares the reports for each feasible solution. SNAP II is able to solve problems with over 1000 road segments and 1000 units for 30 periods. A more recent version, SNAP III, solves problems

with up to 9000 polygons over fifty periods.

A new heuristic, simulated annealing was developed in the early 1980's for solving combinatorial optimization problems. It is based on the analogy to the energy states occurring in a cooling metal during annealing. The general simulated annealing algorithm

begins with an initial random solution. The next step is to randomly generate a new solution by randomly choosing variables to enter or leave the solution. If the new solution

is the better than the previous solution it will accept that move, If the new solution has a lower objective value then a random number is generated. If the random number is greater

than a value from a user-defined function the solution is accepted and an inferior solution is now the basis. This procedure is used to reduce probability of the algorithm being trapped

in a local optimum. The value of this function depends upon the cooling schedule assigned

to each problem. The probability of accepting an inferior solution decreases during the analysis (Aarts and Korst, 1989).

Lockwood and Moore (1992) used simulated annealing to solve a multiple objective forest planning problem. The problem involves scheduling units for harvest subject to meet

maximum clearcut size and the adjacency requirements. The objective function contains

four components. The first component is the penalty cost for the deviation from desired

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volume flow. The second component assigns a penalty to stands with low volume per area

ratio. The third factor is a penalty cost assigned for violating the adjacency constraints. The fourth component is a penalty function invoked when the maximum harvest block size

is exceeded. The goal of the model is to minimize the sum of these four penalties. Lockwood and Moore (1992) applied their model to an area that contained 6,148 units

for twelve five-year periods. Clearcut was the only prescription included in the analysis.

The authors believed their model produced good solutions, but there was no attempt to

compare the results from this model with the optimal solution. They stated that their formulation could not be used to calculate the long-term even-flow harvest volume.

Nelson and Liu (1994) have used simulated annealing to solve spatial harvest scheduling problems. Their problem includes even-flow and adjacency constraints. The

initial solution is randomly generated, but feasibility is maintained. New solutions are generated randomly with a one period look ahead to maintain feasibility. If there is an improvement in the objective function the new solution is accepted. Otherwise the results

are compared with a random number, If the solution is better than the random number it

becomes the new basis for the model. Their results show that the simulated annealing converges quickly and produced larger objective function values than other strict gradient methods.

34

Directed Search Techniques

The last category of solution techniques are the gradient search techniques. These include the nonlinear optimization approach such as steepest decent, Hooke-Jeeves, many

of the network optimization routines and Tabu Search. Gross (1990) used the four-color problem to model adjacency constraints in a tactical

harvest scheduling problem. He utilized the proof of the four-color theorem presented by Appel and Haken (Gross, 1990). The algorithm selects stands with the highest present net

worth that will maintain feasibility. Feasibility is insured by the Welsh-Powell four-color algorithm that assures that the adjacent stands do not share the same color. Roise (1990) used the four-color theorem to model the adjacency problem. He let the

exclusion period be represented by a color; each adjacent stand would be assigned a different color. If the total time to harvest all stands in an area is R and the exclusion period

between adjacent stands is r. The four-color theorem will show that a feasible solution exists if R/r

4.

Roise (1990) incorporated his adjacency model into a tactical harvest scheduling problem with volume constraints. To solve the problem, Roise used a penalty function to encourage feasibility. Roise has applied his technique to problems with two hundred stands.

The solution times were reasonable, but the formulation is limited to small-sized and medium-sized problems due to the algorithm's limitations.

Hof and Kent (1992) have developed a nonlinear programming approach for land allocation to promote the development of two types of wildlife habitat. Their example included a hypothetical species that requires an edge between old growth forest and recently

35

harvested areas. Besides the edge dependent constraints, there are late seral forest dependent forest species. The problem is formulated as a nonlinear multiple objective function. The cardinal weights assigned to these objectives are maximized using GINO, a nonlinear optimization package. Sessions (1992) has solved the wildlife corridor problem that is often a subproblem in

tactical harvest scheduling with wildlife constraints. The problem is to locate a path between user-defined stands that will be maintained throughout the planning horizon. Each

unit that meets the criteria for a corridor becomes a node on a directed graph. Two arcs are used to connect every pair of nodes. The resulting network is the set of all potential paths for the corridor. The goal is to minimize the cost to connect the two critical areas.

This is a well-studied mathematics problem known as the Steiner problem. The Steiner problem has no known polynomial solution time algorithm. Several heuristics have been developed using the various shortest path routines. Sessions selected Dijkstra shortest path algorithm. The algorithm begins by selecting a destination from the set of critical areas. All

other critical areas become source nodes with the goal to flow to the destination. A series

of shortest path algorithms are solved. Once a link has been used, its opportunity cost is

assigned a value of zero. This encourages the continued use of the link. The algorithm provides feasible solutions quickly.

One of the first applications of Tabu Search in forestry was developed by Murray and

Church (1995). Their paper describes three methods for generating operational forest plans. The methods investigated were interchange, simulated annealing and Tabu Search. The first two methods are similar to methods that have already been discussed. Tabu Search

is the final method studied by Murray and Church. Their algorithm begins like most hill

36

climbing algorithms, selecting units that yield the greatest improvement in the solution. To

avoid being trapped in a local optimum recent moves are restricted; thus, forcing the

algorithm to investigate other areas of the solution space. Of the three methods investigated, Tabu Search obtained the best solution. All of the methods generated solutions within 10 percent of the optimal solutions. Although Tabu Search produced the highest values it also had the longest solution time. Another tactical harvest problem using Tabu Search was developed by Bettinger et al.

(1995). It schedules stands for harvest while maintaining cover and forage habitat for elk using the distances and size of cover and forage blocks. Bettinger et al. (1996) used Tabu Search to select cutting units to minimize the impacts

on stream temperature and sediment potential on a 14,643 acre watershed in Eastern Oregon. Sixteen of the twenty solutions were within 10 percent of the estimated optimal

answer. This was determined using extreme value theory. These techniques for solving spatial harvest scheduling problems are summarized in table 1.

Tabu Search

In the previous section, many techniques were described to solve spatial harvest scheduling problems. Some are based on mathematical programming principles such as cutting plane algorithms or branch and bound algorithms. These techniques can guarantee

an optimal solution, but are limited to small-sized and medium-sized problems. New techniques have been developed to solve large combinatorial problems. Some of these

Approach Zero-one mixed integer Zero-one mixed integer Zero-one mixed integer Zero-one mixed integer Zero-one mixed integer Zero-one mixed integer Cutting plane algorithm Relaxations techniques Dynamic programming Decomposition Decomposition, heuristic Decomposition Decomposition Monte Carlo Monte Carlo Monte Carlo Monte Carlo, heurisitcs Simulated annealing Simulated annealing Gradient method Gradient method Gradient method Gradient method Tabu Search Tabu Search

Table 1: Summary of Spatial Harvest Scheduling Techniques

Author Weintraub and Navon Kirby et al. Jones et al. Weintraub et al. Hof and Joyce Guignard and Wang Weintraub et al. Torres-Rojo et al. Hoganson et al.

Hofet al. Yoshimoto et al. Weintraub et al. Barahona et at. Nelson et al. Clements et al. OHara et al. Sessions and Sessions Lockwood and Moore Nelson and Liu Gross Roise Hof and Kent Sessions Murray and Church Bettinger et al.

Problem Tactical planning with transportation system Tactical planning with transportation system Tactical planning problem Tactical planning problem Spatial wildlife layout Corridor problem Tactical planning with transportation system Tactical planning problem Tactical planning problem Tactical planning problem Tactical planning problem Tactical planning problem Tactical planning problem Tactical planning with tranportation system Tactical planning problem Tactical planning problem Tactical planning with transportation system Tactical planning problem Tactical planning problem Tactical planning problem Tactical planning problem Spatial wildlife layout Corridor problem Tactical planning problem Spatial wildlife layout, Tactical planning with aquatic system

38

techniques are simulated annealing, genetic algorithms, Lagrangean relaxation, and Tabu Search.

Tabu Search is a directed search technique that incorporates memory into the search procedure (Glover, 1989), (Glover, 1990). The core element of a Tabu Search algorithm is a hill climbing routine. It differs from other gradient search techniques in that it uses a memory restriction to avoid being trapped in a local optimum and to allow the exploration

of a larger portion of the solution space. These restrictions on allowable solutions have resulted in the name Tabu Search, Tabu meaning forbidden. A flow chart for a generalized

Tabu Search is contained in figure 1. Tabu Search begins with an initial solution. The algorithm will evaluate the neighborhood looking for the best move. If a move produces

the best overall value for the objective function, it becomes the candidate move. This variable will be selected as the candidate move even if it is currently on the tabu list. The ability to override a Tabu restriction is the aspiration criteria described in the Tabu Search

literature (Glover, 1989, Glover, 1990). If the solution is not the best overall solution, it

will select the best move that is not tabu. After each move, the short-term tabu list is updated. The short-term memory is used by the algorithm to avoid being trapped in a local

optimum (Glover et al., 1993). This will allow the algorithm to pivot away from a local optimum into a less explored region of the solution space. There are two other types of memory commonly used in Tabu Search. The first is the

intensification search. This directs Tabu Search to select a portion of the solution space where a number of good solutions have been found. This is accomplished by biasing the

search technique to select variables that have produced the largest improvement in the objective function. This forces the algorithm to investigate combinations of variables that

39

Define Initial Neighborhood Has

Neighborhood Been Fully Explored

Make Temporary Move

Is Move Best Overall Move

Yes

Save

Is Move Best eration Move

Move

Is

Save

Move Tabu

Move Yes

Calculate New Neighborhood I

Update Tabu List

Another Iteration

Save

Move

Yes

No

Display Results

Figure 1: Generalized Tabu Algorithm

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have produced good solutions in the past. The hope is that a better solution can be found with new combinations of variables that have already produced good solutions. The second type of memory is the diversification search routine. Diversification is used

to force Tabu Search to explore areas that have been infrequently included in the solution.

The goal is to find a distinctly different solutions. Diversification often uses a frequency

table to select a new solution. This will force Tabu Search to increase the portion of solution space investigated, increasing the likelihood of the algorithm finding good solutions. There are many applications of Tabu Search in industry. Daniels et al. (1993) developed

a Tabu Search heuristic to solve the flexible resources flow shop scheduling problem. In 480 test problems with known optimal answers, Tabu Search found the optimal answer to

70 percent of the problems. The average deviation from optimality was 0.3 percent. The maximum deviation was 2.5 percent of the optimal answer. Not only did Tabu Search find

good solutions it required only a fraction of the solution time. The average solutions required 4.8 CPU seconds while 625 CPU seconds were required to find the optimal answer

(Daniels et al., 1993).

Crainic et al. (1993) used Tabu Search to solve a multicommodity location and allocation model. This problem selects the location of the transfer yards and assigns customers to each yard. The problem is a mixed-integer programming problem with side constraints. The discrete choices that the model makes are to select the yards to be opened,

while the number of containers to be shipped to each yard are the continuous variables. Multiple containers can be shipped to each owner. This example shows the flexibility of

41

Tabu Search to solve problems that contain both discrete and continuous variables (Crainic

et al., 1993). Several medium-sized problems were formulated with twenty-five potential depots and

125 customers. Eight large problems were formulated with 44 depots and 220 customers.

Tabu Search found the optimal answer to nine of the twenty problems. The maximum deviation between the Tabu Search algorithm and the optimal solution was 3.5 percent (Crainic et al., 1993).

The last example I will review used Tabu Search to solve the fixed-charge problem.

Forty-five problems with known optimal solutions were formulated and solved. Each

problem contained twenty columns and eighty rows. Tabu Search found the optimal solution to forty-two of the forty-five problems (Sun and McKeown, 1993). The largest difference was 2.3 percent of the optimal value.

These examples show the great promise for Tabu Search to generate good, often optimal solutions to large combinatorial problems. Tabu Search is slower than many other

heuristics at obtaining the solutions; the exploration of the neighborhood and the incorporation of memory in the search routine requires more time to execute than other heuristics such as simulated annealing. However it is much faster than using mathematical

programming to find solutions to these problems.

Genetic Algorithms

Holland developed genetic algorithms in the 1960ts to solve combinatorial problems.

Using the genetic analogy, a family of solutions are generated using random search

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procedure. New solutions are created by mating the initial populations of solutions with each other. It is hoped that the offspring are more fit than the parents (Reeves, 1993). For combinatorial optimization problems, fitness is usually the objective function. During the

mating, mutations can occur based on a random function. The pairing of solutions for matings can be random. Some genetic algorithms use a biased technique that attempts to

mate parents with a high fitness values in the hope of producing superior offspring. The results from these matings are two new solutions. In most algorithms only one offspring survives to form the next generation of solutions. The process of mating continues until a predetermined number of generations have occurred (Reeves, 1993). It is a technique that is often combined with other techniques for problem solving. One example would be to use

genetic algorithms for an intensification search routine in a Tabu Search algorithm. Pesonen et al. (1995) developed a genetic algorithm to predict the potential harvest from nonindustrial lands in Finland.

Extreme Value Theory and Heuristic Performance

There are a number of techniques that can be used to evaluate heuristics. One method

is to compare the value from the heuristics with a known optimal solution. Another technique that is often applied to linear mixed-integer problems is to compare the integer solution from the heuristic with a solution from a linear program that has relaxed the integer

constraints. For problems that do not have a known solution or cannot be solved as a linear programming problem, another technique, extreme value theory can be used to estimate the

performance of the heuristic. Extreme value theory estimates the performance of a

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heuristic by estimating the optimal value for combinatorial problems. For optimization problems, extreme value considers the heuristic a sampling scheme from a finite population

bounded by a, the location parameter. For a series of samples s, each of size m, as m

becomes large, the distribution of the best solution from each sample approaches a three-parameter Weibull distribution (Golden and Stewart, 1985).

From the three-

parameter Weibull distribution, the location parameter, a, is an estimate of the optimal

value. Figure 2 shows the shape of generalized three-parameter Weibull function. The three-parameter Weibull distribution has the property that the cumulative density function

between the location, parameter a, and scale parameter, parameter b, is equal to 1 - l/e. Expanding this for samples of size s, the confidence interval around the estimated optimal

value can be estimated by the following equation:

Pr[v a+b] = 1 - Pr[v> a+b] = [v,v-b] = l-e

5

To generate the estimate of the optimal value requires that the three parameters, the location, scale, and shape parameters be estimated. A number of techniques can be used to estimate these parameters. Castillo (1988) uses the maximum likelihood to calculate the parameters for Weibull distribution. The maximum likelihood estimator finds the values for

the parameters that maximize the product of the probability density function for a set of observations. For the three-parameter Weibull distribution the probability density function is:

pdf = c/b*((x_a)/b)' *exp(_(x..a)/lo)c

6.

Once the three parameters have been estimated, the estimated optimal value is the location

parameter, a.

44

Observations

Figure 2: Generalized Weibull Distribution with Shape> 0

45

Golden and Alt (1979) developed an approach to obtaining initial estimates for the Weibull function. It begins by generating and sorting the best solutions from the s samples

from highest to lowest in the array x. The initial values are estimated by the following equations:

a = x(l) - (x(2)-(x(l)) b

x(0.063*s+l) - a

c = In(-ln(.05)/(In(x(l 0)-a)-ln(b)))

7. 8.

9.

These can be used to define the starting points for enumerating the maximum likelihood estimators solution to the three-parameter Weibull problem.

This technique has been used by others to calculate the confidence interval for five traveling salesman problems. In each problem, the estimate obtained from extreme value procedures contained the actual optimal value (Golden and Stewart, 1985).

Bettinger et al. (1996) used this technique to estimate the performance of their Tabu Search algorithm that was used to schedule harvesting units with water quality constraints.

He found that 80 percent of the solutions were within 10 percent of the estimated optimal

value. Extreme value theory assumes that the heuristic generates a representative sample of the solution space, and the best value from each sample is a representative sample of the

optimal value. If the samples do not represent the solution space, the estimate of the optimal value will have limited utility.

46

JUSTIFICATION

Tactical harvest scheduling is necessary in industrial forests in the Western United States. The potential impacts of harvesting on wildlife habitat, water quality, and visual resources are well documented. To mitigate these impacts, state forest practices require industrial owners to account for wildlife habitat requirements on their timberlands. The growing complexity of these rules requires a systematic approach to tactical forest planning.

This will insure that spatially feasible harvesting plans that are generated are economically

efficient. This will allow for continued operations on private forest lands.

Solving spatially constrained plans is difficult due to the large number of discrete variables in these problems. Solution techniques can be grouped into two strategies. The first strategy is the mathematical programming approach. This includes zero-one integer programming approaches that are solved using branch and bound algorithms, cutting plane

algorithms, dynamic programming, and decomposition algorithms. These techniques can guarantee an optimal solution but only to small problems. This has led to the development

of heuristic algorithms, the second solution strategy. These include Monte Carlo integer programming, Lagrangean and surrogate relaxation techniques, simulated annealing, genetic

algorithms, and Tabu Search to solve spatially explicit harvest scheduling problems.

The objective of the spatial wildlife constraints and goals is to design a desired landscape structure. To illustrate the problem solving technique, three measures of landscape structure will be used to model spatial wildlife goals and constraints. The first goal is the contagion index. It will control the landscape aggregation for all seral stages in the landscape. By using a high value for the contagion index, the algorithm will attempt to

47

aggregate the harvesting pattern. The second goal incorporated into the model will be a shape index. The higher the shape index, the less edge habitat exists for a closed-canopy

forest. The final component in the model is a percolation model. It combines minimum area requirements and controls the connectivity for closed-canopy patches. The minimum spanning cluster is a constraint, and must be maintained in all periods. To create a desired landscape for a late seral forest species, the landscape goals would be to create a forest with

less edge, high level of aggregation, and a large minimum spanning cluster for the closed-

canopy forests. The contagion index, the shape index and the minimum spanning cluster should be able to provide the controls necessaiy to develop the desired landscape structure.

The model will tly to create this desired landscape in an economically efficient manner. In

addition to the landscape constraints, the model will limit the maximum opening that can be created in any period, and includes an even-flow goal. The Tabu Search algorithm will generate a set of solutions to the problem with twenty random starting points. The results from these solutions will be used to estimate the optimal

solution for the problem using extreme value theoiy. This will provide the manager with

several candidate solutions and an estimate of the optimal solution. By comparing the

solutions from the heuristic with the estimate of the optimal solution, the heuristic's performance can be evaluated.

48

OBJECTIVES

Industrial timberland owners need to develop a tactical forest plan to maintain the

financial efficiency of forest lands while lessening the impacts of industrial forest management activities on wildlife habitat. This will require foresters to look at two scales. The first scale is within the stand. It includes stand characteristics such as tree size, quantity

and quality of snags, and amount of woody debris. The second scale will be the landscape scale. This includes the number, type and location of patches on the landscape. This study

will concentrate on the quantity and arrangement of stands on the landscape. It will develop the methods to maintain the necessary quantity and arrangement of stands to maintain wildlife habitat in an economically efficient manner.

A fifty-year tactical forest plan will be developed for the Horse Creek Drainage in the

Oregon Coast Range. The goal for the plan will be to maximize the present net revenue

less the penalty functions subject to a variety of spatial and nonspatial constraints. The

spatial constraints will limit the maximum opening to 120 acres. The second spatial

constraint will be a user-defined minimum spanning cluster to connect the northern boundary to the southern boundary of the watershed. This cluster will be composed of the closed-canopy seral stages. There will be three goals for the tactical plan. The first spatial goal will control the shape of the closed-canopy forests. It will be modeled by calculating

the perimeter of the closed-canopy forest and comparing it with the perimeter of a circle with equivalent area. The second spatial goal will be a user defined contagion index. This

will control the aggregation of patch types in the forest. Even-flow of harvest volume is the nonspatial goal.

49

There are three objectives for this study. The first will be to develop a system that gathers and formulates the tactical forest plan with spatial and nonspatial constraints. This

will involve developing a geographic information system and a series of programs to estimate both the financial and ecological yields from a series of silvicultural activities. The geographic information system will collect the spatial information for each logging unit. The

results from the yield stream generators and the spatial information will be used to formulate the problem.

The second objective will be to solve the spatially constrained harvest scheduling problem with the heuristic, Tabu Search. Tabu Search will use both short-term memory restrictions and a long-term diversification strategy. Twenty solutions will be generated; each solution will begin with a random starting solution.

The final objective will be to test the performance of the heuristic. Extreme value theory will be employed to estimate the optimal value for the problem from the twenty solutions. The maximum likelihood estimator for the optimal solution will be calculated from these samples for a three-parameter Weibull distribution. The estimate of the optimal

solution will be calculated from the Weibull distribution. A comparison will be made between the estimated optimal value and the values from the heuristic.

50

DATA COLLECTION AND CALCULATION OF VARIABLES

The objective of this study is to develop a methodology to incorporate spatial wildlife

habitat requirements into a tactical harvest scheduling model. The goal is not to produce a detailed operational plan; therefore, some data will be estimated. These estimates will be described in their individual data section.

Inventory Data

A stand map was generated in 1995 by a local consulting firm from 1:40000 colorinfrared photography. Figure 3 is a map of the existing stand types for the Horse Creek Drainage. Associated with each polygon in the map are some stand attributes. These are the basal area, and number of trees per acre for the three dominant tree species, the average

age of the tree species. A complete listing of the stand data for each inventory unit is shown in Appendix 1. To estimate yields using a growth simulator, a tree list needs to be

generated. Usually this information is gathered from temporary or permanent plots

associated with a forest inventory. No plot-based inventory data is available for the planning area. The STAG model was be used to generate a tree list (Biging et al., 1994). STAG was developed for California, but this technique has been used for other areas. The inputs to the model are elevation as well as basal area and number of trees per acre. Using

these stand parameters, STAG will calculate a tree list that is representative for the area. It is an extrapolation of the STAG model, but it will produce a tree list that can be used to

demonstrate the methodology of incorporating growth and yield data into the tactical

51

Figure 3: Existing Stand Map for the Horse Creek Drainage

52

harvest scheduling system.

This method would not be suitable for developing an

operational inventory data base.

Growth and Yield

ORGANON (Hester et al., 1989) was used to estimate the volume harvested and the resulting stand structure.

ORGANON is a distance independent growth model calibrated

for the Western Willamette Valley. It has been calibrated for both even-aged and uneven-

aged prescriptions. Stands will be limited to five possible silvicultural prescriptions. The five prescriptions are:

Shelterwood Clearcut Thin from below

Group selection Individual tree selection

Log Values

Log values will be estimated for each species in the planning area. Prices were obtained

for Log Lines (1995), a log price subscription service. Only domestic prices will be used for each log grade. The only conifer in the project area from the inventory data is Douglas-

fir. A camprun sort based on 30 percent of the stand producing #2 sawlogs and the remaining being #3 sawlogs for all prescriptions. The average price is $672.70 per Mbf.

ORGANON does not produce a detailed log list in a format that can easily be incorporated

53

into a tactical planning system log evaluation. The prices are shown in table 2.

Table 2: Log Prices by Grade for the planning area (Log Lines, 1995).

Species

Grade

Price

Douglas-fir

#2 Sawlog

$ 735.00

Douglas-fir

#3 Sawlog

$ 646.00

Discount Rate

The real discount rate used was 4 percent. This value represents the average opportunity cost of capital in the private economy (Row et al., 1981). All revenues and cost were estimated for the middle of the five-year period.

Logging Cost

Accurate contour data with a reliable contour interval of less than 20 feet was unavailable for this study so it is not possible to select between ground based systems and

cable systems. It is assumed that all logging can be accomplished with cable logging systems. Logging costs contain two components, falling cost and yarding cost. The

following equation is used to estimate the yarding cost (Fight et al., 1984): YCF = 737.4-61 .09*DBH+1 .2926*DBH2+0. 1497* SYD+52.7/VAC

YCF = Yarding cost in dollars per 1000 cubic feet DBH = Diameter at breast height in inches SYD

Slope Yarding Distance in feet

10.

54

VAC = Volume removed in cubic feet per acre The average slope distance was obtained from the setting layer that was prepared at the same time as the inventory layer (figure 4). Falling cost in dollars per thousand cubic feet is estimated from the following equation (Fight et al., 1984):

FC=-17.4+876/DBH

11.

The average DBH for each seral stage will be used when calculating the logging cost. Figure 5 contains the graph varying the logging cost by distance, tree size and harvested volume per acre.

Transportation Cost

Since elevation data was unavailable, earthwork quantities cannot be calculated. An average road cost of $40,000 dollars per mile will be used for new road construction. An

average operating cost of $50 per hour will be used for hauling cost. Three travel speeds will be used in this study. For single lane roads, the travel speed is 20 miles per hour, 45

miles per hour for county roads, and 55 miles per hour for state highways. The existing transportation network is shown in figure 4. The complete transportation network data are in Appendix 3.

Riparian Areas

Riparian rules for all forest lands have undergone large changes in recent years. In 1994, the Oregon Department of Forestry changed the riparian rules for private forest

55

Figure 4: Transportation Network and Logging Units for Horse Creek Drainage

56

400 350

° 300

-9300 AYD

250-

-0-

200

600 AYD

o 150

900 AYD

ioo 50-.. 0

10

15

20 DBH

25

30

Figure 5: Yarding Costs for Various Distances and Tree Sizes

57

lands. The width for the riparian areas are listed in Table 3. Figure 6 contains the location and classification of all streams in the project area.

Table 3: Riparian Area Classification and Stream Buffers, Distances in Feet (Lorensen et al., 1994).

Stream Class

Large

Fish and Domestic Use

No Fish or Domestic Use

Domestic Use Only

100

70

70

Medium

70

50

50

Small

50

20

None

No vegetation will be removed from the riparian within twenty feet to the stream. Table 4 contains the residual basal area for even-aged and uneven-aged silvicultural prescriptions

(Lorensen et al, 1994).

Table 4: Residual Basal Area for Streams in the Oregon Forest Practice Rules using Evenaged and Uneven-aged Silvicultural Systems.

Fish and Domestic Use

No Fish or Domestic Use

Stream Class

Even Uneven

Even Uneven

Large

230

300

90

140

Medium

120

140

50

60

40

50

None

None

Small

58

Figure 6: Stream Systems for Horse Creek Drainage

59

S era! Stages

Seral stages will represent the within-stand characteristics. The c!assifications are based

on the average tree size, number and quantity of snags and down woody debris. Hansen et al. (1993) used three categories for managed forest stands, they are open, young, and mature. They also had four categories for unmanaged forest; open, young, mature, and old growth. This study considers five seral stages for the managed area based on a combination

of stand age and the quadratic mean diameter.

Tab!e

5

contains the sera! stage

c!assification. Figure 7 shows the distribution of existing sera! stages in the Horse Creek watershed.

Tab!e 5: Seral Stage Classification

Stage

Size Requirements

Seed!ing

0 to

Sap!ing

5

Pole

1 to 7 inches in diameter

Sma!! Sawlog

7 inches to 20 inches in diameter

Large Saw!og

Greater than 20 inches in diameter

to

5

years

15

years

0

61

METHODS AND PROCEDURES

Site Selection

The Horse Creek Drainage was selected for this study site. The Horse Creek watershed

typifies the small watersheds in the Oregon Coast Range. It contains a mix of young and mature inventory types, a large stream network, and logging systems that are common in

Coastal Oregon. The area is part of the Coastal Landscape Analysis Modeling Systems (CLAMS) study area. Figure 8 contains a vicinity map of the Horse Creek drainage. Many

data layers have been gathered as part of the CLAMS study. This will allow for the potential development of many forest planning models with minimum data collection costs.

However detailed and accurate contour data and inventory data were unavailable.

Procedures

The first objective of this study is to develop a system to formulate a fifty-year tactical forest plan for the Horse Creek Drainage. This involves combining geographic information

systems applications with other customized programs to gather and organize the data needed to develop a tactical forest plan. The process begins by capturing the spatial data and existing inventory data in the geographic information system. The next step calculates

the economic and ecological yields for the set of five possible silvicultural prescriptions for each setting. The geographic information system will provide the topology needed to

formulate the spatial constraints. The second objective is to develop a Tabu Search algorithm to solve the tactical forest plan. The final objective is evaluate the performance

62

Horse Creek Drainage

Figure 8: Vicinity Map For Horse Creek Drainage

63

of the heuristic by estimating the optimal value using extreme value theory and comparing

the estimated optimal value with the values from the scheduling model.

Problem Formulation

There are four principal coverages in the geographic information system that contain the basic information used to formulate the problem. The first coverage is the road layer. It will contain the length and road status for each road segment. The status will be used to

determine the travel speed and whether the road exists or needs to be constructed. The second layer will be the stream layer. It stores the location and classification of all streams

in the planning watershed that will be used to define the riparian management areas. The third layer is the stand map. This is a polygon coverage will have the location of all stand types in the planning watershed. The last layer is the setting layer. It is the smallest feasible

operating unit for harvesting defined by the limitation for silvicultural or harvesting activities.

The first step in the process is to calculate the yields for the suite of silvicultural prescriptions. For each existing inventory type, a tree list is estimated using STAG and the

parameters for each stand type contained in table 6 in Appendix 1. This estimated tree list

becomes the inventory data used to generate the yield estimates for each inventory type

using ORGANON. There are some difficulties with using ORGANON to estimate the volume and stand structure. ORGANON does not contain a species code for red alder,

madrone was used in its place to maintain the representative basal area. It does not separate the hardwood and conifer cubic foot volume in the summary reports.

The

64

optimization model allows five prescriptions that are commonly used on commercial forest

in the Western United States to be specified for each setting. They are: Clearcut Individual tree selection

Group selection longer rotation even-age silviculture Shelterwood The clearcut prescription removes all trees except two trees per acres are left as snags.

The individual tree selection has a goal to maintain a dQ-value of 1.25 with a maximum

diameter of forty inches. The target residual basal area is 150 square feet with a re-entry

period of twenty years. The goal is to develop a structurally diverse stand. Another technique to develop a structurally diverse stand is group selection. It will remove 25

percent of the existing volume in small patches every twenty years. The shelterwood prescription removes all trees greater than twelve inches, except four trees with a diameter

greater than eighteen inches. The goal is to promote the development of a stand with diverse structure with minimal impacts on the financial returns. The last prescription is a long rotation even-aged prescription. It has two thinnings followed by a final harvest. The first thinnings will be from below and will have a residual basal area of one hundred square

feet per acre. Twenty years are allowed to pass before the second thinning; it is also a thinning from below with a residual basal area of 150 square feet per acre. The final harvest

occurs twenty years after the second thinning. These prescriptions have not been subject

to any minimum volume requirements to be feasible. The goal was to incorporate the

65

information from growth and yield models for multiple prescriptions into the tactical harvest

scheduling system. Once the prescriptions have been generated, the program collects the board feet volume

for the conifers for each stand type. The next step calculates the extraction costs. A set of rays were digitized from the landing to the boundaries of each setting. The length of these

rays were calculated by the geographic information system, Arc Info by ESRJ. The rays

were used to calculate the average logging distance used in the logging cost equation developed by Fight et al. (1984). For each setting, the length of the ray calculated in the geographic information system was divided by two, producing an estimate of the average yarding distance. This assumes a uniform distribution of volume throughout the setting and

parallel corridors.

The transportation cost is the next cost to be calculated. One attribute required is the road standard. This was estimated from the road standard shown on a U.S.G.S. 7.5-minute

topographic map sheet. The length of each road segment is the digitized length stored in

the geographic information system. Since no estimate of earthwork quantities can be computed without accurate topographic data, a standard cost of $40,000 per mile of road

was used for new road construction. These proposed roads are primarily spur roads built to a low standard. Using the geographic information system, the entry node for each setting

was assigned to the transportation network. After the extraction costs were calculated, the master planning coverage was created.

The first step is to buffer the stream using the buffering command in the geographic information system. There are two possible buffers for each stream. The first buffer is a

twenty-foot no treatment buffer for all class I and class II streams. The second buffer

66

creates the remainder of the riparian area specified in Oregon Department of Forestry Riparian rules (table 3). The buffered stream coverage, the inventory coverage and setting coverage are combined using an overlay command in the geographic information system.

A weighted average of inventory type by setting, and riparian units was used to calculate

the yields for each setting used in the optimization model. The results of the buffers and overlays are shown in figure 9; the master planning coverage. The yields for each logging unit are shown in Appendix 2.

Once the set of possible yields have been calculated, the next step is to formulate the tactical plan. The mathematical formulation is shown below.

The Objective Function

TRN Maximize

T

-

T

T

VP - AP- CP-

T Fc1t*Rit

12.

Rev1Gross revenue of setting i harvested with silvicultural prescription j in period t. C1Logging cost for setting i harvested with silvicultural prescription j in period t.

Il= Hauling cost for setting i in period t. Volume harvested in setting i harvested with prescriptionj in period t.

Fc= Fixed transportation cost associated with road segment Tin period t. = A 0-1 variable for setting ito be treated with prescription j in period t. VP = Volume penalty for period t. AP = Area-perimeter penalty for period t. CP = Contagion index penalty for period t.

67

Figure 9: Master Planning Coverage for Horse Creek Drainage

68 = A 0-1 integer variables for road segment i in period t. T = number of periods.

R = number of silvicultural prescriptions.

N = number of settings.

The Constraints

Maximum Opening Size This is calculated for all adjacent settings.

Na N (

A1)

maximum opening

13.

= Area for setting i in period t.

Na = number of stands adjacent to stand i. Minimum Cluster Size Constraint.

XI XI

mm cluster

14.

adjacent units with seral stages greater than or equal to three.

NI = number of stands with a closed canopy, those stands with a seral stage of three or four.

Volume Goal.

TRN Q,

(( VX) - Vmax)"l.5 )*$500.00 )/(( 1+1 )At )-VP, = 0

Vmax = Target volume to be harvest in period t. = Discount rate

15.

69

Shape Goal The shape goal is the diversity index described mBowen and Burgess (1991). The first step is to calculate the total area for all settings with a closed canopy seral stage for each period.

TN1 (

AIx1- TA ) =0

16.

TA = Total area of settings with a closed canopy seral stage. The next step is to calculate the total perimeter for the late seral forest in each period.

TN1 (PXIt-. TP) = 0

17.

TP = Total perimeter of settings with a closed-canopy seral stage that do not border a setting with a closed-canopy forest.

The final step is to calculate the perimeter for a circle with equivalent area. The ratio

between the existing perimeter and the perimeter of a circle with equivalent area is compared with the user-defined ratio. A penalty for failing to achieve of the desired percentage in each period is calculated and subtracted from the objective function. T ,

(TCJ TP - Shape) = 0

18.

Shape = Shape index in period t TC = Perimeter of a circle with equivalent area.

If the Shape is less than the Dshape then the shape penalty is calculated, otherwise it is zero. T

$800,000.00*( 1+Dshape- Shape)- AP= 0 Dshape = Desired percentage of a circle with equivalent area.

19.

70

Landscape Aggregation Goal The landscape aggregation goal is the contagion index describe in Li and Reynolds (1993).

TRN ,

(

N/NSln( N/NS,) - EEL) = 0

20.

= Total length of perimeter of shared between units with seral stage i and units with seral stage j where i is not equal to j in period t. NS1 = Total length of perimeter of each settings with seral stage i in period t.

EE = contagion measure in period t. T

( 1+ EE I NoSt*ln( No5) - RCont ) = 0

21.

RCont = Relative contagion index in period t.

NoS = Number of seral stages at time t. If RCont is greater than RC then the contagion penalty is calculated, otherwise it is zero. T

$800,000.00*( 1+RC-RCont) - CP = 0

22.

RC = Desired relative contagion index in time t.

The Search Procedure

The second objective is to solve the formulation using Tabu Search. The model begins

by assigning the values that define the desired landscape and desired harvested volume. They are: Maximum opening size.

Target harvested volume by period. Minimum spanning cluster and connectivity points.

71

Desired shape index. Desired contagion index.

Before exploring the neighborhood on the first iteration, the algorithm randomly assigns

the clearcut prescriptions to units until 10 percent of the targeted volume is scheduled in each period. This provides the routine with a partial solution that will reduce solution time,

but still allow for manipulation of the cutting unit pattern to achieve the desired state. The algorithm provides for a different starting point that will increase the percentage of the area

explored by the heuristic. The random starting points provide the initial independent samples required by extreme value theory to estimate the optimal solution. The maximum

opening constraint and minimum cluster are checked for each unit to insure an initial feasible solution. After the initial solution has been generated the program evaluates the

contagion index, and the shape index and their penalties if necessary. It calculates the objective function. This is the starting point for the heuristic.

The program evaluates the entire neighborhood at each step. This problem has two sub-neighborhoods. The first is the unit neighborhood. It contains the current silvicultural

activities assigned to the units. The second sub-neighborhood is the road neighborhood.

It contains the flow across all road segments during each period. At each iteration, the

algorithm will make one of the following decisions. It will schedule a new unit for treatment, change the timing or prescription for a previously scheduled unit, remove a scheduled unit, or modify the transportation system. The decision made at each iteration is to change the unit neighborhood or transportation system while meeting the constraints in a manner that generates the highest present net worth less the penalties for deviating from

72

the goals. Tabu Search is a systematic procedure that investigates all possible moves from

a neighborhood, or a sample of possible moves from a neighborhood, and insures the feasibility of the move prior to calculating the new objective function and penalty values for

that move. The systematic evaluation of all of the units begins by calculating the maximum opening

created by one of the even-aged prescriptions. If the maximum opening constraint is not violated, the minimum spanning cluster is calculated. A depth-first graph connectivity algorithm is the core of the minimum spanning cluster

algorithm (Sedgewick, 1990). The first step is to create a graph of the closed-canopy stands for each period. This is based on the growth of the stands and the current treatments

assigned to each stand. The vertices on the graph represent the settings. The arcs between the vertices represent an adjacent closed-canopy setting. A starting and ending vertices are assigned in the geographic information system. These represent the source and sink nodes

used in many network flow algorithms. The algorithm begins to travel from the source to

the sink. It will select the first unvisited node for each node that has been found. The

algorithm will continue descending the graph until it reaches the ending node with a minimum cluster size or until it can travel no further. If the end of a branch is reached and the minimum cluster has not been achieved, the algorithm backtracks to the last visited node

and then continues to descend towards the sink on a unique path. This continues until the ending node is reached and the minimum number of settings have been placed on the tree, or until all of the nodes have been visited. If all nodes have been visited and the connection has not been found or the minimum cluster size has not been reached the move is infeasible.

The algorithm will evaluate the next element in the neighborhood.

73

After satisijing both of the constraints, the algorithm calculates the transportation cost. Dijkstra's shortest variable cost algorithm (Sedgewick, 1990) is used to determine the initial

route to the mill. The fixed cost for each arc requiring construction is added to the transportation cost. The logging costs are combined with the transportation cost to calculate the extraction cost. Using the gross revenue from the yield tables, the net revenue

is calculated for the potential move. The next step in the algorithm is to calculate the penalties for deviating from the goals.

The first goal is the volume goal. A polynomial penalty function was used to promote harvesting to the user-desired volume targets. The objective for the penalty functions is to provide incentives for meeting the goals but allow for a flexibility to prevent a large number

of infeasible solutions. The penalty function value is the gross revenue less the average estimated logging cost. The base penalty value is $500.00 per Mbf. The total penalty is the base penalty multiplied by the difference between the goal and the current harvested volume

raised to a power of 1.25 in scenario one and 1.05 in scenario two. The final calculation reduces the penalty function by the discount rate for each period. The rationale is to place

a greater emphasis on meeting the desired volume targets in the early periods where the information is more precise than in the later periods. The second goal is a shape goal. The area for each setting and the length of the shared

boundaries between settings are obtained from the geographic information system. The algorithm calculates the existing area and perimeter for all settings with a closed-canopy

forest, those stands that have a seral stage of three or higher. The perimeter for a circle with equivalent area is calculated. If the existing area-perimeter ratio is lower than desired percentage of a circle with an equivalent area, a linear penalty function was used. The goal

74

for this penalty function is to manipulate the spatial arrangement of stands after it has neared the desired volume targets. The base penalty value is $800,000.00. The base penalty

is multiplied by one plus the desired shape index less the actual shape index. This will penalize solutions based on the amount that they deviate from the desired goal. The base penalty value is based on a twenty-acre unit with 60 Mbf per acre with a camprun value of

$666.67 perMbf. This value exceeds the average revenue that is generated from one unit.

The algorithm will select a lower value stand for treatment and avoid the penalty rather than selecting a higher value stand for treatment and incur the penalty.

The last goal is the landscape aggregation goal. The contagion index is computed for

each feasible move. If the value of the contagion index is less than the desired value, the

same linear penalty function used for the shape goal is repeated. The base value is $800,000.00. The base penalty is multiplied by one plus the desired shape index less the actual shape index. This will penalize solutions based on the amount that they deviate from

the desired contagion goals. The base penalty value is based on the value of a twenty-acre

unit with 60 Mbf per acre with a camprun value of $666.67 per Mbf. The same logic is used for landscape aggregation goal as was used for the shape goal that is to manipulate the

landscape after it nears the volume targets. Once the penalties are calculated, the objective function is calculated for each potential move, with the best current move for each iteration becoming the candidate move until the

entire neighborhood has been evaluated. There are several possibilities when evaluating a

move. The first is when the move generates the best overall objective function value. In all cases this move becomes the candidate move. If the objective function value is not the best overall value, but has the highest objective function value for this iteration, the setting

75

is compared with the short-term tabu list. If the setting is not on the short-term tabu list, then the setting with the prescription and timing becomes the candidate move. If it is tabu,

it is restricted from changing its status, and another setting must become the candidate move. The last potential outcome for a move is to yield an inferior solution.

This process

is completed for all combinations of silvicultural and timing possibilities in the ten-period planning horizon. Figure 10 contains a flow diagram for the unit neighborhood search.

Once the unit neighborhood is completed, the algorithm explores the road neighborhood. The initial transportation routes are assigned using Dijkstra's shortest path algorithm. The objective of the road neighborhood is to reduce the transportation cost by finding new combinations of arcs and sales that will reduce the overall transportation cost. The algorithm will select each arc that currently has traffic flowing across it and a fixed cost

greater than zero, and assign an artificially high variable cost of $9999.99 per Mbf. Dijkstra's shortest path algorithm is used to calculate the new transportation cost for all of the current settings. The fixed cost are added to the variable cost. The objective is to force the flow of volume to other links to investigate other paths that may reduce the fixed cost

component of the transportation system leading to an increase in the objective function value. The outcomes for evaluating the road neighborhood search are the same as the unit neighborhood. If the new transportation network improves the overall objective function, then the road segment becomes the candidate move. If a move yields the best value for the

objective function for the current iteration and the move is not tabu, the road segment becomes the candidate move. Figure 11 contains the flow diagram for the transportation neighborhood.

76

Select Timing

Select Unit

-I

Select Prescription

'IMove

Save

Best Overall

Move

Move

Yes

Best Cunent Move

Is Move Tabu

No Save Move

Yes Calculate Transportation Cost

Calculate Shape Index Calculate Contagion Index Calculate Volume Penalty Calculate Objective Function

Another Prescription

Another Unit

Another Unit

Calculate New Neighborhood

Update Tabu Lists

Figure 10: Unit Neighborhood Procedures

77

Select Road Segment With Fixed Cost and Traffic Flow Assign Vaiiable Cost = For All Active Units

Calculate Extracqon Cost

Goto Next Unit

Update Tabu Lists

Figure 11: Road Neighborhood Procedures

78

At the end of each iteration the candidate move becomes the move, and the road and unit neighborhoods are updated. The short-term tabu list and long-term diversification list

are updated. The program begins investigating the new neighborhood. After two hundred iterations, the algorithm begins a diversification routine using the

long-term frequency table calculated during the first two hundred iterations.

The

goal is to force the model to visit areas of the solution space that have not been intensively explored. Using the frequency of units in the solution as the basis, the algorithm begins with

a new starting solution composed of the least used settings until at least 10 percent of the target volume has been scheduled for harvested in each period. Feasibility is guaranteed by

calculating the maximum opening size and maintaining the minimum spanning cluster. This becomes a new starting neighborhood for the algorithm which continues the search for

another two hundred iterations.

Evaluation of the Heuristic

This process of solving the tactical plan is repeated for twenty randomly assigned starting solutions. Each analysis represents a sample from a finite population of solutions.

To test the performance of the heuristic, a three-parameter Weibull function was used to estimate the optimal objective function for the problem. The process begins by sorting the

best solution from each run from highest to lowest cost. Using the approach developed by

Golden and Alt (1979), initial estimates for the three parameters were made. These estimates were used to calculate the range of values for enumerating the possible values for

a, b, and c for the maximum likelihood estimators for the three-parameter Weibull

79

probability density function. If the highest value for maximum likelihood estimators is on the boundary of the range of possible values, the algorithm will change these endpoints and

solve the maximum likelihood estimators until a nonboundary solution has been found. If

a nonboundary solution is found, these represent the estimates for the parameters that

yield the maximum likelihood estimators. The estimate for the optimal solution is the location parameter, a.

80

RESULTS

The results are categorized into two sections. The first section will describe the results

from four scenarios. The four scenarios demonstrate the use of an integrated geographic information system for formulating tactical forest planning problems and Tabu Search to

solve tactical forest planning problems as described in the objectives for this study. The second section describes the performance of the heuristics using extreme value theory for

the first two scenarios.

Results for Scenario One

Scenario one requires the minimum spanning cluster contain at least one third of the units in the area in each period. The maximum opening size is restricted to 120 acres. The

landscape goals are to develop a landscape with a shape index of 0.15 and a contagion index of 0.40. The volume goal is ten MN'lbf per period. These are arbitrary goals designed

to show the ability of the model to create a desired landscape. There is very little information relating spatial indices and quality of wildlife habitat. The achieved volume target is never less than 98 percent of the desired level in the first

scenario. In all analyses, the volume achieved greatly exceeds the target in the last two

periods. The harvest volume for the analysis with the five best objective functions are shown in figure 12. The remaining fifteen runs are shown in Appendix 4.

81

20000

15000

Goal Analysis 18

10000 0

Analysis 17

Analysis 16

5000

VA

Analysis 14 0

0

1 23456 7

Analysis 4 8

9

Period

Figure 12: Harvest Volume by Period for the Best Five Solutions - Scenario One

82

The shape goal is achieved in all periods but one for the twenty analyses. The values

range from 0.21 to 0.14. Figure 13 contains the shape index for the best five runs, while the remaining fifteen runs are displayed in Appendix 4.

There is a great deal of variation in the contagion index in the analyses. It varies from

0.27 to 0.57. The contagion index is lower in the early periods. The average contagion index is 0.35. The goal is achieved in period seven. The contagion value then drops below

the goal in the last two periods. Figure 14 contains the contagion values for the five best

results. The remaining fifteen runs in Appendix 4. Maps showing the location and silvicultural treatments for scenario one are in figure 15 through figure 24.

Results for Scenario Two

The second scenario has a minimum spanning cluster containing at least one-half of the

units in the watershed. The maximum allowable opening remains at 120 acres. The volume

goals and landscape goals are the same as in scenario one. The achieved volume exceeds the goal in many of later periods. The harvest volume is shown in figure 25 for the five best

analyses. The remaining fifteen analyses are shown in Appendix 5.

The shape goal is exceeded in all periods for the second scenario. The large minimum spanning cluster dominates the shape goal. Figure 26 contains the shape index for the five

best analyses, while the remainder of the results are shown in Appendix 5. The larger minimum spanning cluster has increased the average contagion index to 0.40.

It now ranges from 0.32 to 0.50. Figure 27 contains the results for the five best analyses, while the results from the remaining fifteen analyses are in Appendix 5. Maps showing the

83

0.25

0.2

Goal Analysis 18 Analysis 17

j

0.15

VA

Analysis 16 14 0.1

Analysis 4 0

1

2

3

4 5 Period

6

7

8

9

Figure 13: Area Perimeter Ratio for the Best Five Solutions - Scenario One

84

0.6

0.5

Goal

0.4 Analysis 18

0

Analysis 17

0.3

Analysis 16 VA

0.2

Analysis 14 Analysis 4

0.1

0

1

2

3

5 4 Period

6

7

8

9

Figure 14: Contagion Index by Period for the Best Five Solutions - Scenario One

85

Figure 15: Location of Silvicultural Treatments in Period 0 for Scenario One


86



87



88



89



90

35000 30000 25000 Goal

20000 -

Analysis 8

115000

Analysis 19

110000

Analysis 1

5000

Analysis 6 Analysis 112

0 0

1

2

3

4

5

6

7

8

9

Period

Figure 25: Harvest Volume by Period for the Five Best Solutions - Scenario Two

91

0.25

Goal

O.2

Analysis 8 Analysis 19 0.15

Analysis 1

Analysis 6

Analysis 12

0.1

0

1

2

3

4 5 Period

6

7

8

9

Figure 26: Area Perimeter Ratio for the Five Best Solutions - Scenario Two

92

0.6 0.55 0.5 0.45

Goal

0.4 .

Analysis 8

0.35 0.3

Analysis 19

0.25

Analysis 1

A

0.2

Analysis 6

0.15

Analysis 12

0.1

0

1

2

3

4

5

6

7

8

9

Period

Figure 27: Contagion Index by Period for Five Best Solutions - Scenario Two

93

location of the silvicultural treatments for the ten periods are shown in figure 28 through figure 37.

Results for Wildlife Scenarios Three and Four

The primary motivation for this model was to develop methodology to aid industrial timberland managers. in meeting the spatial wildlife constraints. Scenarios three and four were developed to illustrate the model's ability to generate different wildlife habitat patterns.

Scenario three has the goal of creating a large closed-canopy forest with minimum edge influences. This habitat will be beneficial for the pine marten, Martes americana (Buskirk

an Powell, 1994). The desired shape goal was 0.5. The volume penalty only penalizes solutions that exceeded the volume target in each period. The base volume penalty value

was $5000, ten times the average stumpage rate, and it is not discounted with time. The minimum spanning cluster remains at one-third of the units and the maximum opening size

is 120 acres. The objective function maximizes present net worth less the penalty functions

as in scenario one and two. The results from this analysis are shown in figure 38. The shape index increases throughout the analysis. The volume target is not met in the early periods. Figure 39 contains the percolation network for period seven. It shows a landscape

with little edge, and a large interior forest area.

Scenario four creates habitat for elk, Cervus elephus. Elk needs both closed-canopy forest and young seral forest types in close proximity to each other. The desired harvesting

pattern has a dispersed cutthg pattern that contains a large amount edge habitat. The shape

goal was changed to be less than 0.15 with a contagion index less than 0.30. The volume

94

Figure 28: Location of Silvicultural Treatments in Period 0 for Scenario Two


95



96



97



98



99

-o

0

Contagion Index Area Perimeter

Volume Period Figure 38: Results for Pine Marten Analysis - Scenario Three

100

Open Canopy Forest Closed-Canopy Forest

Figure 39: Percolation Network for Pine Marten Analysis - Scenario Three

101

penalty was not discounted. This will motivate the program to generate stands with early seral stage characteristics in all periods. This is similar to a strict even-flow constraint. The results for this analysis are shown in figure 40. The percolation network is shown in figure

41 for period seven. It clearly shows the minimum spanning cluster and the large amount of edge that will provide suitable elk habitat.

Evaluation of the Heuristic

The distribution of solutions and the Weibull distribution showing the estimated optimal

value are shown in figure 42. The estimated optimal value for scenario one is 15,605,432.

The best value from the heuristic is 15,335,932; this is within 98 percent of the estimated optimal. The lowest value is 8,636,236 or 55 percent of the estimated optimal value. The

results from scenario two show less variation in the range of the solutions than scenario

one. The estimated optimal solution is 27,436,642. The best value from the heuristic is 25,880,342; or 94 percent of the estimated optimal solution. The lowest value from the heuristic is 23,039,015. This is within 84 percent of the optimal solution. The distribution of solutions and the Weibull distribution are shown in figure 43.

Discussion of Results

The first objective for this study was to develop a system to gather the data and formulate a tactical forest plan. The geographic information system provided the spatial

data base necessary for tactical harvest scheduling. The relational data base, which is a component of this geographic information system, maintained the results for the yield

102

0.55 0.5

0.45 ci

0.4 0.35

- 12000

/

10000

8000

0.3

6000

0.25 2-.

0.2 N

> 0.1

\ 2000

0.05 0

4000

12345678 Period

Figure 40: Results for Elk Analysis - Scenario Four

Contagion Index Area Perimeter

Volume

104

4E-07

-3E-07

- 2E-07

F

1E-07

0

70126

90226 11032 13042 Objective Function Value x 1 0''3

15052

Figure 42: Weibull Distribution and Solutions for Scenario One

105

1E-06

- 8E-07

3-.

0 4-.

.0

ti)

6E-07

C.)

4E-07

- 2E-07 0

20796

22096 23396 24696 25996 Objective Function Value x 10 A 3

0

27296

Figure 43: Weibull Distribution and Solutions for Scenario Two

.0 ti)

106

generation models and created files used by the optimization routine. The geographic information system was used to combine multiple layers of spatial data from multiple

resources into a single integrated data layer. An important advantage to using the geographic information system is that it provides a standard format used to describe lines

and polygons.

This will allow for similar problems to be solved with minimum

modifications to the program.

The second study objective was to develop a Tabu Search algorithm and solve the tactical forest planning problem. The algorithm used a combination of goals and constraints

to develop a desired landscape structure while producing timber outputs. The minimum

spanning cluster constraint has an important influence on the landscape structure. In scenario one, there was a large range in the landscape aggregation goal with a minimum spanning cluster of one-third of the units. Expanding the minimum cluster size in scenario two created a more aggregated landscape and reduced the variation in the contagion index,

and reduced the number of periods when the goal was not achieved. Increasing the weight of the penalty function would likely reduce the variation in contagion index by reducing the

occurrences when the goal is not met. The last two scenarios illustrate the flexibility of the

model to create a variety of habitat patterns by manipulating the penalty functions. Tabu Search incorporates problem-specific information into the algorithm. The first is the length of the short-term memory restriction. If this length is too short, the solution will cycle between a set of common solutions, resulting in the algorithm being trapped in a local

optimum. If the list is too long, it will limit the search areas by excluding possible moves

and add unnecessarily to the computation time. The aspiration criterion eliminates some of the problems of a longer than necessary short-term tabu list. For this problem, a short-

107

term restriction of twenty moves was used. No cycling was observed in any of the forty solutions. No examination of a shorter tabu list was explored. The second component used

is a long-term diversification strategy. Many of the analyses found their best solution after performing a long-term diversification search. The random starting procedure assigned an

initial 10 percent of the desired volume allowed the model to develop initial solutions without being trapped in a single part of solution space. This technique increases the percentage of the solution space explored for a set of analyses. The algorithm used two constraints and a series of penalty functions to develop a desired landscape structure and harvest volume. The polynomial penalty function provides a strong incentive to meet the desired volume flow in the early periods. In the later periods where the information is less certain, the discounted penalty function allows for larger variatiOn in the harvest volume.

The harvest volume never fell below the 95 percentile of the desired target levels in the scenario one, two and four (elk analysis). Only in scenario three (pine marten analysis) where the failure to meet the desired volume was not penalized did the harvest levels fall significantly below the targets. The difficulty with the area-perimeter and contagion index penalty functions is to find values for the penalties that will allow the solution to investigate

solutions that initially favor timber production. When a solution nears the desired volume targets, the shape and aggregation penalties functions should increase their influence on the

objective function by having their penalties dominate the choice in the selection of units by

the algorithm. This assumes that the volume targets are the primary goal for a commercial

forest land owner. If these penalty functions are too high, large portions of the solution space will not be explored, if they are too low they will have an insignificant impact on the

108

solution. The manipulation of the penalty functions can be used to create a variety of wildlife habitat patterns.

The final objective of the study is to evaluate the performance of the heuristic using extreme value theory. In scenario one, fifteen of the twenty solutions are within 70 percent

of the optimal value. In scenario two, all solutions are within 16 percent of the estimated

optimal solution. The increase in precision is probably due to the increased minimum spanning cluster constraint. This reduced the number of feasible solutions allowing the algorithm to find the better solutions in two hundred iterations.

There are many assumptions made when using extreme value theory. This procedure assumes that each sample is random and independent. This is violated, because each sample

has a bias of trying to generate the best solution. However there is empirical evidence that solutions from combinatorial problems are not statistically different from a random sample,

but no test was performed for this analysis. Another assumption concerns the tail of the distribution for the solutions. This study assumes that the tail distribution is well-behaved. If the heuristic consistently provides inferior solutions or the population of solutions are not

well behaved, then the estimate for the optimal value will be of little meaning. The assumption is that the heuristic provides good results and these results can be used to estimate the optimal value for the tactical forest plan. The results from other Tabu Search algorithms show that Tabu Search does provide good results when solving combinatorial optimization problems. Extreme value theory did show that this version of a Tabu Search

heuristic performs well when compared to the estimate of the optimal answer. The best solution for scenario one and two are within 94 percent of the estimated optimal answer. The solutions for scenario one range from 55 percent to 98 percent of the estimated optimal

109

solution. Scenario two has a range of 84 percent to 94 percent of the estimated optimal solution. This is a similar to the range of values reported by Bettinger et al. (1996). The variation in the solutions could be decreased by increasing the number of iterations for each

analysis. This would improve the sampling scheme and would increase the likelihood that

a Tabu Search algorithm would generate a better estimate of the optimal solution.

For large problems there is always the question of how good are the results. It is unfortunate that this question cannot be answered. Tabu Search has a history of generating

good solutions to a variety of problems. The results that are generated from the model

produce the expected results. We cannot estimate the quality of the results for the optimization model until the problem has been solved with other techniques.

The model appears to perform well with the highly constrained problems that have a

limited number of local optimum. Problems with a large number of local optimum will result in the algorithm spending a large portion of its time finding these local optimum, and potentially missing the global optimum. This is due to the hill climbing algorithm that is the

core of Tabu Search algorithm. It will continue to explore these areas until a local optimum

has been found.

110

CONCLUSION

The procedure used in this study to develop a tactical forest plan built on an existing geographic information system provides a flexible planning environment. The accessibility of both tabular and spatial data, along with the ability to buffer spatial features, and overlay

coverages allows the analyst using the geographic information system to quickly generate

the spatial data for these problems. Tabu Search with its customized approach to problem solving can solve the nonlinear integer formulation, which many other techniques cannot solve. With a short-term tabu list

of twenty, cycling was never observed. The long-term diversification strategy produced

superior solutions in twenty-nine of the forty analyses completed in this study. The polynomial penalty function was effective at meeting the desired volume goals. The linear

penalty function was more successful at satisfying the shape goals than the landscape

aggregation goals. The minimum spanning cluster size has a strong influence on the landscape aggregation goal. Extreme value theory provides a quantitative technique for evaluating the performance

of the heuristic when it is impossible to formulate and solve these problems exactly using traditional mathematical programming techniques. The best performance by the heuristic was within 98 percent of the estimated optimal value.

There are two categories of recommendations in this study. The first relates to improvements to the existing system for the development of integrated tactical harvest scheduling systems. The recommendations are divided into data preparation and analysis.

111

Recommendations for Data Preparation

Increase the efficiency of developing and utilizing the results from the growth and yield

model. A new generation of growth and yield models should be developed that allows for the execution of common prescriptions on a variety of stands. The results from this analysis

will be a tree list that will be used to estimate log mixes, and structural characteristics for wildlife habitat classification.

Obtain the data directly from the geographic information system. The current system uses files generated from the geographic information system. This will eliminate a potential

source of errors that can result from manipulating files. To do this will requires access to the binary data files that are used by the geographic information system.

Recommendations for Analysis

1. Improve stopping rules. One of the questions that needs to be answered when using heuristics is how many iterations should be completed before termination. There is limited

information on stopping rules for heuristics. Some authors use a predetermined number of

iterations without an improvement in the objective function as a stopping rule. The algorithm developed for this study uses an arbitrary number of solutions. The development of a good stopping rules will likely improve estimates of the, optimal value while leading to

more efficient algorithms.

112

2. Investigate intensification routines. The heuristic incorporates a long-term diversification

routine to explore different regions of the solution space. An intensification routine could be developed using the concepts developed from genetic algorithms. A genetic algorithm

would allow good solutions to mate and form a new neighborhood for the Tabu Search algorithm to investigate.

The second categoly of recommendations are for additional research for incorporating

tactical harvest scheduling into forest management. They are:

Develop the relationships for a species persistence and landscape pattern that can be incorporated into spatial optimization models.

Develop a decomposition algorithm that will consider regional goals and policies and

assign them to the various watersheds that can best achieve these goals. The model developed in this study considers one watershed in isolation. A model might be developed

using a parallel computer algorithm and hardware to produce results in a timely manner.

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BIBLIOGRAPHY

Aarts, Emile, Jan Korst. 1989. Simulated Annealing and Boltzmann Machines. New York: John Wiley and Sons.

Anonymous. 1995. Log Lines: Log Price Reporting Service. 7(10): 1-8. Barahona, Francisco, Andres Weintraub, Rafael Epstein. 1992. Habitat Dispersion in Forest Planning and The Stable Set Problem. Operations Research.40(1):S14-S20.

Beier, Paul. 1993. Determining Minimum Habitat Areas and Habitat Corridors for Cougars. Conservation Biology. 7(1):94-107.

Bettinger, Pete, John Sessions, Kevin Boston. 1995. Using A Tabu Search to Schedule Timber Harvest Subject to Spatial Wildlife Goals for Big Game. In press, Ecological Applications. Bettinger, Pete, John Sessions, K. Norman Johnson. 1996. Ensuring the Compatibility of Aquatic Habitat and Commodity Production Goals in Eastern Oregon with Tabu Search Procedure. Submitted to Forest Science. Biging, Greg S., Timothy A. Robards, Eric C. Turnbolom, Paul C. Van Deusen. 1994. The Predictive Models and Procedures Used in the Forest Stand Generator (STAG). Illilgardia. 61:(1).

Bowen, G. W., R. L. Burgess. 1981. A Quantitative Analysis of Forest Island Pattern in Selected Ohio Landscapes. Oak Ridge National Laboratory, Environmental Sciences Division # 1719. Brodie, J. Douglas, John Sessions. 1991. The Evolution of Analytical Approaches to Spatial Harvest Scheduling. Systems Analysis in Forest Resources Symposium. Charleston, South Carolina.

Buskirk, Steven W., Roger A. Powell. 1994. Habitat Ecology of Fishers and American Martens. In Martens, Sables, and Fishers Biology and Conservation ed. Steven Buskirk, Alton Harestad, Martin G. Raphael, Roger A. Powell. Ithaca, New York: Comstock Publishing Associates. Canada, John R., William G. Sullivan. 1989. Economic and Multiattribute Evaluation of Advanced Manufacturing Systems. Englewood Cliffs, New Jersey: Prentice Hall.

Castillo, Enrique. 1988. Extreme Value Theory in Engineering. Berkeley, California: Academic Press Inc.

114

Clements, Stephen E., Patrick L. Dallain, Mark S. Jamnick. 1990. An Operational, Spatially

Constrained Harvest Scheduling Model. Canadian Journal Forest Research. 20:1438-1447. Clutter, J. L., J. C. Fortson, L. V. Pienaar. 1968. MAX MILLION - A Computerized Forest Management Planning System. University of Georgia. Athens.

Crainic, T. G., M. Gendreau, P. Soriano, M. Toulouse. 1993. A Tabu Search Procedure for Multicommodity Location and Allocation with Balancing Requirements. Annals of Operations Research. 41:359-384.

Daniels, R. L., J. B. Mazzola. 1993. A Tabu Heuristic for the Flexible-Resource Flow Shop Scheduling Problem. Annals of Operations Research. 41:207-230. Davis, Robert G., David L. Martell. 1992. A Decision Support System that Links ShortTerm Silvicultural Operating Plans with Long-Term Forest-Level Strategic Plans. Canadian Journal of Forest Research. 23:1078-1095. Dykstra, Dennis P. 1984. Mathematical Programming for Natural Resource Management. New York: McGraw Hill Book Company. Fahrig, Lenore, Gary Merriam. 1985. Habitat Patch Connectivity and Population Survival. Ecology. 66(6): 1762-1768.

Fight, Roger D., Chris B. LeDoux, Tom L. Ortman. 1984. Logging Costs for Management Planning for Young-Growth Coast Douglas-Fir. Pacific Northwest Forest Range Experiment Station PNW-176. Fomian, Richard T.T., Miichel Gordon. 1986. Landscape Ecology. New York: John Wiley and Sons.

Franklin, Jerry F, Richard T. T. Forman. 1987. Creating Landscape Patterns by Forest Cutting: Ecological Consequences and Principles. 1(1):5-18. Gardner, Robert H. Monica G. Turner, Virginia H. Dale, Robert V. O'Neill. 1992. A Percolation Model of Ecological Flows. In Landscape Boundaries: Consequences for Biotic Diversity and Ecological Flows, ed. Andrew J. Hansen, Francesco di Castrie. Berlin: Springer-Verlag.

Glover, Fred. 1989. Tabu Search - Part I. ORSA Journal of Computing. 1(3):190-206. Glover, Fred. 1990. Tabu Search - Part II. ORSA Journal of Computing. 2(1):4-32. Glover, Fred, E. Taillard, D. de Werra. 1993. A User's Guide to Tabu Search. Annals of Operations Research. 41:3-28.

115

Golden B. L., F. B. Alt. 1979. Interval Estimation of a Global Optimum for Large Combinatorial Problems. Naval Research Logistics Quarterly. 26(1): 69-70.

Golden B. L., W. R. Steward. 1984. Empirical Analysis of Heuristics. In The Traveling Salesman Problem, ed E. L. Lawler, J. K. Lenstra, A. H. G. Rinnooy Kan, D. B. Shnoys. New York: John Wiley and Sons. Gross, Thomas. 1990. Timber Harvest Scheduling with Temporal Non-Adjacency Constraints. In 1990 Environmental Systems Research Institute 1990 Conference. Redlands, California. Guignard, Monique, Xiaopei Wang. 1993. Habitat Connection Problems in Forest Planning. In International Symposium on Systems Analysis and Management Decisions in Forestry, ed Gonzalo L. Paredes. Valdivia, Chile.

Hansen, Andrew J., Steven L. Garman, Barbara Marks. 1993. An Approach for Managing Vertebrate Diversity Across Multiple-Use Landscapes. Ecological Applications. 3(3):48 1-496. Harrison, Robert L. 1992. Toward a Theory of Inter-Refuge Corridor Design. Conservation Biology. 6(2):293-295.

Hester, Arlene S., David W. Hann, David R. Larsen. 1989. Organon: Southwest Oregon Growth and Yield Model User Manual. Forest Research Lab. Oregon State University. Corvallis, Oregon. Hof, John, Michael Bevers, Linda Joyce, Brian Kent. 1994. An Integer Progranmiing Approach for Spatially and Temporally Optimizing Wildlife Populations. Forest Science. 40(1):177-191. Hof, John G., Linda A. Joyce. 1992. Spatial Optimization for Wildlife and Timber in Managed Forest Ecosystems. Forest Science. 38(3):489-508. Hof, John G., Linda A. Joyce. 1993. A Mixed-integer Approach for Spatially Optimizing Wildlife and Timber in Managed Forest Ecosystems. Forest Science. 39(4):816-834.

Hof, John G., Brian M. Kent. 1990.Nonlinear Progranmiing Approaches to Multistand Timber Harvest Scheduling. Forest Science. 36(4):894-907. Hof, John, Brian Kent, Tony Baltic. 1992. An Iterative Multilevel Approach to Natural Resource Optimization: A Test Case. Natural Resource Modeling. 6(1):1-22.

116

Hoganson, H.M., D.W. Rose, J.G. Borges, 1995. Addressing Adjacency Problems with Dynamic Programming. In Society of American Foresters Systems Analysis Conference. ed John Sessions, Douglas Brodie. Pacific Grove, California. Hulshoft R. Maureen. 1995. Landscape Indices Describing a Dutch Landscape. Landscape

Ecology. 10(2):101-111. Hyberg, Bengt T. 1987. Multiattribute Decision Theory and Forest Management: A Discussion and Application. Forest Science. 33(4):835-845.

Jamnick, Mark S., Karl R. Walters. 1992. Spatial and Temporal Allocation of StratumBased Harvest Schedules. Canadian Journal of Forest Research. 23:402-413. Johnson, K. N., H. L. Scheurman. 1977. Techniques for Prescribing Optimal Timber Harvest and Investments Under Different Objectives-Discussion and Synthesis. Forest Science Monograph 18.

Jones, J. Greg, James F. C. Hyde III, Mary L. Meacham. 1986. Four Analytical Approaches for Integrating Land Management and Transportation Planning on Forest Lands. U.S.D.A. Forest Service INT-361. Jones, J. G.,M. L. Meachani, A. Weintraub, A Magendoza. 1991. A Heuristic Process for Solving Large-Scale, Mixed-Integer Mathematical Programming Models for Site-Specific Timber Harvest and Transportation Planning. In Proceedings of 1991 Symposium on Systems Analysis in Forest Resources. U.S.D.A General Technical Report SE-74.

Kangas, Jyrki, Timo Pukkala. 1996. Operationalization of Biological Diversity as a Decision Objective in Tactical Forest Planning. Canadian Journal of Forest Research. 26(1)103-111. Kirby, Malcom W., P. Wong, W. A. Hager, M. E. Huddleston. 1980. A Guide to the Integrated Resource Planning Model. U.S. Department of Agriculture Forest Service. Berkeley, California. LaGro, James Jr., 1991. Assessing Patch Shape in Landscape Mosaics. Photogrammetric Engineering & Remote Sensing. 57(3):285-293. Lamberson, Roland H., Barry R. Noon, Curtis Voss, Kevin S. McKelvey. 1994. Reserve Design for Territorial Species: The Effect of Patch Size and Spacing on the Viability of the Northern Spotted Owl. Conservation Biology. 8(1): 185-195. Li, Habin, James F. Reynolds. 1994. A New Contagion Index to Quantify Spatial Patterns of Landscapes. Landscape Ecology. 8(3): 155-162.

117

Li, Habin, Jerry F. Franidin, Frederick J. Swanson, Thomas A. Spies. 1993. Developing Alternative Forest Cutting Patterns: A Simulation Approach. Landscape Ecology. 8(1):63-75. Lindenmayer, David B., Henry A. Nix. 1993. Ecological Principles for the Design of Wildlife Corridors. Conservation Biology. 7(3):627-629.

Liu, Jiangua. 1993. ECOLECON: An ECOLogical-ECONomic Model for Species Conservation in Complex Forest Landscapes. Ecological Modeling. 70:63-87.

Lockwood, Cary, Tom Moore. 1992. Harvest Scheduling with Spatial Constraints: A Simulated Annealing Approach. Canadian Journal of Forest Research. 23:468478.

Lorensen, Ted, Chip Andrus, John Runyon. 1994. The Oregon Forest Practices Act Water Protection Rules: Scientific and Policy Considerations. Oregon Department of Forestry. Salem Oregon. Mader, H. J. 1984. Animal Habitat Isolation by Roads and Agricultural Fields. Biological Conservation. 9:81-96.

Manley, Bruce. 1993. New Zealand Experiences in Linking Short-Term and Long-Term Forest Planning. In International Symposium on Systems Analysis and Management Decisions in Forestry. ed Gonzalo L. Paredes. Valdivia, Chile. McGarigal, Kevin, Barbara J. Marks. 1993. FRAGSTATS: Spatial Pattern Analysis Program for Quantifying Landscape Structure. Oregon State University. Corvallis, Oregon. Mendoza, Guillermo A., B. Bruce Bare, Gene E. Campbell. 1987. Multiobjective Programming for Generating Alternatives: A Multiple-Use Planning Example. Forest Science. 33(2):458-468.

Mendoza, Guillermo A., William Sprouse. 1989. Forest Planning and Decision Making Under Fuzzy Environments: An Overview and Illustration. Forest Science. 35(2) :481-502.

Morganti, Roberto. 1993. Landscape Patterns in Wildlife Habitat: The Landscape Ecology of Northern Spotted Owl Habitat in the Eastern High Cascades Mountains of

Southern Oregon. Master Of Landscape Architecture Thesis. University of Oregon. Eugene, Oregon. Murray, Alan T., Richard L. Church. 1995. Heuristic Solution Approaches to Operational Forest Planning Problems. OR Spektrum. 17:193-203.

118

Navon, Danial I. 1971. Timber RAM. A Long Range Planning Method for Commercial Timber Lands und Multiple Use Management. U.S.D.A. Research Paper PSW70.

Nelson, John, J. Douglas Brodie. 1990. Comparison of Random Search Algorithm and Mixed-integer Programming for Solving Area-Based Forest Plans. Canadian Journal of Forest Research. 20:934-942. Nelson, John, J. Douglas Brodie, John Sessions. 1991. Integrating Short-term, Area-Based Logging Plans with Long-Term Harvest Schedules. Forest Science. 37(1): 101122.

Nelson, John D., D. Enrico. 1993. Multiple-Pass Harvesting and Spatial Constraints: An Old Technique Applied to a New Problem. Forest Science. 39(1):137-151.

Nelson, John, Guoling Liu. 1994. Scheduling Cut Blocks with Simulated Annealing. In International Seminar on Forest Operations Under Mountainous Conditions IUFRO Subject Area 3.06. ed John Sessions. Harbin, China. Noss, Reed F., Larry D. Harris. 1986. Nodes, Networks, and MUM5: Preserving Diversity at All Scales. Environmental Management. 1O(3):299-309.

Noss, Reed F., 1991. Landscape Connectivity: Different Functions at Different Scales. In Landscape Linkages and Biodiversity. ed Wendy E. Hudson. Covelo, California: Island Press. OHara,, Anthony, J., Bruce H. Faaland, B. Bruce Bare. 1989. Spatially Constrained Timber Harvest Scheduling. Canadian Journal of Forest Research. 19:715-724. O!Neill, R, V., D. L. DeAngelis, J. B. Waide, T. F. H. Allen. 1986. A Hierarchical Concept

of Ecosystems. Monographs in Population Biology. No 23. Princeton, New Jersey: Princeton University Press. O!Nelll, R. V., J. R. Krummel, R. H. Gardner, G. Sugihara, B. Jackson, D. L. DeAngelis, B. T. Milne, M. G. Turner, B. Zygmunt. 1988. Indices of Landscape Pattern. Landscape Ecology. 1(3):156-162.

OtNeill, R. V., R. H. Gardner, M. G. Turner. 1992. A Hierarchical Neutral Model for Landscape Analysis. Landscape Ecology. 7(1):55-61.

Pesonen, Mauno, Arto Kettunen, Petri Rasanen. 1995. Non-Industrial Private Landowners's Choices of Timber Management Strategies: Genetic Algorithm in Predicting Potential Cut. Acta Forestalia Fennica 250.

119

Reeves, Cohn R., 1993. Genetic Algorithms in Modern Heuristic Techniques for Combinatorial Problems. ed Cohn R. Reeves. New York: John Wiley Sons. Roise, Joseph P. 1990. Multicriteria Nonlinear Programming for Optimal Spatial Allocation of Stands. Forest Science. 36(3):487-501.

Row, C., H. F. Kaiser, and J. Sessions. 1981. Discount Rate for Long-Term Forest Service Investments. Journal of Forestry. 79:367-369.

Schumaker, Nathon. 1994. Using Landscape Indices to Predict Habitat Connectivity. Sedgewick, Robert. 1990. Algorithms in C. Menlo Park, California:Addison-Wesley.

Sessions, John. 1992. Solving for Habitat Connections as a Steiner Network Problem. Forest Science. 38(1):203-207. Sessions, John, Sarah Crim. 1995. Incorporating Habitat Suitability Index Models into Large Scale Linear Programming Models. In INFORMS Annual Meeting April 1995. Los Angeles, California. Sessions, John, J. B. Sessions. 1991. Tactical Harvest Planning. Society of American Foresters. National Convention. San Francisco, California.

Spies, Thomas A., William J. Ripple, G. A. Bradshaw. 1994. Dynamics and Pattern of Managed Coniferous Forest Landscapes in Oregon. Ecological Applications. 4(3): 555-568.

Sun M., P. G. McKeown. 1993. Tabu Search Applied to the General Fixed Charge Problem. Annals of Operations Research. 41:405-420. Torres-Rojo, Juan M., J. Douglas Brodie, John Sessions. 1991. Solution to the Area-Based Harvest Scheduling Problem Through Lagrangian Relaxation. In press.

Wallin, David 0., Frederick J. Swanson, Barbara Marks. 1994. Landscape Pattern Response to Changes in Pattern Generation Rules: Land-Use Legacies in Forestry. Ecological Applications. 4(3): 569-580. Weintraub, Andres, Francisco Barahona, Rafael Epstein. 1994. A Column Generation Algorithm for Solving General Forest Planning Problems with Adjacency Constraints. Forest Science. 40(1): 142-161. Weintraub, Andres, Greg Jones, Adrian Magendzo, Mary Meachani, Malcolm Kirby. 1994. A Heuristic System to Solve Mixed-integer Forest Planning Models. Operations Research. 42(6): 1010-1024.

120

Weintraub, Andres, Daniel Navon. 1976. A Forest Management Planning Model Integrating Silvicultural and Transportation Activities. Management Sciences. 22(12): 12991309.

Yoshimoto Atsushi, J. Douglas Brodie, John Sessions. 1994. A New Heuristic To Solve Spatially Constrained Long-Term Harvest Scheduling Problems. Forest Science. 40(3):365-396.

121

APPENDICES

122

APPENDIX 1

Inventory Data

123

Table 6: Existing Inventoiy Data: BA = Basal Area ft'2; TPA = Trees Per Acre ID Sp 1 1

2 3

4 5

6 7 8 9

RA RA DF DF RA DF DF DF DF

10 DF 11 DF

12DF 13 DF

14RA 15RA 16DF 17RA 18DF 19DF 2ODF 21 DF

BA TPA 40

386

95

83

222

62

83 40

113

0 0 111

148

218 0 123 83

92 59 106 77 46 69

204

386 0 0

139 41 55

38 113 82 74 144 96 63

108 57 135 0 83 63

25 DF

26DF 27DF 28DF 29RA

83 106 121 93

113 113 144 144 91

3ODF

64 40

94 386

81

152 97

31RA 32RA 33 DF

45

34DF 35DF

0 0

36 DF

37DF 38DF 39RA

58 94 0 85

4ORA 41 DF

48 80

42DF

80

RA RA RA

BA TPA 0 16

0 16 15

23

56

0 17

205

55

0

55

32 48

8

8

RA RA DF DF RA DF RA RA RA

50 23

65 56

RA DF RA RA RA RA DF DF

23 23

19

0

84 0 95 46 83

22DF 23RA 24DF

Sp 2 DF DF RA RA DF RA

0 0 83

124 0 144 109 115 115

17

5

70 6 54

21 14

18 16

43

32

23

0 55

0 16

18

43 56 56

18

49

6 9

14

70

22

DF DF

0 17

0

RA RA RA RA DF DF DF RA RA

17

9

34 18 17 18 31

29 29

4

20 177 72 88 43 5

20 41

72 72

124

Table 6: Existing Inventory Data: BA = Basal Area fV'2; TPA = Trees Per Acre (Continued) ID Sp 1

BA TPA

43DF 44 DF

58 185

83 51

45DF 46DF 47DF 48DF 49RA

44

69 38 0 0

5ORA 51 DF 52 DF

53RA 54 DF 55 DF 56 DF

57DF 58 DF

59DF 6ORA 61 DF 62 DF 63 DF 64 DF 65 DF

123

0 0 80 95 0

92 93 108

202 83 63 185 80 93

198

91 145 60 130 99 51

115 91

76DF

96

77 DF

113

78RA 79DF

76

122 165 180

8ODF

215

81DF 82DF

91

69RA 7ORA 71 DF

72DF 73 DF 74 DF

RA RA RA RA RA RA DF

34

88

31 21

34

DF

17

5

RA RA RA RA RA DF RA

14

19 15

50 8 17 18

68 65 102 177 6

0 134

124 134

67 DF 68 DF

BA TPA

121

94 92 0 92 0 106 92 92 21 21 0 223 0 136

66DF

Sp 2

5

27

18

86 34 72 22 43

RA RA

0 6

0 14

DF DF

23

25

39 39

RA

15

17

RA

7

7

RA

11

27

31

29 70

0

134 0

144 134 134 68 68 0 60 0 112

75 None

83 RA

83

0 95

113 73

124 0 83

DF RA RA RA DF

8

11

23

56

5

5

6

14

55

16

125

Table 6: Existing Inventory Data: BA = Basal Area ft"2; TPA = Trees Per Acre (Continued)

IDSp1

84DF 85DF

BA TPA Sp2 186 0

69 0 130

86 DF

83

87RA

86 205 184 76

111 55

29

94DF 95DF

90 218 205 0

88 DF

89DF 9ORA

54 180

RA RA RA DF RA RA DF

BA TPA 15 8

16 153

5

15

17

31

6 33 28

8

11

RA RA RA RA

39

38

8

8

30 9

33 72

DF RA

70 30

21 33

DF RA DF RA

8 8

11

30

91 None

92DF 93 DF

55 55

0

96 DF

113

165

97RA 98DF 99DF

59 205 0

74

100DF

95 83

1O1RA 1O2DF 1O3RA 1O4DF 1O5DF 1O6DF 1O7RA 1O8DF 1O9DF 11ODF

111DF 112DF 113DF 114DF 115DF 116DF 117RA 118DF 119DF 12ODF

121RA 122DF

55 0 144 192

228

70

87 148 45 32

111 41

101

148 78 0 0 83 81

62 0

228 93

97 76 99 41 93 0 0 130 149

114 0 70 91 0

0 210 228 87

111

123

38

64 70

52 55

8 17

48

DF RA RA RA RA RA

42

5

51 33 15

RA

5

23

RA DF RA RA RA DF RA

7

9

70 4

22

16

14

8

8

52

17 65

55

24 4

4

50

24 48 47

87

126

APPENDIX 2

Silvicultural Yields

127

Table 7: Yields for Even-Aged Prescriptions in Mbf per Unit: Thinnings

Unit Time Clearcut 1

1

1

2

1

3

1

4

1

5

1

6

1

7 8

1 1

9

1

10

2 2 2 2 2 2 2 2 2 2

1

2 3

4 5

6 7 8 9 10

3

1

3

2

3

3

3

4

3

5

3

6 7 8 9 10

3 3 3 3

4 4 4 4 4 4 4 4 4 4

1

2 3

4 5

6 7

0. 0. 0. 2. 3. 5. 6. 8. 9.

11. 138.

232. 358. 499. 650. 811. 975. 1143. 1312. 1489. 46. 83. 126. 191.

260. 344. 437. 535. 641. 754. 279. 427. 636. 891. 1167. 1463. 1783.

8 2118. 9 2426. 10 2753.

First Second Final 0. 0. 0.

0. 0.

1.

3.

3.

4.

4.

6. 7. 8. 9. 10.

5. 6. 8. 9. 138.

1.

628.

0. 0. 3. 5. 6. 8. 10. 11. 10. 12.

1265. 849. 1073. 1297. 25. 1522. 33. 1746. 0. 1164. 0. 1187. 0. 1211. 0. 1235. 28. 28. 30. 773. 123. 48. 1044. 182. 60. 1297. 242. 72. 1549. 301. 84. 1802. 360. 60. 1347. 413. 125. 1554. 466. 182. 1736. 519. 248. 1943. 0. 0. 0. 255. 876. 2009. 366. 1154. 2498. 478. 1430. 2984. 589. 1706. 3470. 701. 1982. 3956. 812. 1637. 2689. 888. 1475. 3043. 963. 1313. 3397. 1038. 1150. 3748.

42. 106. 170. 235. 299. 363. 370. 378. 385. 28. 65.

0. 8. 17.

Shelterwood 0. 0. 0. 1.

2. 3. 5.

6. 7. 8. 8. 17. 25. 33.

41. 50. 58. 71. 84. 97. 9. 14. 19.

24. 29. 34. 40. 47. 55. 62. 110. 107. 104. 102. 99. 96. 93. 106. 119. 131.

128

Table 7: Yields for Even-Aged Prescriptions in Mbf per Unit: (Continued)

Unit Time Clearcut 5 5 5 5

2

28. 51. 78. 139. 210. 295. 392. 491. 596. 707. 46. 75.

3

117.

4

241. 395. 568. 760. 956. 1154. 1356.

257. 317. 374. 431. 481.

8. 12. 18.

8. 15. 18.

28. 112. 220. 346. 491. 634. 785. 173. 262. 385. 585. 822. 1084. 1371. 1655. 1944.

54. 89. 125. 161. 195.

1

2 3

4

5

5

5

5

6 7

5

8

5

9 10

5

6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7

7 7 8 8 8 8 8 8 8 8 8 8

Thinnings First Second Final

1

5

6 7 8

9 10 1

2 3

4 5

6 7 8

9 10 1

2 3

4 5

6 7 8

9

10 2234.

20. 43. 78. 126. 173. 221. 269. 313. 356. 398. 43. 61. 79. 138. 198.

20. 20. 21. 471. 124. 883. 158. 1088. 193. 1292. 227. 1497. 240. 1274. 306. 1450. 276. 1366. 346. 1546. 43. 43. 43. 329. 388. 1310. 490. 1561. 591. 1813. 693. 2065. 777. 2049. 897. 2289. 676. 1611. 808. 1863. 8.

8.

230. 265.

32. 353. 438. 522. 607. 674. 747. 819. 578.

9.

9.

64. 921. 1084. 1247. 1410. 1523. 1683. 1842. 1159. 9. 953.

426. 853. 2003. 275. 1061. 2396. 365. 1268. 2790. 454. 1476. 3184. 543. 1391. 2758. 613. 1407. 3078. 678. 1111. 2566. 742. 1138. 2896. 134. 186.

Shelterwood 5. 8. 12. 15. 19.

23. 30. 39. 48. 56. 7. 11. 15. 19.

23. 27. 44. 63. 81. 100. 3. 3. 3. 3. 4. 6. 18.

31. 43. 56. 63. 64. 64. 66. 67. 69. 83. 103. 123. 143.

129


Unit Time Clearcut 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10

1

2 3

4 5

6 7 8 9 10 1

2 3

4 5

6 7 8

9

10 10 11

1

11

2

11 11

3

11 11

5

11 11

4 6 7

105. 174. 260. 358. 481. 610. 742. 880. 1040. 1187. 137. 229. 354. 489. 638. 784. 929. 1089. 1231. 1377. 5. 8. 18. 172.

374. 612. 888.

1161. 11 9 1449. 11 10 1742. 12 1 0. 12 2 1. 12 3 6. 12 4 157. 12 5 355. 12 6 588. 12 7 857. 12 8 1123. 12 9 1404. 12 10 1689. 8

Thinnings First Second Final 27. 73. 136. 201. 264. 327. 391. 449. 506. 564. 0. 57. 115. 173.

231. 289. 347. 394. 441. 488. 0. 4. 9. 88. 167.

27. 56. 84. 105. 124. 143. 108. 172.

236. 289. 0. 0. 12. 24. 35. 47. 2. 71. 140. 210. 26. 35. 665. 852. 1038.

27. 854. 1102. 1327. 1550. 1773. 1216. 1402. 1588. 1745. 0.

922. 1119. 1315. 1511. 1707. 1038. 1195. 1351. 1509. 63. 77. 1764. 2124. 2484.

247. 1225. 2844. 326. 1386. 3140. 404. 1558. 3497. 481. 1110. 2182. 547. 1303. 2560. 16. 19.

16. 19.

Shelterwood 13.

20. 27. 34. 41. 49. 57. 68. 78. 89. 10. 19. 28. 37. 46. 55. 63. 76. 88. 100. 2. 2. 2. 3. 3. 3.

27. 52. 77. 102.

16. 19.

0.

21. 639. 1684. 98. 818. 2030. 175. 997. 2376. 252. 1177. 2722. 329. 1356. 3068. 406. 1535. 3415. 483. 1096. 2097. 547. 1295. 2463.

1.

1.

5. 9. 14.

42. 70. 98. 126.

130


Unit Time Clearcut 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14

291. 446. 3 663. 4 929. 5 1216. 6 1524. 7 1857.


1

0.

0.

0.

2

287. 399. 511. 623. 735. 846. 863. 881. 898.

1071. 1354. 1638. 1921. 2204. 1704. 1738. 1773. 1808.

2350. 2852. 3354. 3856. 4358. 2797. 2853. 2910. 2968.

11.

11.

11.

94. 131. 169.

206. 243. 281. 317. 352. 389.

268. 347. 426. 506. 585. 486. 446. 403. 362.

654. 823. 992. 1161. 1329. 938. 1077. 1214. 1354.

1.

1.

1.

9 2382. 10 2678.

218. 321. 424. 527. 629. 732. 785. 838. 891.

823. 1011. 1199. 1387. 1576. 1160. 1042. 924. 806.

1912. 2352. 2792. 3232. 3671. 2418. 2663. 2907. 3152.

49. 81. 126. 173. 226. 277. 328. 385. 435. 486.

7.

27. 48. 68. 88. 109. 129. 146. 162. 179.

7. 7. 11. 15. 19.

8 2206. 9 2527. 10 2868. 1

2 3

4 5

14 6 14 7 14 8 14 9 14 10 15 1 15 2 15 3 15 4

112. 170.

247. 328. 421. 522. 630. 738. 845. 953. 315. 483. 708. 947. 1214.

15

5

15 15 15 15 15 16 16 16 16 16 16 16 16 16 16

6 1500. 7 1794. 8

1

2 3

4 5

6 7 8

9 10

2091.

23. 7.

32. 56. 81.

7.

332. 401. 470. 538. 607. 371. 427. 482. 538.

Shelterwood 115. 112. 109. 106. 103. 100. 97. 110. 124. 137.

41. 41. 42. 42. 42. 42. 43. 48. 52. 57. 103. 105. 107. 109. 111. 113. 115. 130. 144. 159. 4. 7. 11. 14. 17. 20. 24. 28. 33. 37.

131


Unit Time Clearcut 17 1 17 2 17 3 17 4 17 5 17 6 17 7 17 8 17 9 17 10 18 1 18 2 18 3 18 4 18 5 18 6 18 7 18 8 18 9 18 10 19 1 19 2 19 3 19 4 19 5 19 6 19 7 19 8 19 9 19 10

20 20 20 20 20 20 20 20 20

1

2 3

4 5

6 7 8

9

20 10

187.

296. 437. 613. 805. 1015. 1229. 1468. 1690. 1913. 103. 173.

267. 368. 481. 590. 700. 820. 927. 1037. 59. 99. 148. 204. 273. 345. 418. 494. 584. 666. 8. 12. 19.

27. 43. 66. 93. 124. 154. 187.

Thinnings First Second Final 25. 175.

117.

522. 595. 1435. 714. 1713. 834. 1992.

243. 311. 384. 958. 2276. 457. 1082. 2559. 530. 879. 1902. 594. 812. 2133. 658. 744. 2364. 722. 677. 2595. 0. 43. 87. 130.

0. 0. 9. 17.

174.

26. 34.

218. 262. 297. 332. 367. 6.

29. 65. 101. 137. 173. 209. 242. 274. 307. 40. 53. 69. 85. 100. 116. 133. 167. 202. 236.

0. 52. 105. 157. 6. 12. 17.

22. 26. 31. 9.

49. 88. 128. 40. 58. 68. 79. 89. 100. 101. 115. 129. 144.

0.

695. 842. 990. 1137. 1285. 780. 899. 1017. 1136. 6.

484. 610. 737. 863. 989. 660. 763. 866. 969. 40. 193.

261. 329. 397. 465. 394. 481. 569. 656.

Shelterwood 12.

29. 46. 63. 80. 96. 113. 130. 146. 162. 8. 14.

21. 28. 34. 41. 48. 57. 66. 76. 5. 9.

14. 18.

22. 26. 30. 36. 41. 47. 2. 4. 5.

7. 8.

9. 11. 13. 16. 19.

132


Unit Time Clearcut 21 1 110. 21 2 182. 21 3 281. 21 4 409. 21 5 561. 21 6 721. 21 7 902. 21 8 1088. 21 9 1278. 21 10 1468.

22 22 22 22 22 22 22 22 22

3

3. 5. 13.

4

170.

5

377. 620. 902. 1182. 1477. 1776. 44. 69. 108. 160. 226. 301. 386. 474. 569. 661. 67. 109. 166. 252. 360. 487. 623. 757. 906. 1060.

1

2

6 7 8 9

22 10 23 1 23 2 23 3 23 4 23 5 23 6 23 7 23 8 23 9 23 10 24 1 24 2 24 3 24 4 24 5 24 6 24 7 24 8 24 9

24 10


209. 289. 366. 444. 522. 576. 630. 684. 0. 3. 6.

414. 906. 542. 1446. 656. 1742. 770. 2038. 882. 2332. 994. 2625. 701. 1723. 677. 1960.

653. 2196. 629. 2433. 41. 22. 50. 669. 1785. 17.

86. 862. 2159. 166. 1052. 2527.

247. 328. 407. 487. 554. 25. 69. 121. 173.

224. 276. 328. 371. 412. 453. 0.

56. 113. 171. 232. 292. 352. 391. 429. 467.

1242. 2894. 1415. 3222. 1597. 3587. 1136. 2227. 1336. 2606. 34. 39. 52. 65. 78. 91. 53. 110. 166.

221. 342. 458. 595. 730. 855. 981. 765. 707. 628. 558.

47. 651. 870. 1089. 1308. 1527. 1167. 1344. 1519. 1694. 830. 1018. 1263. 1499. 1706. 1913. 1290. 1456. 1566. 1697.

Shelterwood 12.

25. 39. 52. 65. 78. 91. 107. 123. 139. 1. 1.

2. 2. 2. 2. 27. 52. 78. 103. 10.

20. 30. 40. 50. 60. 70. 82. 95. 107. 28. 29. 31. 33. 35. 37. 40. 49. 59. 68.

133


Unit Time Clearcut 25 1 146. 25 2 237. 25 3 358. 25 4 490. 25 5 634. 25 6 777. 25 7 921. 25 8 1077. 25 9 1218. 25 10 1363. 26 1 222. 26 2 435. 26 3 707.

26 4 1030. 26 5 1379. 26 6 1741. 26 7 2113. 26 8 2512. 26 9 2871. 26 10 3233. 27 1 204. 27 2 324. 27 3 475. 27 4 651. 27 5 840. 27 6 1039. 27 7 1241. 27 8 1464. 27 9 1671.

27 10 28 1 28 2 28 3 28 4 28 5 28 6 28 7 28 8 28 9 28 10

1877. 43. 68. 100. 138. 185.

241. 301. 367. 431. 500.

Thinriings First Second Final 129. 192.

129. 190.

245. 302. 359. 416. 473. 522. 571. 620.

215. 243. 272. 301. 239. 293. 346. 399. 428.

55.

297. 400. 504. 608.

129. 1013. 1200. 1391. 1582. 1773. 1143. 1299. 1454. 1610. 1061.

33. 47. 61. 75. 89. 103. 117. 134. 152. 170. 7.

1154. 2660.

19.

1417. 3154. 1681. 3649.

31. 44. 56. 68. 100. 128. 157. 185. 7.

1946. 4144.

712. 2210. 4638. 816. 902. 988. 1074. 0. 159. 223. 287. 353. 420. 486. 541. 595. 650.

1677. 2933. 1703. 3373. 1729. 3814. 1754. 4255. 0. 455. 577. 699. 823.

46. 1392. 1679. 1965. 2255.

948. 2544. 752. 704. 655. 607.

2059. 2285.

15.

16.

17.

44. 68. 92.

119. 136. 153. 169. 186. 114. 117. 120. 122.

422. 539. 656. 772. 889. 628. 723. 818. 913.

116. 139. 163. 193.

223. 253.

Shelterwood

1608. 1834.

19.

32. 45. 58. 70. 83. 95. 106. 117. 12. 15. 18.

21. 24. 27. 30. 35. 41. 46.

134


Unit Time Clearcut 29 29 29 29 29 29 29 29 29

1

2 3

4 5

6 7 8

9

29 10 30 30 30 30 30 30 30 30 30

30 31 31 31 31 31 31 31 31 31 31

1

2 3

83. 129. 188.

257. 335. 416. 498. 585. 670. 759. 26. 93. 181.

4

285. 402. 6 521. 7 644. 8 772. 9 887. 10 1003. 5

1

2 3

4 5

6 7 8

9 10

32 1 32 2 32 3 32 4 32 5 32 6 32 7 32 8 32 9 32 10

105. 162.

237. 328. 424. 527. 636. 752. 858. 969. 38. 65. 101. 174. 262. 358. 468. 579. 692. 807.

Thinnings First Second Final 0. 55. 83. 110. 138. 166. 193.

201. 209. 216. 0. 49. 83. 117. 150. 184. 218. 245. 273. 301.

3.

9.

17.

258. 619. 279. 744. 301. 869. 323. 994. 344. 1119. 164. 681. 149. 722. 134. 762. 119. 803. 227. 610. 360. 889. 442. 1046. 524. 1204. 606. 1361. 688. 1518. 497. 935. 558. 1092. 620. 1249. 682. 1407.

20. 23. 26. 28. 31. 34. 41. 48. 55.

0.

0.

0.

93. 127. 162.

331. 417. 506. 596. 686. 539. 492. 444. 396.

729. 883. 1039. 1197. 1355. 877. 996. 1114. 1233. 425. 507. 884. 1027. 1169. 1310. 1057. 1187. 1023. 1157.

200. 237. 275. 303. 332. 360. 30. 56. 83. 122. 161. 199. 237.

267. 298. 326.

Shelterwood

199.

249. 408. 490. 570. 650. 561. 569. 468. 480.

1.

2. 3. 4. 5. 6. 18.

31. 43. 56. 35. 40. 46. 51. 57. 62. 68. 77. 85. 94. 3. 7. 12. 18.

24. 30. 41. 52. 63. 74.

135


Unit Time Clearcut 33 33 33 33 33 33 33 33 33 33

34 34 34 34 34 34 34 34 34

1

167.

2

281. 437. 652. 907. 1173. 1466. 1779.

3

4 5

6 7 8

9 2088. 10 2397. 1

167.

2

281. 435. 645. 892. 1148. 1433. 1733.

3

4 5

6 7 8

9 2031. 34 10 2329. 35 35 35 35 35 35 35 35 35 35

36 36 36 36 36 36 36 36 36

1

2 3

4 5

6 7 8

9 10 1

2 3

4 5

6 7 8 9

36 10

80. 133.

205. 304. 421. 542. 677. 820. 961. 1103. 26. 41. 63. 99. 268. 486. 738. 1021. 1308. 1609.


774. 1822.

3.

984. 2370. 1196. 2793. 1408. 3217. 1621. 3640. 1833. 4063.

16.

229. 344. 460. 576. 691. 1258. 2483. 767. 1157. 2828. 842. 1055. 3172. 918. 954. 3517. 21. 790. 1830. 130. 1000. 2295. 239. 1211. 2689. 349. 1422. 3082. 458. 1633. 3475. 567. 1844. 3868. 677. 1277. 2349. 748. 1170. 2673. 819. 1062. 2997. 891. 955. 3321. 31. 361. 810. 86. 463. 1098. 141. 559. 1296. 196. 656. 1494. 250. 751. 1692. 305. 847. 1889. 359. 597. 1184. 396. 556. 1345. 432. 514. 1505. 467. 472. 1665. 0. 131. 317. 22. 175. 389. 43. 219. 461. 64. 818. 2025. 153.

241. 330. 410. 490. 570.

Shelterwood

1021. 2405. 1224. 2786. 1296. 2849. 1429. 3214. 1562. 3579. 1141. 2451.

29. 42. 54. 67. 80. 98. 115. 133. 6.

20. 34. 49. 64. 79. 93. 112. 131. 150. 7. 15. 22. 30. 38. 46. 54. 64. 74. 84. 11. 11. 12. 13. 13. 14.

34. 56. 79. 101.

136



1

2 3

4 5

6 7 8 9

37 10 38 1 38 2 38 3 38 4 38 5 38 6 38 7 38 8 38 9 38 10 39 1 39 2 39 3 39 4 39 5 39 6 39 7 39 8 39 9

42. 73. 111. 161. 218. 283. 355. 429. 509. 592. 74. 120. 181. 266. 364. 479. 599. 720. 851. 987. 323. 487. 684. 897. 1136. 1373. 1621. 1860.

2112.

39 10 2354. 40 40 40 40 40 40 40 40 40

1

2 3

6. 10. 19.

4

168.

5

360. 586. 847. 1105. 1377. 1652.

6 7 8

9

40 10

Thinnings First Second Final 0.

28. 68. 108. 148. 188.

227. 262. 297. 332. 0. 64. 117. 170. 223. 277. 330. 363. 397. 430. 19.

0. 11.

80. 561.

27. 727. 42. 892. 58. 1057. 74. 1223. 67. 867. 99. 1002. 132. 1137. 164. 1272. 0. 702. 147. 988. 257. 1175. 367. 1361. 477. 1548. 588. 1735. 663. 1108. 600. 1254. 537. 1400. 474. 1546. 19.

19.

711. 858. 1006. 416. 484. 1153. 553. 1300. 621. 982. 672. 902. 714. 813. 765. 733. 35. 62. 42. 73. 49. 661. 125. 837. 202. 1012. 278. 1188. 355. 1337. 429. 1501. 504. 1087. 567. 1270.

1733.

279. 348.

2082. 2431. 2779. 3127. 2021. 2268. 2506. 2753. 99.


20. 23. 26. 32. 37. 42. 23. 26. 28. 31. 33. 35. 38. 45. 53. 61. 89. 90. 90. 91. 92. 92. 93. 105. 116. 128. 0.

115. 1684.

1.

2021. 2357. 2694. 2967. 3301. 2082. 2435.

5. 9. 13.

1.

40. 66. 93. 119.

137



42 42 42 42 42 42 42 42 42

1

2 3

4 5

6 7 8 9 10 1

2 3

4 5

6 7 8

9

42 10 43 1 43 2 43 3 43 4 43 5 43 6 43 7 43 8 43 9 43 10

44 44 44 44 44 44 44 44 44

44

1

2

0. 0. 0.

4. 115.

262. 435. 636. 834. 1043. 195. 292. 407. 538. 685. 830. 982. 1125. 1277. 1418. 31. 50. 75. 107. 150. 205. 265. 334.

413. 495. 94. 159.

247. 369. 5 513. 6 661. 7 825. 8 999. 9 1170. 10 1342. 3

4


0. 0. 0.

468. 602. 736.

0. 0. 0. 1259. 1519. 1780.

870. 2040. 226. 1004. 2300. 283. 1138. 2560. 339.

804.

1562.

0. 159. 193. 229. 266. 302. 339. 363. 387. 410.

0.

0.

440. 565. 668. 772. 876. 699. 643. 557. 501.

1.

1.

35. 69. 104. 138. 172. 206. 280. 354. 428.

1.

925. 1175. 1364. 1554. 1743. 1167. 1303. 1363. 1501. 414. 564. 713. 863. 1013. 1163. 900. 1136. 1372. 1609. 1115. 1331. 1548. 1765. 1981.

0.

61. 122. 183. 245. 306. 367. 405. 443. 482.

1. 1. 1. 1. 1.

42. 83. 124. 473. 602. 730. 858. 986. 1115. 2198. 770. 1300. 696. 1477. 623. 1654. 550. 1831.

Shelterwood 0. 0. 0. 0. 0. 0. 16. 32. 49. 65. 55. 53. 51. 50. 48. 46. 46. 52. 58. 64. 16.

22. 29. 36. 42. 49. 55. 67. 78. 89. 0. 6. 12. 18.

24. 30. 36. 45. 53. 62.

138


Unit Time Clearcut 45 1 46. 45 2 87. 45 3 152. 45 4 264. 45 5 404. 45 6 572. 45 7 744. 45 8 928. 45 9 1128. 45 10 1322. 46 1 217. 46 2 357. 46 3 543. 46 4 783. 46 5 1056. 46 6 1369. 46 7 1708.

46 46

8 2059. 9 2429.

46 10 2779. 47 47 47 47 47 47 47 47 47

1

2 3

4 5

6 7 8 9

47 10

29. 47. 72. 106. 148. 198.

250. 302. 359. 419.

48 1 191. 48 2 297. 48 3 440. 48 4 598. 48 5 790. 48 6 986. 48 7 1191. 48 8 1392. 48 9 1599. 48 10 1795.

Thinnings First Second Final 63. 109. 155. 215. 275. 335. 395. 442. 417. 462. 1.

145.

289. 432.

63. 162. 364. 495. 625. 756. 886. 865. 668. 648. 1041. 1339. 1637. 1935.

925. 1100. 1548. 1781. 2014. 2246. 1616. 1830. 1697. 1913. 2426. 2923. 3421. 3918.

576. 2233. 4416. 720. 2531. 4913. 864. 956. 1048. 1140. 0. 24. 49. 73. 97. 122. 146. 162. 177. 192. 0. 186. 245. 305. 364. 424. 483. 527. 570. 614.

1789. 2986. 1618. 3396. 1448. 3805.

1278. 4215. 0.

48. 97. 145. 194. 242. 290. 263. 236. 209.

349. 440. 522. 605. 688. 771. 493. 558. 623. 688.

0.

0.

626. 781. 937. 1093. 1248. 964. 868. 771. 675.

1389. 1675. 1961. 2248. 2534. 1617. 1833. 2050. 2267.

Shelterwood 5. 13.

21. 29. 37. 46. 58. 72. 87. 101. 4. 21. 38. 55. 72. 89. 106. 127. 149. 170. 12. 13. 13. 14. 15. 16. 17.

20. 24. 27. 0. 8. 17.

25. 34. 42. 51. 59. 67. 74.

139



1

15.

0.

2

24. 39. 58. 91.

2. 4.

3

4 5

6 7 8 9

49 10 50 50 50 50 50 50 50 50 50 50 51 51 51 51 51 51 51 51 51 51

Thinnings Final

First Second

128. 171.

219. 272. 320.

1

168.

2

259. 384.

3

4 5

6 7 8 9 10 1

2 3

4 5

6 7 8 9

538. 705. 886. 1081. 1283. 1474. 1675. 281. 423. 595. 785. 1000. 1218. 1447. 1669. 1905.

10 2129.

52 1 302. 52 2 453. 636. 52 3 52 4 862. 52 5 1120. 52 6 1383. 52 7 1661. 52 8 1926. 52 9 2207. 52 10 2472.

6. 8. 11. 13. 15. 17. 19. 5. 161.

0. 0. 0. 1. 1. 1.

0. 3. 5. 8. 5.

247. 360. 454. 549. 643. 737. 557. 826. 1095. 860. 135. 1375. 1663. 1954.

574. 228. 738. 297. 905. 366. 1072. 2245. 435. 1239. 2535. 504. 1002. 1632. 552. 907. 1848. 601. 812. 2064. 649. 717. 2280. 239. 5. 5. 241. 629. 1621. 310. 802. 1952. 378. 975. 2284. 447. 1148. 2614. 515. 1321. 2945. 584. 1119. 1954. 634. 1016. 2203. 685. 913. 2452. 736. 811. 2701. 0. 0. 76. 248. 682. 1506. 302. 961. 2119. 372. 1151. 2468. 442. 1342. 2817. 511. 1532. 3166. 581. 1293. 2268. 630. 1224. 2536. 679. 1032. 2471. 726. 967. 2742.

Shelterwood 9. 23. 37. 51. 66. 80. 94. 130. 166. 202. 72. 75. 77. 80. 83. 86. 89. 101. 114. 126. 74. 75. 76. 76. 77. 78. 79. 91. 102. 114. 84. 82. 79. 77. 75. 73. 75. 88. 101. 114.

140


Unit Time Clearcut 53 53 53 53 53

53 53 53 53 53 54 54 54 54 54 54 54 54 54 54 55 55 55 55 55 55 55 55 55 55 56 56 56 56 56 56 56 56 56 56

1

129.

2

219. 339. 506. 703. 906. 1129. 1368. 1602. 1837.

3

4 5

6 7 8

9 10

3

0. 0. 3.

4

104.

1

2

237. 393. 574. 8 753. 9 941. 10 1133. 1 76. 2 112. 5

6 7

3

158.

4

220. 287. 370. 463. 569. 678. 791.

5

6 7 8 9 10 1

2 3

4 5

6 7 8 9 10

99. 158.

239. 337. 442. 559. 687. 815. 948. 1082.

Thinnings First Second Final 3. 87. 170. 253. 337. 420. 503. 556. 608. 660. 21. 22. 23. 75. 126. 178. 229. 280. 332. 374. 39. 115. 173. 232. 289. 347. 404. 513. 621. 730. 66. 162. 207. 252. 297. 342. 387.

421. 454. 488.

649. 824. 999. 1174. 1348. 1523. 1053. 953. 853. 753. 21. 22. 442. 562. 683. 804. 925.

1523. 1819. 2114. 2410. 2705. 3001. 1776. 2018. 2259. 2500. 21. 22. 1149. 1383. 1617. 1851. 2085.

1045. 2318. 747. 881. 39. 41. 58. 75. 92. 108.

1425. 1673. 41. 688. 937. 1187. 1436. 1684. 50. 1360. 123. 1692.

195. 2023. 267. 2355. 66. 443. 558. 670. 783. 895. 733. 671. 606. 544.

129. 967. 1172. 1370. 1568. 1765. 1173. 1323. 1465. 1615.

Shelterwood 1.

10. 19.

28. 36. 45. 54. 66. 79. 91. 0. 0. 0. 1.

3. 4. 22. 39. 57. 74.

40. 50. 60. 70. 79. 89. 99. 116. 133. 150. 43. 45. 46. 48. 49. 51. 52. 60. 67. 74.

141



1

2 3

4 5

6 7 8 9

57 10 58 58 58 58 58 58 58 58 58 58 59 59 59 59 59 59 59 59 59

1

2 3

4 5

6 7 8

9 2609. 10 2961. 1

2 3

4 5

6 7 8 9

59 10 60 60 60 60 60 60 60 60 60

43. 69. 105. 150. 209. 285. 368. 463. 572. 684. 300. 461. 685. 958. 1254. 1572. 1916. 2276.

100. 169.

262. 392. 545. 703. 877. 1062. 1244. 1427.

1

109.

2

203. 362. 593. 882. 1229. 1577. 1957.

3

4 5

6 7 8

9 2372.

60 10 2770.

Thinnings First Second Final 24. 71. 119. 166.

214. 261. 308. 409. 510. 611. 0.

24. 25. 26. 27. 27. 28. 28. 85.

586. 792. 997. 1202. 1406. 1611.

1253. 1575. 141. 1898. 198. 2220. 0. 27. 1080. 2414. 1365. 2932. 1654. 3452. 1942. 3973.

290. 403. 519. 635. 751. 2230. 4493. 867. 1728. 2899. 949. 1560. 3304. 1031. 1393. 3709. 1113. 1225. 4059. 5. 503. 1177. 69. 638. 1406. 134. 775. 1639. 199. 911. 1869. 264. 1047. 2098. 328. 1183. 2328. 393. 821. 1384. 434. 744. 1572. 475. 666. 1754. 516. 590. 1942. 2. 2. 2213. 117. 254. 2656. 231. 571. 3273. 355. 843. 3753. 479. 1115. 4234. 603. 1387. 4714. 727. 1659. 2983. 820. 1541. 3417. 910. 1357. 3675. 1002. 1242. 4110.

Shelterwood 22. 32. 42. 52. 62. 72. 82. 98. 115. 131. 122. 123. 125. 126. 127. 129. 130. 150. 170. 190. 1. 8.

15.

22. 30. 37. 45. 55. 65. 75. 3. 15.

27. 39. 51. 63. 78. 99. 120. 141.

142


Unit Time Clearcut 61 61 61 61 61 61 61 61 61 61 62 62 62 62 62 62 62

1

2 3

4 5

6 7 8 9 10

105. 179.

81. 126.

279. 425. 605. 795. 1003. 1231.

213. 304. 394. 481. 568. 620. 672. 724.

1460. 1687. 1 48. 2 79. 3 121. 4 184. 265. 5 6 363. 7 475. 62 8 594. 62 9 722. 62 10 853. 63 142. 1 63 2 233. 63 63 63 63 63 63 63 63

64 64 64 64 64 64 64 64 64

7 8 9 10

355. 510. 687. 888. 1106. 1331. 1568. 1794.

1

178.

3

4 5 6

2 3

4 5

6 7 8 9

64 10


268. 379. 528. 702. 884. 1081. 1273. 1476. 1672.

60. 115. 170.

228. 285. 343. 401. 452. 503. 553. 0. 101. 192. 282. 373. 464. 555. 614. 672. 731. 0. 150. 194. 252. 310. 368. 426. 471. 515. 557.

320. 644. 692. 1514. 901. 1897.

1091. 2220. 1281. 2544. 1467. 2865. 1122. 1876.

1038. 2119. 927. 2288. 844. 2531. 60. 716. 188. 933. 339. 1211. 473. 1440. 608. 1670. 742. 1900. 877. 1473. 818. 1675. 737. 1817.

Shelterwood 8. 18.

27. 40. 53. 66. 80. 99. 117. 135. 3. 10. 18.

679. 2020.

25. 33. 41. 49. 63. 77. 91.

609. 1420. 850. 1861.

8. 16.

1042. 2184. 1234. 2507. 1427. 2830. 1619. 3153.

25. 34. 42. 51. 60. 71. 83. 95. 46. 46. 47. 47. 47. 48. 52. 64. 76. 88.

1152. 1923.

1041. 2186. 930. 2449. 819. 2712. 210. 423. 1047. 655. 1561. 805. 1833. 18.

956. 2106. 1106. 2378. 1004. 1801. 963. 2021. 807. 1935. 769. 2159.

143


Unit Time Clearcut 65 1 0. 65 2 0. 65 3 4. 65 4 116. 65 5 262. 65 6 434. 65 7 633. 65 8 830. 65 9 1038. 65 10 1248. 66 1 117. 66 2 186. 66 3 281. 66 4 395. 66 5 516. 66 6 650. 66 7 796. 66 8 940. 66 9 1092. 66 10 1241. 67 1 106. 67 2 180.

67 67 67 67 67 67 67

51. 53. 56. 113. 171.

1.

116. 166.

463. 589. 715. 841. 966. 745. 671. 598. 525. 525. 660. 795. 931.

1037. 1259. 1481. 1703. 1925. 1226. 1390. 1554. 1717. 1202. 1431. 1660. 1889.

5. 6. 15.

5.

16.

770. 964. 25. 1158. 34. 1352. 43. 1546. 7. 1020. 68. 1212. 129. 1403. 190. 1594.

23. 30. 37. 44. 51. 58. 68. 79. 89.

216. 266. 316. 366. 401. 436. 471. 24. 89.

145.

50.

3

219. 303. 396. 499. 605. 715. 831. 945.

103. 155.

6 7 8 9

4 5

6 7 8

9 10

0. 0. 0. 3. 6. 9. 30. 51. 72. 93. 52. 50. 49. 48. 47.

0.

2

5

Shelterwood

0.

1

4

51. 51. 53. 53. 513. 1285. 646. 1542. 779. 1798.

228. 912. 2055. 286. 1045. 2311. 342. 1177. 2567. 399. 852. 1593. 446. 999. 1863.

277. 410. 566. 727. 904. 1093. 1278. 1464. 89.

3

67 10 68 68 68 68 68 68 68 68 68 68


154.

218. 283. 1066. 2118. 347. 1202. 2346. 412. 837. 1398. 453. 760. 1585. 494. 683. 1772. 535. 607. 1960. 5.

207. 259. 311. 371. 431. 491.

46. 45. 50. 55. 60. 7. 18. 28. 39. 50. 61. 71. 85. 98. 111.

144


Unit Time Clearcut 69 1 69 2 69 3 69 4 69 5 69 6 69 7 69 8 69 9 69 10 70 1 70 2 70 3 70 4 70 5 70 6 70 7 70 8 70 9 70 10 71 71 71 71 71 71 71 71 71 71

72 72 72 72 72 72 72 72 72

6 7

58. 106. 181. 280. 401. 545. 688. 845. 1014. 1178. 172. 268. 396. 538. 711. 888. 1072. 1253. 1440. 1616. 24. 39. 59. 84. 118. 162. 209. 264. 327. 392. 323. 503. 729. 995. 1303. 1626. 1968.

8

2312

1

2 3

4 5

6 7 8

9 10 1

2 3

4 5

9 2669. 72 10 3025.

Thinnings Final

First Second 128. 182.

234. 287. 341. 395. 449. 490. 381. 420. 0. 167.

221. 274. 328. 381. 435. 474. 514. 553. 0.

27. 54. 81.

128.

252. 363. 475. 588.

1027. 1252. 1444. 1638. 1833.

701. 2027. 800. 747. 544. 488. 2. 564. 704. 844. 984. 1124. 868. 781. 695. 608. 0. 0. 0. 0. 2.

1286. 1459. 1482. 1653. 4. 1251. 1508. 1766.

2023. 2281. 1455. 1650. 1845.

2041. 325. 442. 560. 678. 800. 919. 713. 900. 1087. 1273. 1322.

Shelterwood 11.

23. 35. 47. 58. 70. 82. 96. 111. 126. 0. 8. 16.

24. 31. 39. 47. 54. 61. 69. 12. 18.

719. 2269. 4520.

23. 28. 33. 38. 43. 52. 61. 70. 62. 69. 76. 83. 90. 97.

1693. 2821. 1527. 3191. 1361. 3560. 1195. 3931.

104. 120. 137. 154.

107. 135. 162.

220. 278. 336. 2. 258. 373. 488. 603. 834. 906. 978. 1051.

2. 3.

35. 68. 101. 535.

1189. 2631. 1459. 3103.

1729. 3576. 1999. 4048.

145



74 74 74 74 74 74 74 74 74

1

167.

2

282. 439. 656. 913. 1180. 1473. 1788.

3

4 5

6 7 8

9 2098. 10 2408. 1

2 3

4 5

6 7 8

9

74 10

65. 106. 161.

230. 313. 404. 502. 605. 711. 821. 24. 44. 78.

75 1 75 2 75 3 75 4 124. 75 5 182. 75 6 251. 75 7 320. 75 8 396. 75 9 478. 75 10 557. 76 1 178. 76 2 273. 76 3 407. 76 4 570. 76 5 746. 76 6 935. 76 7 1140. 76 8 1354. 76 9 1551. 76 10 1759.


Shelterwood

0. 102.

787. 1852.

0.

1058. 2365. 214. 1294. 2765.

11.

327. 440. 553. 665. 735. 805. 874.

1531. 3166. 1767. 3566. 2003. 3967.

0.

49. 89. 129. 169. 209. 248. 273. 298. 323. 0.

25. 50. 75. 100. 125. 150. 168. 186. 204. 0.

176. 245. 313. 382.

1394. 2363.

231. 286. 329. 299. 269. 239.

2685. 3007. 3329. 624. 827. 973. 1119. 1264. 1410. 874. 994. 1115. 1235. 478. 575. 671. 767. 863. 959. 577. 663. 749. 834.

0.

0.

1262. 1129. 997. 261. 372. 457. 542. 627. 712. 515. 465. 415. 366. 12. 66. 121. 176.

657. 1442. 831. 1750.

1005. 2058. 1179. 2366. 451. 1353. 2674. 519. 1046. 1716. 567. 942. 1942. 615. 838. 2169. 664. 734. 2395.

22. 33. 44. 55. 66. 82. 97. 113. 4. 8. 11. 15. 18.

22. 25. 31. 36. 41. 0. 2. 5.

7. 9. 11. 14. 17. 21. 25. 70. 69. 67. 65. 63. 61. 60. 68. 76. 84.

146



1

2 3

4 5

6 7 8 9

77 10 78 78 78 78 78 78 78 78 78

1

2 3

4 5

6

55. 90. 139. 246. 380. 535. 712. 892. 1083. 1274. 311. 495. 750. 1053. 1376. 1733.

7 2121. 8 2506. 9 2909.

78 10 3308. 79 79 79 79 79 79 79 79 79

1

2 3

4

1

98. 201. 323. 463. 603. 749. 897. 79.

2

145.

3

251. 394. 570. 778. 987. 1218.

5

6 7 8

9

79 10 80 80 80 80 80 80 80 80 80

7. 10. 19.

4 5

6 7 8

9 1466. 80 10 1706.

Thinnings First Second Final 91. 142. 193.

267. 340. 414. 470. 524. 577. 627. 0.

189. 693. 262. 862. 526. 1543. 654. 1818.

781. 2093. 812. 2143.

939. 2001. 957. 2221. 785. 1929. 810. 2156. 0.

0.

308. 1234. 2764. 442. 1570. 3356. 575. 1905. 3947. 709. 2240. 4539. 842. 2575. 5131. 976. 1984. 3266. 1069. 1789. 3703. 1162. 1594. 4140. 1255. 1399. 4577. 4. 4. 4. 10. 4. 111. 20. 293. 927. 65. 377. 1128. 109. 461. 1329. 154. 545. 1531. 198. 622. 1631. 250. 715. 1841. 303. 521. 1277. 349. 623. 1496. 47. 149. 1498. 124. 316. 1790. 201. 483. 2081. 278. 649. 2373. 355. 816. 2664. 432. 983. 2956. 509. 1048. 1796. 564. 958. 2055. 564. 813. 2259. 618. 722. 2516.

Shelterwood 4. 11. 18.

25. 32. 40. 54. 72. 90. 108. 137. 134. 131. 128. 125. 122. 119. 133. 147. 161. 4. 9. 15.

21. 26. 32. 49. 72. 95. 118. 1.

10. 19.

27. 36. 45. 53. 66. 78. 91.

147



82 82 82 82 82 82

2

2. 3.

3

5.

4

7. 9.

1

5

6 7 8 9 10 1

2 3

4 5

6 7

82 82 8 82 9 82 10 83 83 83 83 83 83 83 83 83 83

1

2 3

4 5 6

7 8 9 10

11. 13. 15. 18.

20. 71. 118. 182.

266. 367. 479. 602. 731. 863. 1001. 2. 4. 7.

51. 107. 174.

250. 326. 406. 487. 224. 367. 553. 781.

84 1 84 2 84 3 84 4 84 5 1023. 84 6 1284. 84 7 1564. 84 8 1848. 84 9 2128. 84 10 2404.


2. 3. 3. 4. 4. 5. 5. 6. 7. 0.

53. 103. 154. 205. 256. 307. 340. 372. 404. 32. 34. 37. 59. 82. 105. 128. 150. 172. 191. 88. 223. 325. 426. 528. 625. 721. 782. 843. 904.

0. 7. 7. 6. 6. 6. 6. 6. 5. 5. 348.

0. 15. 17. 18. 20. 21. 23. 24. 26. 27. 830. 1027. 1223. 1406. 1590. 1773. 1110. 1263. 1402. 1556. 32.

461. 572. 679. 786. 893. 647. 587. 522. 463. 32. 34. 48. 204. 507. 254. 606. 304. 704. 354. 803. 403. 887. 453. 985. 335. 628. 391. 731. 652. 1373.

1035. 2147. 1250. 2513. 1466. 2879. 1681. 1892. 1365. 1244.

3245. 3606. 2221. 2513.

1123. 2804. 1002. 3095.

Shelterwood 0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1.

6. 11. 16.

21. 25. 30. 37. 44. 51. 1. 1. 1.

3. 5. 8. 16. 25. 34. 43. 33. 45. 57. 69. 81. 93. 105. 120. 136. 151.

148



1

8.

2

13. 18.

3

4 5

6 7 8 9 10

23. 35. 111. 210. 327. 459. 593.

86 1 2. 86 2 3. 86 3 4. 86 4 5. 86 5 9. 86 6 103. 86 7 224. 86 8 368. 86 9 534. 86 10 698. 87 1 140. 87 2 228. 87 3 343. 87 4 486. 87 5 637. 87 6 819. 87 7 1016. 87 8 1212. 87 9 1423. 87 10 1634. 88 1 221. 88 2 351. 88 3 520. 88 4 711. 88 5 920. 88 6 1137. 88 7 1363. 88 8 1590. 88 9 1821. 88 10 2038.


212. 260. 312. 28. 30. 31. 32. 33. 81. 128. 176. 224. 272. 96. 142. 212. 282. 351.

430. 509. 594. 679. 764. 53.

219. 296. 374. 450. 526. 602. 667. 731. 795.

54. 57. 60. 63. 323. 399. 468. 550. 628. 710. 28. 29. 30. 31. 413. 522. 632. 742. 853.

54. 155. 197.

240. 975. 1161. 1253. 1455. 1653. 1856. 29. 40. 43. 47. 1075. 1291. 1497. 1713. 1929.

964. 2145. 96. 98. 106. 115.

250. 1273. 1537. 1802.

204. 2286. 235. 2595. 235. 1817.

337. 2119. 439. 2421. 541. 2723. 53. 53. 468. 1573. 577. 1892.

685. 2210. 793. 2526. 900. 2843. 706.

1805.

689. 2052. 671. 2300. 654. 2547.

Shelterwood 4. 6. 7. 9. 11. 13.

24. 35. 46. 57. 1.

2.

2. 3.

4. 5. 18.

32. 45. 58. 20. 32. 44. 56. 68. 80. 95. 116. 137. 157. 63. 68. 74. 79. 85. 91. 96. 110. 124. 138.

149


Unit Time Clearcut 89 1 225. 89 2 349. 89 3 511. 89 4 697. 89 5 896. 89 6 1100. 89 7 1317. 89 8 1535. 89 9 1750. 89 10 1951. 90 1 160. 90 2 248. 90 3 364. 90 4 496. 90 5 639. 90 6 785. 90 7 941. 90 8 1097. 90 9 1250. 90 10 1394. 91 1 48. 91 2 81. 91 3 128. 91 4 277. 91 91 91 91 91 91

92 92 92 92 92 92 92 92 92

5

6

7 8 9 10 1

2 3

4 5

6 7 8

464. 675. 915. 1156. 1407. 1654. 171. 289. 452. 656. 904. 1168. 1454. 1775.

9 2091.

92 10 2416.


18.

18.

231. 653. 1418. 288. 810. 1703. 346. 966. 1987. 403. 1122. 2272. 461. 1278. 2556. 519. 1010. 1653. 566. 916. 1869. 614. 821. 2085. 662. 726. 2301. 0. 153. 193. 233. 274. 314. 354. 387.

419. 452. 79. 121. 163. 252. 341. 427. 478. 530. 581. 625. 0. 118. 236. 354. 472. 590. 708. 781. 854. 927.

0.

0.

461. 573. 685. 797. 909. 713. 642. 571. 500. 267. 273. 666.

1012. 1216. 1420. 1624. 1828. 1173. 1327. 1481. 1635. 527. 622. 1760.

783. 2071. 900. 2381. 825. 2251. 938. 2467. 1048. 2695. 770. 892. 891. 1139. 1386. 1633. 1880. 2127. 1483. 1341. 1199. 1058.

1880. 2121. 2099. 2525. 2950. 3375. 3800. 4226. 2552. 2912. 3272. 3632.

Shelterwood 83. 83. 83. 82. 82. 82. 82. 91. 100. 110. 57. 55. 53. 51. 48. 46. 44. 49. 54. 59. 0. 3. 5. 12.

20. 27. 49. 72. 94. 117. 0. 11.

23. 34. 45. 57. 68. 83. 97. 112.

150


Unit Time Clearcut 93 93 93 93 93 93 93 93 93 93 94 94 94 94 94 94 94

1

130.

101.

2

233. 393. 602. 860. 1156. 1456. 1793.

216. 330. 444. 558. 672. 786. 865. 830. 907.

422. 667. 911. 1155. 1399. 1643. 1566. 1434. 1188. 1054.

0. 2.

11. 14.

5.

477. 612. 802.

3

4 5

6 7 8

9 2146. 10 2491. 1

16.

2

29. 50. 181. 349. 544. 768. 990. 1222. 1457. 106. 171.

3

4 5

6 7

94 8 94 9 94 10 95 95 95 95 95 95 95 95 95 95

96 96 96 96 96 96 96 96 96


1

2

63. 121. 200. 279. 342. 405. 459. 42. 83. 135. 187.

6 7 8 9 10

257. 358. 472. 592. 716. 844. 977. 1106.

1

5.

9.

2

20. 41. 67. 98. 130. 165. 200. 233. 267.

20. 33. 47. 60. 73. 86. 104.

3

4 5

3

4 5

6 7 8 9

96 10

238. 290. 341. 381. 419. 470.

122. 140.

2216. 2640. 3065. 3490. 3915. 4339. 2650. 3023. 3282. 3654. 29. 49. 1298. 1565. 1957.

980. 2297. 1091. 2470.

1219. 2759. 888. 1810.

1031. 2115. 163. 197.

236. 275. 314. 352. 245. 267. 286. 318. 57. 72. 88. 103. 118. 133. 95. 119. 142. 166.

327. 946. 1124. 1302. 1480. 1658. 1012. 1156. 1297. 1452. 140.

246. 304. 362. 419. 477. 329. 395. 460. 526.

Shelterwood 3. 17.

31. 45. 59. 74. 88. 107. 126. 145. 0.

2. 3. 5. 6. 8.

27. 48. 69. 90. 21. 32. 42. 54. 65. 76. 88. 101. 115. 129. 3. 7. 12. 17.

21. 26. 33. 45. 57. 68.

151


Unit Time Clearcut 97 1 97 2 97 3 97 4 97 5 97 6 97 7 97 8 97 9 97 10 98 1 98 2

128.

215. 334. 512. 726. 956. 1211. 1470. 1738. 1990.


516. 1191. 516. 1428.

211. 333. 456. 578. 608. 639. 670. 698.

684. 2116. 732. 2447. 2777.

68. 137. 206. 274. 343. 389. 420. 450. 480.

781. 319. 367. 415. 296. 349. 658. 851. 1043. 1236. 1429. 1622. 1165. 1054. 942. 836. 428. 518. 613. 704. 795. 761. 550. 499. 444. 394.

4.

6.

9.

129.

8.

219. 338. 492. 676. 882. 1105. 1341. 1581. 1834.

101. 193.

98 3 98 4 98 5 98 6 98 7 98 8 98 9 98 10 99 1 89. 99 2 150. 99 3 233. 99 4 337. 99 5 462. 99 6 599. 99 7 748. 99 8 904. 99 9 1063. 99 10 1225. 100 1 145. 100 2 222. 100 3 328. 100 4 457. 100 5 596. 100 6 745. 100 7 905. 100 8 1073. 100 9 1228. 100 10 1392.

286. 378. 471. 563. 622. 678. 741. 0.

139. 191. 247. 304. 360. 416. 456.

496. 537.

1923. 2040.

2157. 1824. 1948. 1559. 1888. 2217. 2546. 2875. 3204. 1983. 2259. 2533. 2814. 1015. 1227. 1452. 1666. 1881. 1803. 1243. 1380. 1505. 1642.

506. 1105. 639. 1340. 775. 1579. 912. 1817. 1048. 2056. 817. 1328. 741. 1505. 666. 1681. 591. 1857.


20. 27. 34. 48. 62. 75. 89. 5. 19.

33. 47. 61. 75. 88. 105. 121. 138. 0. 6. 12. 18.

24. 29. 36. 43. 50. 58. 62. 65. 69. 72. 75. 78. 81. 92. 103. 113.

152



1

2 3

4 5

6 7 8 9

101 10 102 102 102 102 102 102 102 102 102

1

2 3

4 5

6 7 8 9

102 10 103 103 103 103 103 103 103 103 103

1

2 3

4 5

6 7 8

9

103 10 104 104 104 104 104 104 104 104 104

122. 193.

293. 411. 537. 676. 827. 977. 1135. 1290. 79. 132. 202. 280. 366. 458. 551. 645. 745. 841. 150. 238. 361. 506. 662. 833. 1020. 1205. 1399. 1591.

1

118.

2

248. 413. 619. 844. 1079. 1329. 1583. 1824.

3

4 5

6 7 8 9

104 10 2063.


0.

0.

120. 172.

481. 612. 743. 874.

1078. 1309. 1539. 1770.

1. 1.

1.

224. 276. 328. 1004. 2001. 381. 774. 1274. 417. 698. 1444. 453. 622. 1614. 489. 546. 1785. 1.

29. 71. 113. 155. 197.

239. 275. 311. 347. 0.

674. 6. 820. 12. 966. 18. 1111. 24. 1257. 1. 757. 49. 875. 96. 993. 144. 1111. 0.

0.

594. 1329. 212. 755. 1614. 277. 916. 1898. 341. 1077. 2183. 405. 1239. 2468. 469. 954. 1571. 514. 861. 1781. 559. 767. 1991. 604. 673. 2201. 54. 257. 599. 87. 320. 789. 121. 400. 967. 157. 469. 1110. 190. 915. 2119. 367. 1280. 2765. 545. 1057. 1928. 602. 1076. 2212. 653. 1071. 2445. 709. 1090. 2730. 148.

Shelterwood 54. 53. 51. 50. 49. 48. 47. 52. 58. 63. 6. 12. 17.

23. 28. 34. 39. 47. 54. 62. 66. 65. 63. 62. 60. 59. 57. 64. 71. 77. 2. 12.

23. 33. 44. 55. 77. 99. 121. 144.

153



1

2 3

4 5

6 7 8

9

105 10 106 106 106 106 106 106 106 106 106

16.

2

26. 38. 56. 78. 104. 132. 165. 198. 232. 94. 146. 215. 293. 387. 483. 583. 682. 783. 879. 284. 444. 651. 892. 1149. 1415. 1698. 1984.

3

4 5

6 7 8

9 1

2 3

4 5

6 7 8

9

107 10 108 108 108 108 108 108 108 108 108

242. 324. 415. 520. 625. 734.

1

106 10 107 107 107 107 107 107 107 107 107

50. 79. 115. 172.

1

2 3

4 5

6 7 8

9 2262. 108 10 2528.


215. 245. 274. 303. 332. 393. 414. 477. 69. 81. 90. 99. 108. 117. 126. 146. 166. 186. 0.

91. 116. 142. 167. 192.

217. 243. 268. 293. 120. 376.

455. 534. 613. 689. 765. 824. 884. 943.

148. 159. 168. 178. 188. 198. 166. 202. 199. 237. 70. 70. 73. 76. 79. 82. 72. 84. 96. 109. 0. 306. 297. 288. 279. 270. 261. 252. 243. 234. 191. 963. 1169.

153. 892. 1100. 1308. 1516. 1724. 1242. 1447. 1612. 1818. 71. 303. 369.

436. 502. 568. 412. 478. 544. 610. 0. 680. 748. 815. 883. 950. 1018. 1086. 1153. 1221. 282. 1967. 2336.

1375. 2705. 1581. 3074. 1783. 3440. 1409. 2238. 1283. 2517. 1157. 2796. 1032. 3076.

Shelterwood 10. 17.

24. 31. 38. 47. 55. 67. 78. 89. 4. 7. 10. 13. 16. 18. 21. 25. 28. 32. 0. 4. 8. 12. 17.

21. 25. 29. 33. 36. 100. 104. 107. 110. 114. 117. 121. 136. 150. 165.

154



1

2 3

4 5

6 7 8

9

82. 141.

217. 320. 453. 604. 774. 955. 1142.

109 10 1328. 110 110 110 110 110 110 110 110 110

1

2 3

4 5

6 7 8

9

110 10 111 111 111 111 111 111 111 111 111

1

2 3

4 5

6 7 8 9

111 10 112 112 112 112 112 112 112 112 112

1

2 3

4 5

6 7 8

9

112 10

69. 114. 174.

240. 313. 392. 471. 550. 635. 716. 10. 15.

23. 31. 45. 203. 406. 641. 911. 1178. 110. 175. 257. 356. 543. 764. 1005. 1278. 1540. 1809.


243. 312. 381. 453. 528. 595. 646. 692. 739. 786.

430. 539. 670. 813. 954. 980. 943. 886. 822.

2197. 1782. 1969. 2100. 2212.

6.

6. 6. 11. 16.

6.

30. 66. 101. 137. 172. 208. 238. 268. 300. 185. 198.

204. 210. 216. 293. 370. 448. 355. 438. 99. 191.

225. 259. 335. 410. 486. 558. 630. 701.

1092. 1320. 1605. 1921.

936. 2176.

574. 697. 820. 21. 943. 26. 1066. 7. 645. 47. 744. 87. 843. 129. 944. 185. 185. 221. 260. 223. 270. 225. 281. 814. 1870.

985. 2207. 1155. 2544. 1327. 2881. 1327. 3048. 1504. 3391. 99. 99. 370. 852. 439. 1008.

853. 2093. 1021. 2442. 1189. 2790. 1166. 2476. 1235. 2791. 1305. 3106. 1029. 2493.

Shelterwood 15.

31. 48. 66. 87. 107. 130. 157. 184.

211. 7. 13. 18.

23. 28. 34. 39. 46. 53. 60. 0. 0. 1. 1.

2. 10. 37. 64. 91. 117. 2. 8. 13. 19.

30. 40. 63. 84. 105. 127.

155



1

2 3

4 5

6 7 8

9

113 10 114 114 114 114 114 114 114 114 114

1

2 3

4 5

6 7 8

0. 0. 0. 0. 2. 80. 179.

295. 429. 561. 199. 328. 490. 691. 903. 1146. 1408. 1679.

9 1946. 114 10 2209. 115 115 115 115 115 115 115 115 115

1

2 3

4 5

6 7 8 9

96. 177.

309. 487. 709. 971. 1234. 1525. 1839.

115 10 2141. 116 116 116 116 116 116 116 116 116

1

2 3

4 5

6 7 8

9

116 10

51. 87. 135. 201. 280. 366. 462. 561. 663. 761.

Thinnings First Second Final 128. 131. 133. 136. 139. 177.

216. 255. 158. 201. 122.

210. 296. 382. 469. 551. 643. 704. 765. 826. 0.

128. 131. 133. 136.

435. 523. 611. 699. 651. 744. 763. 942.

128. 131. 133. 136. 937. 1105. 1273. 1441. 1474. 1647. 1585. 1888.

1116. 1290. 1463. 1700.

2180. 2472. 2763. 3231.

1246. 2088. 1173. 2374. 1100. 2661. 1027. 2947. 104.

1839.

314. 2207. 524. 2575. 288. 734. 2944. 385. 944. 3312. 481. 1154. 3680. 96. 192.

577. 1260. 2209. 645. 1145. 2536. 714. 1030. 2863. 782. 914. 3190. 33. 219. 559. 79. 238. 678. 125. 284. 867. 174. 311. 1000. 223. 337. 1133. 270. 177. 833. 284. 202. 793. 298. 201. 843. 313. 174. 824. 326. 174. 876.

Shelterwood 0. 0. 0. 0. 0. 7.

22. 38. 54. 69. 18. 35. 53. 70. 88. 105. 125. 145. 166. 186. 0. 9. 18.

26. 35. 44. 52. 66. 80. 93. 0. 4. 7. 13. 18.

24. 30. 38. 45. 53.

156



1

2 3

4 5

6 7 8

9

117 10 118 118 118 118 118 118 118 118 118

23. 37. 55. 83. 125. 176. 234. 301. 369. 440.

22. 43. 61. 80. 101. 123. 144. 180.

216. 252.

127.

6.

215. 3 332. 4 479. 654. 5 6 847. 7 1055. 8 1274.

100. 194.

1

2

9 1498.

118 10 1726. 119 119 119 119 119 119 119 119 119


1

2 3

4

42. 77. 123. 193.

289. 408. 548. 705. 872. 119 10 1044. 120 1 124. 120 2 209. 120 3 323. 120 4 471. 120 5 648. 120 6 846. 120 7 1061. 120 8 1288. 120 9 1519. 120 10 1764. 5

6 7 8 9

95. 22. 36. 433. 53. 549. 92. 727. 116. 856. 139. 985. 147. 742. 870. 164. 180. 999. 174. 1067. 607. 1432. 742. 1730. 877. 2029.

289. 1012. 2328. 383. 1147. 2627. 477. 1135. 2585. 545. 817. 1738. 589. 739. 1938. 632. 661. 2138. 679. 586. 2341. 23. 23. 770. 89. 167. 1147. 153. 313. 1431. 218. 458. 1714. 281. 603. 1997. 344. 748. 2280. 408. 886. 1691. 476. 826. 1946. 544. 766. 2202. 613. 706. 2457. 6. 634. 1507. 96. 821. 1826. 186. 1008. 2145. 275. 1195. 2465. 365. 1382. 2784. 455. 1569. 3103. 545. 1128. 1921. 601. 1021. 2189. 656. 912. 2456. 716. 808. 2726.

Shelterwood 3. 7. 10. 14. 17.

21. 25. 32. 39. 46. 4. 15. 27. 39. 50. 62. 73. 87. 100. 114. 5. 14.

24. 33. 43. 52. 62. 80. 99. 118. 4. 16.

28. 41. 53. 65. 77. 92. 107. 122.

157



1

2 3

4 5 6

7 8 9

121 10 122 122 122 122 122 122 122 122 122

1

2 3

4 5

6 7 8 9

122 10 123 123 123 123 123 123 123 123 123

1

2 3

4 5

6 7 8 9

123 10 124 124 124 124 124 124 124 124 124

1

2 3

4 5

6 7 8

9

124 10

23. 37. 54. 81. 116. 156. 201. 254. 306. 360. 119. 201. 313. 476. 675. 890. 1129. 1374. 1628. 1869. 11. 18.

27. 40. 57. 76. 98. 124. 150. 176. 181. 295. 441. 622. 814. 1021. 1241. 1463. 1680. 1894.


8. 8.

28. 43. 57. 72. 86.

20. 24.

101. 132. 163. 194. 5. 105.

27. 46. 64. 464. 486.

204. 319. 435. 550. 584. 618. 652. 684. 21. 31. 38. 46. 54. 61. 69. 85. 100. 116. 21. 127.

202. 276. 351. 426. 500. 547. 572. 619.

12. 16.

8.

8.

396. 506. 616. 726. 836. 577. 685. 792. 900. 1174. 1421.

643. 2031. 704. 2353. 764. 2676. 374. 1950. 426. 1962.

454. 2092. 347. 379. 21. 23. 26. 29. 32. 36. 30. 39. 47. 56. 494. 772. 934.

1858. 1993. 28. 204. 257. 310. 363. 416. 297. 350. 403. 457. 1099. 1641. 1918.

1096. 2196. 1258. 2474. 1420. 2752. 1001. 1665. 906. 1889.

790. 2091. 696. 2316.

Shelterwood 3. 6. 8. 11. 13. 16. 18.

22. 26. 30. 0. 7. 14.

21. 28. 35. 48. 61. 75. 89. 2. 4. 6. 8. 9. 11. 13. 16. 19.

21. 19.

26. 32. 39. 46. 53. 59. 69. 78. 88.

158



1

125 125

2

125

4

125 125

5

125 125 125

7

3

6 8

9

125 10 126 126 126 126 126 126 126 126 126

1

2 3

4 5

6 7 8

9

126 10 127 127

127 127 127 127 127 127 127

1

2 3

4 5

6 7 8

9

127 10 128 128 128 128 128 128 128 128

1

2 3

4 5 6

7

79. 123. 182.

247. 326. 407. 492. 575. 660. 741. 36. 67. 121. 194.

284. 394. 502. 622. 752. 877. 86. 144. 224. 327. 451. 590. 741. 901. 1064. 1237. 247. 402. 600. 831. 1103. 1393. 1697.

8 2025. 128 9 2339. 128 10 2648.


Shelterwood

0.

0.

0.

77. 98. 119.

258. 251. 243. 235. 228. 220. 212. 205.

1118. 802. 725. 648. 571.

574. 631. 688. 745. 802. 859. 916. 973. 1030. 752. 903. 1054. 1205. 1355. 1506. 905. 1039. 1174. 1309. 1074. 1302. 1530. 1758. 1986. 2215. 1369. 1561. 1752. 1943.

1.

1.

5.

369. 1338. 457. 1620. 642. 2164.

18.

141. 162. 183.

205. 226. 247. 0.

39. 78. 117. 156. 195. 234.

263. 291. 319. 0.

64. 128. 192.

256. 321. 385. 425. 465. 505. 1.

131. 197.

263. 340. 489. 639. 719. 800. 881.

197. 0.

86. 172.

257. 343. 429. 515. 468. 421. 374. 449. 583. 717. 850. 984.

948. 2933. 1212. 3521. 1002. 990. 978. 869.

2470. 2816. 3163. 3249.

0. 4. 7. 11. 14. 17.

21. 24. 28. 31. 0. 4. 7.

11. 14.

18.

21. 27. 33. 38. 0. 6. 13. 19.

25. 32. 38. 46. 54. 63.

30. 43. 55. 68. 83. 100. 118. 135.

159



1

16.

1.

2

23. 31. 43. 59. 132.

3. 8. 13. 18.

3

4 5

6 7 8 9

129 10 130 130 130 130 130 130 130 130 130

1

2 3

4

223. 329. 450. 570. 296. 465. 687. 952.

1242. 6 1551. 7 1878. 5

8 2201. 9 2526. 130 10 2849. 131 131 131 131 131 131 131 131 131

1

2 3

4 5

6 7 8

9

131 10 132 132 132 132 132 132 132 132 132


1

2 3

4 5

28. 46. 71. 105. 159.

224. 300. 383. 468. 556. 432. 673. 964. 1290. 1659.

6 2012. 7 2398. 8 2764. 9 3130. 132 10 3502.

23. 64. 105. 146. 187. 2.

265. 365. 464. 564. 664. 764. 836. 908. 980. 0.

35. 60. 84. 114. 144. 174.

201. 229. 257. 40. 412. 509. 607. 703.

5.

9.

1.

44. 115. 45. 138. 45. 162. 46. 186. 292. 870. 337. 947. 425. 1132. 514. 1317. 603. 1501. 189. 428. 1019. 2281. 1262. 2733. 1504. 3184. 1747. 3636.

2. 2. 3. 4. 4. 13. 21. 30. 39. 85. 86. 88. 89. 90. 92. 93. 106. 119. 132.

1989. 4088. 1494. 2584.

1349. 2922. 1205. 3261. 1061. 3599. 0. 230. 109. 450. 170. 556. 278. 786. 352. 918. 426. 1050. 452. 824. 434. 940. 416. 1055. 352. 1046. 40. 40.

1161. 2516. 1429. 3020. 1697. 3525. 1964. 4028.

800. 2231. 4531. 896. 980. 1064. 1147.

Shelterwood

1745. 2929. 1582. 3317. 1419. 3704. 1256. 4092.

7. 9. 11. 12. 14. 16. 19.

27. 34. 41. 24. 43. 62 81. 100. 119. 138. 153. 167. 182.

160



231. 2 384. 3 577. 4 818. 5 1073. 6 1347. 7 1638.

134 134 134 134 134 134 134 134 134

1

2

939. 1950.

10.

254. 358. 463. 567. 666. 765. 825. 885. 945.

1150. 2304. 1361. 2657. 1571. 3011. 1782. 3365. 1988. 3714. 1404. 2263. 1284. 2555. 1164. 2847. 1045. 3139.

28. 45. 62. 81.

8.

0.

13. 19.

2.

0. 0. 3. 99. 4. 140. 155. 584. 708. 198. 242. 832. 283. 858. 334. 995. 385. 1132. 286. 866. 239. 812. 352. 1005. 465. 1198. 580. 1393. 695. 1587. 809. 1781. 708. 1187. 653. 1357. 597. 1526. 542. 1696. 11. 11.

1936.

9 2223. 133 10 2506. 3

4 5 6

7 8 9

134 10 135 135 135 135 135 135 135 135 135

1

2 3

4 5

6 7 8

9

135 10 136 136 136 136 136 136 136 136 136

1

2 3

4 5

6

Shelterwood

150.

1

8


27. 73. 133.

204. 284. 367. 453. 73. 125. 194. 279. 383.

498. 627. 764. 906. 1043. 319. 496. 735. 998. 1319. 1647.

7 1988. 8 2326. 9 2671. 136 10 2999.

10. 19.

45. 72. 99. 133. 168.

202. 23. 74. 125. 178.

231. 283. 335. 377. 419. 462. 11.

322. 408. 495. 581. 668. 754. 841. 917. 1004.

100. 119. 138. 158. 177. 0. 3. 6. 8. 11. 14. 22. 33. 44. 55. 7. 17.

26. 36. 46. 56. 65. 79. 92. 105. 1.

1055. 2327.

15.

1024. 2558.

29. 44. 58. 73. 88. 102. 116. 130.

994. 2789. 963. 3019. 933. 3250.

902. 3481. 872. 3712. 831. 3932.

801. 4163.

161



1

147.

2

243. 366. 521. 683. 859.

3

4 5

6

7 1046. 8

1238.

9 1422.

137 10 1604. 138 138 138 138 138 138 138 138 138

1

183.

2

277. 409. 572. 741. 936. 1133. 1341.

3

4 5

6 7 8

9 1536.

138 10 1738. 139 139 139 139 139 139 139 139 139

1

2 3

4 5

125. 193.

289. 405. 523. 659. 796. 941.

6 7 8 9 1073.

139 10 1212. 140 140 140 140 140 140 140 140 140

1

2 3

4 5

6 7 8 9

140 10

83. 128. 190.

267. 349. 438. 533. 634. 726. 823.

Thinnings First Second Final 0. 522. 1191. 66. 659. 1422. 132. 795. 1654. 198. 932. 1885. 264. 1068. 2116. 330. 1205. 2347. 396. 819. 1387. 436. 740. 1581. 476. 661. 1774. 515. 581. 1968. 44. 576. 1219. 115. 764. 1581. 190. 903. 1839.

265. 340. 415. 492. 541. 591. 640. 20. 76. 132. 188.

244. 300. 356. 389. 422. 455. 0. 82. 115. 147. 179.

211. 243. 265. 288. 311.

1042. 2097. 1182. 1335. 901. 828. 756. 684. 425. 537. 646. 756. 867. 976. 679. 618. 557. 497. 0. 307. 388. 470. 551. 632. 489. 440. 392. 343.

2355. 2650. 1612. 1828. 2044. 2260. 914. 1097. 1276. 1455. 1637. 1816. 1095. 1236. 1378. 1519. 0.

675. 819. 963. 1107. 1251. 803. 909. 1015. 1121.


20. 27. 34. 41. 48. 55. 63. 76. 79. 82. 85. 89. 92. 95. 106. 116. 127. 56. 60. 64. 67. 71. 75. 79. 88. 97. 106. 33. 32. 31. 30. 30. 29. 28. 32. 36. 39.

162



27. 38. 51. 65. 81. 97. 113. 130.

3. 10. 16.

44. 56. 68.

22. 28. 35. 41. 45. 49. 54.

1

1.

0.

2

0.

4

2. 3. 4.

81. 93. 105. 77. 71. 65. 59. 0. 0.

5

7.

6 7

57. 123.

8

201. 291. 380.

1

2 3

4 5

6 7 8 9

141 10 142 142 142 142 142 142 142 142 142

3

9

142 10 143 143 143 143 143 143 143 143 143

1

2 3

4 5

6 7 8

9

143 10 144 144 144 144 144 144 144 144 144


1

2 3

4 5

6 7 8

11. 18.

88. 152.

229. 332. 441. 567. 705. 849. 999. 1156. 205. 343. 525. 737. 981. 1237. 1514. 1796.

9 2087. 144 10 2355.

1.

2. 2.

28. 53. 79. 104. 129. 135. 190.

265. 340. 415. 485. 556. 617. 646. 706. 4. 92. 186.

291. 395. 500. 604. 677. 749. 822.

Shelterwood

98.

3.

119. 140. 160. 181.

5. 8. 10. 12. 15. 17.

201. 127. 144. 161. 179.

0. 0.

0. 9. 10. 12.

207. 266. 325. 385. 444. 504. 254. 289. 332. 374. 420. 459. 344. 389. 403. 448. 664.

570. 687. 795. 912. 1028. 1144. 406. 1165. 1465. 1765. 2073. 2370. 1730. 1976. 2190. 2434. 1539.

863. 2033. 1038. 2374. 1223. 2725. 1408. 3077. 1593. 3428. 1088. 2054. 1010. 2352. 932. 2651. 854. 2950.

20. 22. 25. 0. 0. 0. 0. 0. 0. 7. 14.

20. 27. 17.

30. 42. 55. 68. 81. 94. 108. 123. 138. 17.

40. 62. 85. 107. 129. 152. 175. 198. 221.

163



19.


31. 48. 66. 90.

28. 37. 48. 58. 69.

199.

121.

334. 145 8 491. 145 9 668. 145 10 844. 146 1 119. 146 2 190. 146 3 280. 146 4 382. 146 5 501. 146 6 617. 146 7 740. 146 8 869. 146 9 998. 146 10 1119. 147 1 20. 147 2 28. 147 3 36. 147 4 48. 147 5 65. 147 6 85. 147 7 111. 147 8 136.

173.

1

145 145 145

2

145

5

145 145

6 7

147

3

4

9

147 10 148

1

166. 196.

229. 322. 441. 606. 797.

148 148 148

2

148

5

148

6 1003. 7 1205.

148 148

3

4

1415. 148 9 1639. 148 10 1861. 8

224. 275. 325. 37. 71. 118. 165. 213. 260. 307. 351. 395. 439.

28. 30. 33. 36. 396. 500. 596. 709.

Shelterwood

28.

1.

173.

3.

205. 238.

4.

1232. 1461. 1555. 1779.

6.

23. 38.

822. 2002. 935. 2226.

53. 68.

49.

5. 9.

151. 163. 174. 186. 197. 84. 134. 184. 234.

63. 840. 1019. 1198. 1377. 1555. 970. 1120. 1270. 1421.

92. 104.

18.

18.

18.

13.

32. 43. 54. 65. 76. 87. 113. 139. 165. 0. 28. 99. 170. 240. 311. 382. 463.

23. 26. 29. 31. 34.

170.

18.

228. 285. 343. 400. 319. 396. 474. 551.

22. 27. 32. 36. 41. 42. 43. 44.

543. 623.

18.

32. 46. 60.

16.

24. 33. 42. 50. 59. 68. 80.

0.

0.

14.

593. 587. 582. 576.

1602. 1944.

0. 1739. 77. 2038.

22. 31. 39. 48. 56. 65. 78.

153. 2338. 229. 2638.

91. 105.

2287. 2629.

571. 2971.

164



1

134.

2

222. 335. 477. 626. 787. 958. 1134. 1303. 1469.

3

4 5

6 7 8 9

149 10 150 150 150 150 150 150 150 150 150

1

2 3

4 5

6 7 8 9

1.

1.

1.

1.

28. 43. 146.

17.

1.

166. 240. 1290. 1565. 1841. 1950.

282. 443. 626. 813. 164.

2

272. 409. 581. 761. 955. 1161. 1372. 1576. 1776.

4 5

6 7 8 9

iSi 10 152 152 152 152 152 152 152 152 152

1

2 3

4 5

6 7 8 9

152 10

1091. 1303. 1515. 1726. 1938. 2150. 1271. 1448. 1625. 1802.

1.

1

3

478. 61. 604. 121. 729. 181. 854. 242. 979. 302. 1104. 363. 750. 399. 678. 436. 605. 472. 533. 0.

12. 19.

150 10 1010. 151 151 151 151 151 151 151 151 151


113. 187.

282. 401. 527. 662. 806. 954. 1096. 1236.

32. 92. 152. 211. 286. 361. 436. 71. 145.

364. 468. 572. 675. 795. 2251.

915. 2552. 672. 1877. 635. 1358. 785. 1611. 936. 1863.

219. 293. 1086. 2116. 367. 1236. 2368. 438. 1383. 2618. 509. 966. 1580. 551. 880. 1789. 594. 794. 1997. 636. 708. 2206. 0. 403. 918. 51. 508. 1096. 102. 613. 1275. 153. 718. 1453. 204. 824. 1631. 254. 929. 1809. 305. 631. 1069. 336. 570. 1218. 367. 509. 1368. 397. 448. 1517.


25. 31. 37. 44. 51. 57. 0. 5. 10. 16.

21. 26. 44. 68. 92. 116. 6. 17.

29. 40. 52. 63. 74. 86. 98. 110. 0. 5. 10. 16.

21. 26. 31. 37. 43. 48.

165



1

128.

153

2

153

3

153

4

153

5

153

153

6 7

216. 329. 451. 598. 763. 932.

153

8

153

9

153 10 154 154 154 154 154 154 154 154 154

1

2 3

4 5

6 7 8

9

1112. 1296. 1474. 0. 0. 0. 4. 133. 302. 502. 733. 962. 1204.


126. 151.

248. 314. 380. 449. 517. 576. 597. 657.

165.

178.

240.

126. 1119. 1340. 1561. 1914.

263. 2158. 222. 309. 358.

1464. 1668. 1834.

446. 2039.

0.

0.

0. 0. 0. 65.

Shelterwood 12.

22. 32. 42. 52. 67. 83. 104. 124. 144.

0.

0.

0.

0.

0.

0.

0.

0.

540. 694.

1452. 1752.

0.

849. 2053. 1003. 2353. 261. 1158. 2653. 130. 196.

326. 391.

1312.

0. 0. 19.

37. 56. 75.

927.

2953. 1801.

155

1

1.

0.

0.

0.

0.

155

2

0.

10.

0.

3

2. 3.

1.

155

1.

0.

12.

0.

155

4

5.

2.

0.

14.

0.

155 155

5

7.

2.

143.

43.

20. 38. 56. 74.

184.

400. 481. 553. 634. 715. 796. 55. 602. 727. 852. 977. 1102. 695. 790. 885. 980.

0.

6 7

154 10

155 155 155

8

9

155 10 156 156 156 156 156 156

156 156 156

1

2 3

4 5

6 7 8 9

156 10

89. 143.

206. 268. 73. 113. 169.

237. 309. 388. 472. 558. 642. 727.

91. 5.

63. 93. 123. 153. 182. 212. 234. 256. 278.

224. 265. 307. 348. 26. 225. 283. 341. 399. 456. 348. 322. 296. 270.

1.

5.

10. 14.

19.

22. 23. 24. 25. 26. 27. 28. 32. 36. 40.

166



5

23. 38. 58. 82. 112. 151. 196. 241. 293. 347. 26. 44. 68. 94. 124.

6 7

154. 185.

8

2

217. 249. 280. 67. 115.

3

172.

1

2 3

4 5

6

7 8

9

157 10 158

158 158 158 158

158 158 158 158

1

2 3

4

9

158 10 159 159 159 159 159 159 159 159

1

4

245. 5 321. 6 407. 7 498. 8 592. 159 9 687. 159 10 784. 160 1 195. 160 2 305. 160 3 449. 160 4 603. 160 5 773. 160 6 942. 160 7 1111. 160 8 1288. 160 9 1453. 160 10 1621.


226. 268. 310. 19.

31. 44. 56. 69. 81.

93. 102. 110. 119. 129. 165. 208. 252. 295. 334. 374.

404. 402. 432. 26. 131. 190. 249. 307.

366. 425. 470. 496. 541.

89.

329. 96. 417. 102. 505. 108. 593. 114. 681. 121. 769. 103. 593. 121. 728. 138. 864. 156. 999. 60. 111. 71. 230. 84. 271. 97. 312. 110. 352. 122. 392. 89. 245. 91. 278. 92. 310. 94. 343. 257. 421. 295. 783. 336. 942. 377. 1100. 417. 1259. 454. 1413. 347. 990. 354. 1117. 328. 1211. 334. 1338. 26. 26. 188. 1100. 231. 1317. 274. 1535. 316. 1753. 359. 1970. 253. 1219. 286. 1387. 301. 1536. 334. 1705.

Shelterwood 2. 10.

19.

28. 37. 46. 55. 72. 89. 106. 2. 5. 7. 10.

12. 15. 17.

20. 23. 26. 12.

22. 32. 42. 52. 62. 72. 83. 94. 105. 19.

28. 38. 47. 57. 66. 76. 89. 102. 115.

167



1

2 3

4 5

6 7 8 9

161 10 162 162 162 162 162 162 162 162 162

1

2 3

4 5

6 7 8 9

162 10 163 163 163 163 163 163 163 163 163

1

2 3

4 5

6 7 8 9

163 10 164 164 164 164 164 164 164 164 164

1

2 3

4 5

6 7 8 9

164 10

104. 175.

266. 366. 483. 601. 720. 844. 969. 1090. 114. 189.


236. 285. 334. 382. 423. 432. 473. 1.

52. 103. 155.

285. 406. 532. 669. 815. 964. 1108. 1249.

206. 258. 309. 340. 371. 402.

110. 175.

0. 18.

257. 362. 484. 615. 763. 908. 1062. 1218. 207. 290. 394. 539. 706. 897. 1089. 1289. 1504. 1717.

76. 133. 191. 248. 305. 357. 409. 461. 35. 58. 117. 177. 237. 303. 368. 443. 518. 593.

116. 121. 133. 146. 158. 170. 128. 181.

202. 255. 407. 514. 620. 726. 833. 939. 638. 577. 515. 453. 0.

268. 276. 284. 291. 299. 31. 86. 141. 196. 35. 544. 538. 532. 573. 580. 101. 181. 260. 340.

138. 876. 1043. 1209. 1376. 1542. 976. 1111. 1216. 1352. 928. 1108. 1288. 1468. 1648. 1828. 1081. 1232. 1382. 1533. 0. 1045. 1282. 1520. 1757. 1995. 1206. 1401. 1595. 1789. 35. 1412. 1706. 1999.

2417. 2736. 1701. 1985. 2269.

2553.

Shelterwood 11.

21. 30. 40. 49. 59. 68. 81. 93. 105. 0. 5. 11. 16.

21. 27. 32. 38. 43. 49. 12.

20. 28. 36. 44. 51. 59. 70. 81. 92.

22. 32. 42. 52. 62. 72. 83. 98. 114. 129.

168

Table 7: Yields for Even-Aged Prescriptions in Mbf per Unit: (Continued) Unit Time Clearcut 165 165 165 165 165 165 165 165 165

1

138.

0.

2

229. 345. 492. 645. 811. 987. 1168.

62. 125. 187.

3

4 5

6 7 8 9 1342.

165 10 1514. 166 166 166 166 166 166 166 166 166

1

2 3

4 5

6 7 8

9

166 10 167 167 167 167 167 167 167 167 167

1

2 3

4 5

6 7 8

9

102. 169.

255. 362. 476. 598. 728. 861. 990. 1116. 190.

315. 474. 674. 883. 1110. 1350. 1597. 1834.

167 10 2068. 168 168 168 168 168 168 168 168 168


1

16.

2

26. 40. 55. 75.

3

4 5

6

9

100. 128. 156. 189.

168 10

224.

7 8

249. 312. 374. 412. 449. 487. 0. 46. 92. 138. 184. 230. 276. 303. 331. 359. 35. 121. 206.

493. 622. 751. 880. 1009. 1137. 773. 698. 624. 549. 364. 459. 554. 649. 744. 839. 570. 515. 460. 405. 702. 877. 1053.

1124. 1343. 1561. 1779. 1997. 2216. 1310. 1492. 1675. 1857. 829. 990. 1151. 1312. 1473. 1633. 965. 1100. 1235. 1369. 1555. 1852. 2148.

292. 1228. 2445. 377. 1404. 2741. 462. 1578. 3036. 546. 1085. 1811. 596. 984. 2057. 647. 883. 2304. 697. 782. 2551. 66. 76. 222. 79. 80. 277. 92. 85. 332. 105. 89. 387. 119. 93. 442. 130. 96. 495. 142. 88. 392. 168. 99. 475. 193. 110. 558. 219. 122. 642.


26. 32. 38. 45. 52. 59. 0. 5. 9. 14. 19.

24. 28. 33. 38. 44. 3. 14.

24. 35. 46. 56. 67. 78. 90. 101. 4. 11. 18.

26. 33. 40. 48. 60. 72. 85.

169



1

2 3

4 5

6 7 8

9

169 10 170 170 170 170 170 170 170 170 170

1

2

50. 83. 124. 177. 232. 292. 356.

421. 484. 546. 103. 180.

378. 4 617. 5 898. 6 1206. 7 1518. 8 1843. 3

9 2174. 170 10 2476. 171 171 171 171 171 171 171 171 171

1

1.

2

1.

3

1.

4

7.

5

163.

6 7 8

368. 609. 890.

9

1167.

171 10 1460. 172 172 172 172 172 172 172 172 172


178.

23. 45. 67. 90. 112. 135. 148. 162. 175.

224. 271. 317. 363. 410. 279. 252. 225. 198.

405. 484. 562. 641. 720. 798. 472. 538. 603. 669.

0.

0.

0.

57. 155. 252. 351. 451. 550. 640. 722. 804.

538. 696. 866. 1028. 1190. 1257.

2353. 2795. 3212. 3629. 3347.

5. 6. 6. 7.

5. 5.

9

21. 11. 16.

21. 27. 32. 37. 63. 91. 119. 147. 0. 0. 1.

0.

172 10

19.

1.

106. 169.

8

7. 9. 12. 14. 16.

16.

134.

6 7

5. 13.

5.

1768.

256. 409. 586. 789. 985. 1200. 1409. 1611. 1816.

5

1292. 3307.

2.

655. 86. 841. 165. 1027. 244. 1213. 324. 1400. 404. 1587. 484. 1124.

2 4

969. 2544. 1137. 2941.

0.

5.

1

3

1942.

Shelterwood

2132. 2497. 2855. 3221. 3587. 2204.

0. 0. 527. 1358. 666. 1660. 805. 1963.

232. 295. 944. 2265. 358. 1082. 2568. 421. 794. 1621. 472. 813. 1869. 523. 832. 2119. 575. 851. 2369.

1.

2.

25. 48. 71. 94. 2. 9. 15.

22. 28. 35. 51. 65. 79. 93.

170



1

2 3

4 5

6 7 8

9

173 10 174 174 174 174 174 174 174 174 174

1

2 3

4 5

6

7 8

9

8. 13.

7. 16.

20. 54. 99.

24. 46. 68. 90.

154.

219. 283. 353. 425. 23. 118. 291. 502. 750. 1009. 1278. 1554. 1816.

174 10 2071. 175 175 175 175 175 175 175 175 175

1

2 3

4 5

6 7 8 9

91. 153.

236. 326. 439. 553. 670. 801. 919.

175 10 1041. 176 176 176 176 176 176 176 176 176

1

2 3

4 5

6 7 8 9

176 10


36. 61. 92. 135. 186.

243. 305. 374. 448. 520.

7.

112. 151.

Shelterwood 1.

207.

7. 117. 149. 180. 212. 243. 284. 216. 261.

0. 8.

0.

0.

1.

622.

1667.

3. 4. 5. 7. 8.

111. 144. 176.

484. 584. 684. 784. 779. 902. 731. 858.

27. 39. 51. 63.

806. 2054. 991. 2440. 260. 1175. 2827. 92. 176.

344. 1359. 429. 1140. 497. 1102. 561. 1283. 626. 1464. 0. 38. 77. 115. 161. 206.

251. 289. 327. 365. 53. 82. 105. 128. 151. 175. 199. 237. 275. 313.

0. 0. 8.

71. 94. 117. 103. 165.

227. 234. 53. 226. 218. 209. 201. 193. 40. 71. 102. 132.

4.

3214. 2512. 2294. 2653. 3013. 0.

615. 745. 1024. 1185. 1346. 931. 1067. 1202. 1189. 65. 525. 651. 778. 904. 1032. 719. 838. 956. 1074.

8. 12. 15. 19.

37. 66. 94. 123. 7. 13. 19.

24. 30. 36. 44. 54. 64. 75. 10. 19.

28. 37. 46. 55. 63. 76. 88. 100.

171



1

130.

0.

2

216. 326. 455. 606. 771. 938. 1117. 1303. 1479.

63. 138. 213. 288. 362.

249. 2056. 287. 2341.

437. 501. 565. 629.

225. 1767. 279. 2005. 335. 2247.

3

4 5

6 7 8

9

177 10 178

178 178 178 178 178 178 178 178

1

14.

2

22. 33. 48. 67. 92.

3

4 5

6 7 8

118. 148.

9

180.

178 10

211. 163. 273. 412. 579. 762. 950. 1160. 1366. 1569.

179 179 179 179

1

2 3

4

179

5

179 179 179 179

6 7 8

9

179 10 1774. 180 180 180 180 180 180 180 180 180


1

71.

2

102. 140. 192.

3

4 5

6 7 8

9

180 10

254. 320. 385. 454. 528. 601.

0. 13. 26. 40. 54. 68. 82. 97. 113. 129.

2. 136. 195. 254. 312. 371. 430. 479. 528. 577. 37. 48. 70. 91. 112. 134. 156. 183. 210. 237.

106. 134. 173.

211.

170.

242. 1198. 1486. 1771.

1525.

Shelterwood 10.

20. 30. 39. 49. 59. 68. 82. 95..

0.

15.

108. 3.

0.

195.

5.

8.

272. 338. 403. 469. 356. 420. 468. 531.

7.

12. 16.

20. 12.

29. 41. 59. 2.

2. 1158. 1437.

441. 581. 721. 1715. 862. 1993. 1002. 2271. 833. 1535. 760. 1750. 690. 1972. 620. 2194. 37. 224.

220. 215. 211. 207. 27. 52. 77.

102.

10. 12. 14. 17.

21. 24. 28. 1.

9.

17.

25. 33. 41. 49. 57. 65. 73.

37.

10.

542. 653. 764. 875. 987. 605. 704. 803. 901.

15.

20. 26. 31. 36. 41. 49. 56. 63.

172



1

13.

2

20. 31. 44. 98.

3

4 5

6 7 8

9

181 10 182 182 182 182 182 182 182 182 182

1

2

183 183 183 183 183 183 183

0. 0. 1.

4

32. 72. 120. 175. 229. 286. 345.

5

6 7 8 9 1

2 3

4 5

6 7 8

9

183 10 184 184 184 184 184 184 184 184 184

251. 344. 441. 543.

3

182 10 183 183

169.

1

2 3

4 5

6 7 8 9

184 10

10. 18.

31. 109. 210. 330. 466. 603. 749. 896. 48. 80. 124. 174.

330. 518. 731. 974. 1212. 1461.

Thinnings First Second Final 0. 13. 27. 42. 74. 107. 139. 190.

0. 0. 3.

155.

240. 291.

201. 246. 279. 339. 399. 308.

0. 0. 0. 16.

0. 0. 128. 164.

32. 47. 63. 78. 94. 107.

201. 237. 274. 310. 219. 260.

12.

12.

23. 34. 77. 119.

27. 297. 385. 473. 560. 646. 719. 536. 617.

161.

204. 246. 289. 327. 0.

0. 0. 5.

Shelterwood

0.

0.

181.

5. 11.

255. 733. 891. 1049. 1039. 1225. 1411. 1194. 0. 2.

346. 418. 490. 562. 631. 703. 431. 507. 130. 198.

925. 1108. 1290. 1473. 1502. 1685. 1180. 1371. 0.

22. 354. 46. 440. 69. 436. 1676. 144. 563. 2000. 218. 689. 2324. 293. 794. 2316. 370. 944. 2637. 447. 1093. 2957. 524. 816. 2129.

16.

22. 27. 43. 60. 76. 92. 0. 0. 0. 0. 0. 0. 5.

10. 15.

20. 1.

3. 4. 8.

12. 16.

30. 45. 60. 75. 3. 8. 12. 17.

22. 26. 47. 70. 92. 114.

173


Unit Time Clearcut

5

48. 91. 154. 249. 376. 533. 694. 873. 1067. 1258. 26. 38. 53. 70. 90.

6 7 8 9

113. 137. 163. 189.

186 10

220.

187 187 187 187 187 187 187 187 187

158.

185 185 185 185 185 185 185 185 185

1

2 3

4 5

6 7 8 9

185 10 186 186 186 186 186 186 186 186 186

1

2 3

4

1

2 3

4 5

6 7 8 9

187 10 188 188 188 188 188 188 188 188 188

222. 303. 415. 545. 685. 823. 967. 1120. 1272.

1

132.

2

222. 342. 472. 616. 757. 898. 1053. 1190. 1332.

3

4 5

6 7 8 9

188 10


200. 260. 321. 381. 435. 489. 542. 25. 44. 58. 72. 86. 101. 115. 128. 141. 154. 43. 62. 109. 155. 201. 248. 294. 349.

404. 459. 0. 55. 111. 167.

223. 280. 336. 381. 426. 472.

18. 893. 206. 1289. 315. 1539. 423. 1788. 532. 2038. 641. 2287. 686. 1474. 639. 1698. 591. 1922. 545. 2146. 25. 25. 40. 196. 42. 254. 312. 43. 45. 371. 47. 430. 19. 336. 384. 38. 56. 432. 480. 75. 43. 43. 1114. 439. 433. 1345. 427. 1575. 420. 1806. 415. 2037. 33. 1216. 85. 1420. 136. 1624. 188. 1827. 0. 0. 0. 891. 11. 1080. 23. 1272. 34. 1461. 46. 1651. 2. 1005. 70. 1157. 137. 1310. 203. 1460.

Shelterwood 4. 13.

21. 29. 37. 46. 54. 68. 81. 95. 7. 9. 12. 14. 17. 19.

22. 25. 28. 31. 18.

27. 35. 44. 53. 62. 70. 82. 95. 107. 10. 18.

27. 35. 44. 53. 61. 73. 85. 97.

174



1

2 3

4 5

6 7 8 9

189 10 190 190 190 190 190 190 190 190 190

84. 134. 233. 359. 501. 658. 813. 975. 1138. 1299. 104. 159.


19.

19.

41. 97.

197.

970. 1194. 1418. 1642. 1866. 1603. 1362.

152.

208. 263. 317. 370. 419. 468.

253. 308. 363. 418. 445. 363. 450. 1569. 537. 1775.

0.

0.

0.

190 10 1133.

94. 146. 199. 251. 303. 355. 418. 480. 542.

269. 354. 439. 524. 609. 489. 461. 437. 414.

861. 1100. 1340. 1579. 1819. 1306. 1520. 1749. 1977.

45. 76.

0. 17.

0.

115. 158.

45. 73.

211. 267. 324. 383. 453. 517. 43. 72.

101. 128. 156. 182.

0. 0. 4. 8. 11. 15.

191 191 191 191 191 191 191 191 191

1

2 3

4 5

6 7 8 9 1

2 3

4 5

6 7 8

9

191 10 192 192 192 192 192 192 192 192 192

1

2 3

4 5

6 7 8 9

192 10

239. 334. 444. 568. 700. 841. 989.

107. 148. 198.

250. 303. 358. 423. 482.

207. 233. 0. 16.

42. 68. 94. 120. 146. 170. 194. 218.

2. 33. 64. 95. 0. 0. 3. 6. 10. 13. 0.

29. 58. 88.

368. 467. 565. 662. 760. 507. 589. 669. 751. 0.

345. 436. 527. 618. 710. 472. 549. 625. 701.


21. 26. 30. 42. 57. 71. 85. 30. 36. 43. 49. 56. 62. 75. 94. 112. 131. 4. 7. 10. 13. 16. 19.

22. 26. 31. 35. 3. 6. 9. 12. 15. 18.

21. 25. 29. 33.

175



1

2

4.

3

10.

4

141.

5

1

313. 516. 751. 984. 1230. 1478. 86.

2

145.

3

218. 302. 421. 550. 685. 829. 990. 1142.

6 7 8 9

193 10 194 194 194 194 194 194 194 194 194

4 5

6 7 8

9

194 10 195 195 195 195 195 195 195 195 195

2.

1

2 3

124. 193. 399.

4

662. 5 961. 6 1300. 7 1643. 8 2008.

9 2379. 195 10 2718. 196 196 196 196 196 196 196 196 196

1

2 3

4 5

6 7 8

9

196 10

71. 100. 137. 179. 226. 281. 336. 399. 459. 533.


Shelterwood

0. 0.

0. 18.

0. 0.

542. 697. 852. 203. 1007. 269. 1162. 336. 1318. 403. 933. 459. 1108.

1480. 1786.

1.

2092. 2398. 2687. 2992. 1840. 2163. 20. 709. 892. 1269. 1492.

1.

1.

2. 69. 136.

0.

8.

34. 85.

36. 49.

136. 195.

133. 166. 198. 173.

254. 313. 369. 424. 480.

1715. 1267. 247. 1461. 322. 1655. 324. 1654.

12.

15.

19.

125.

885. 1143. 1401. 1659. 1916. 1896.

2197. 2676. 3157. 3636. 4115. 3817.

232. 339. 446. 553. 660. 751. 1482. 2938. 827. 1560. 3364. 908. 1642. 3791. 54. 54. 54. 106. 55. 453. 146. 66. 601. 187. 76. 749. 227. 87. 897. 266. 96. 1044. 305. 54. 844. 337. 104. 962. 369. 154. 1079. 401. 205. 1197.

1. 1.

22. 44. 65. 86. 6. 12. 18.

23. 29. 34. 43. 53. 64. 74. 43. 44. 44. 45. 45. 46. 68. 97. 126. 156. 19. 24. 30. 35. 40.

45. 50. 56. 62. 69.

176



1

2 3

4 5

6 7 8 9

197 10 198 198 198 198 198 198 198 198 198

1

2 3

4 5

6 7 8

9

198 10 199 199 199 199 199 199 199 199 199

1

2 3

4 5

6 7 8

9

199 10 200 200 200 200 200 200 200 200 200

1

2 3

4 5

6 7 8

9

200 10

64. 90. 125. 165.

209. 262. 314. 375. 432. 505. 103. 147. 203. 279. 366.

458. 551. 646. 747. 847. 42. 72. 122. 182. 257. 339. 422. 509. 605. 693. 83. 118. 165. 219. 279. 349.

421. 502. 580. 677.


52. 93. 133. 173. 214. 254. 286. 318. 350. 36. 56. 86. 117. 147. 178. 208. 242. 266. 300. 17.

34. 68. 102. 136. 171. 206. 239. 262. 293. 11.

79. 131. 184. 237. 290. 343. 385. 418. 460.

0. 0. 10. 21. 31.

0.


239. 279.

401. 550. 699. 848. 997. 797. 915. 1034. 1152. 36. 715. 863. 1010. 1158. 1305. 794. 922. 1041. 1169. 42. 525. 648. 795. 923. 1051. 863. 807. 914. 1007.

11.

11.

15.

44. 555. 55. 751. 67. 947. 79. 1144. 90. 1341. 17. 1061. 83. 1218. 140. 1364. 206. 1520.

20. 25. 30. 35. 40. 45. 51. 58. 64.

42. 0. 51. 102. 152. 36.

291. 300. 310. 320. 329. 104. 126. 139. 160. 27. 95. 121. 155. 183.

212. 216. 199.

21. 24. 26. 30. 33. 37. 14.

20. 26. 32. 39. 45. 51. 59. 67. 75. 5. 10. 14. 18.

23. 27. 35. 43. 51. 60.

177



1

2 3

4 5

6 7 8

9

201 10 .202 202 202 202 202 202 202 202 202

1

2 3

4 5

6 7 8

39. 60. 85. 119. 153. 191. 238. 286. 334. 388. 248. 408. 629. 895. 1207. 1521. 1866. 2226.

9 2589. 202 10 2922. 203 203 203 203 203 203 203 203 203

1

2

67. 141.

246. 371. 5 641. 6 952. 7 1304. 8 1691. 3

4

9 2072.

203 10 2461. 204 204 204 204 204 204 204 204 204

1

148.

2

271. 451. 656. 894.

3

4 5

1132. 1391. 1657. 9 1919. 6 7 8

204 10 2171.


Shelterwood

2.

6.

12.

7.

35. 61. 88. 115. 142. 170. 191. 212. 234.

119. 116. 115. 115. 114. 15. 50. 83. 117. 2.

361. 471. 583. 694. 805. 592. 681. 767. 856.

10. 14. 17.

21. 25. 29. 33. 38. 42.

2.

17.

833. 1097. 1360. 1623. 1886.

2016. 2507. 2998. 3489. 3980.

27. 37. 47. 58.

2.

234. 340. 446. 552. 658. 764. 845. 927. 1008. 6.

80. 126. 173.

286. 398. 511. 614. 718. 821. 46. 197.

274. 355. 437. 518. 600. 662. 671. 733.

1558. 2720. 1406. 3065. 1266. 3440.

1125. 3816. 337. 960. 1165. 2829. 3337. 3845. 3527. 4010. 4493. 3519. 117. 237. 660. 1545. 851. 1897. 130.

379. 483. 1129. 1389. 1649. 1628. 1789. 1950. 1570.

1047. 2254. 2611. 2968. 2007. 2299. 997. 2535. 930. 2826.

1243. 1438. 1183. 1117.

.68.

79. 94. 108. 123. 2. 9. 15.

22. 28. 35. 66. 96. 127. 157. 4..

21. 38. 55. 72. 89. 110. 127. 145. 163.

178



1

2 3

4 5

6 7 8

9

205 10 206 206 206 206 206 206 206 206 206

1

2 3

4 5

6 7 8

9

206 10 207 207 207 207 207 207 207 207 207

1

2 3 4 5

6 7 8

56. 98. 159.

240. 439. 678. 952. 1257. 1566. 1879. 97. 172. 282. 423. 594. 779. 982. 1195. 1419. 1631. 200. 337. 512. 723. 981. 1244. 1539. 1821.

9 2108. 207 10 2400. 208 208 208 208 208 208 208 208 208

1

2 3

4 5

6 7 8 9

208 10

60. 91. 128. 181. 233. 289. 363. 436. 511. 593.


Shelterwood

242. 329. 409.

592. 773. 917.

3. 9. 14.

940. 2273. 1150. 2668. 1359. 3063.

20. 26. 32. 54. 76. 98. 120.

14.

55. 95. 135. 230. 324. 419. 503. 583. 666. 13.

87. 160.

1332. 2834. 1421. 3208. 1507. 3579.

1145. 2740. 475. 1181. 629. 1445. 783. 1710.

234. 952. 2016. 310. 1111. 2289. 385. 1269. 2563. 461. 967. 1669. 515. 889. 1905. 569. 811. 2141. 622. 718. 2335. 0.

0.

98. 186.

253. 340. 481. 584. 686. 578. 610. 643. 620. 22. 244. 236. 231. 226. 221. 45. 96.

274. 368. 463. 558. 641. 725. 809. 22. 74. 114. 156. 198. 241. 283. 316. 348. 381.

0. 1478. 1848.

2367. 2769. 3170. 2191. 2522. 2853. 3035. 23. 589. 758. 931. 1104. 1276. 935. 1069. 147. 1203. 197. 1338.

3. 13.

22. 32. 41. 51. 61. 72. 84. 95. 7. 18.

29. 40. 51. 62. 75. 92. 110. 127. 11. 18.

25. 32. 39. 45. 52. 60. 68. 76.

179



1

2 3

4 5

6 7 8

9

49. 134.

23. 94.

251. 388. 584. 791. 1019. 1259. 1489.

145.

209 10 1721. 210 210 210 210 210 210 210 210 210

1

180.

2

320. 3 526. 4 789. 5 1102. 6 1440.

7 1812. 8

2199.

9 2609. 210 10 2994. 211 211 211 211 211 211 211 211 211

199.

272. 343. 415. 477. 539. 601.

252. 464. 581. 860. 1025. 1189. 1021.

1202. 1132. 885. 1174. 1464. 1753.

2589. 2455. 10. 2224. 147. 2722. 284. 3221. 421. 3720. 558. 2043. 4219. 695. 2332. 4718. 833. 1747. 3004. 927. 1587. 3432. 1022. 1426. 3859. 1116. 1266. 4287. 106. 134. 168.

268. 343. 426. 509. 595. 681. 773.

203. 238. 273. 308. 339. 370. 403.

1

15.

2

27. 44. 70. 202. 368. 563. 785. 1007. 1237.

0. 12.

237. 74. 98.

23. 35. 99. 164. 229. 290. 351. 413.

588. 739. 890. 966. 1079. 1192. 863.

2 3

4 5 6

7 8

9

3

4 5 6 7 8

9

212 10

636. 1125. 1345. 1998. 2309. 2618. 1996.

1111. 2293.

90. 137. 195.

1

211 10 212 212 212 212 212 212 212 212 212


106. 176. 176. 177. 178.

178. 114. 154. 194.

123.

Shelterwood 4. 11.

18.

25. 32. 40. 63. 86. 109. 132. 2. 17.

32. 47. 62. 77. 92. 109. 127. 144.

107.

16.

629. 770. 911. 1053. 1195. 841. 957. 1072. 1190.

22. 29. 36. 43. 50. 57. 66. 75. 84.

187.

0.

230. 272. 1502. 1790. 2077. 2177. 2459. 2740. 1835.

1.

2. 3. 5. 6.

22. 39. 55. 72.

180



1

1.

0.

2

2.

1.

3

4

2. 3.

2. 3.

5

4.

6

6.

3. 4.

0. 5. 4. 4. 4. 4.

7

7.

5.

8

8.

9

10. 11.

6. 6.

213 10 214 214 214 214 214 214 214 214 214


7. 11.

0.

18.

1.

1.

21. 24. 26. 125. 699. 865. 1031. 1197. 1363. 882. 1025. 1169. 1312.

1.

2. 3.

56. 73. 92.

121. 165.

111. 131.

214 10

438. 536. 646. 752. 867.

208. 250. 293. 336. 378.

215 215 215 215 215 215 215 215 215

33. 53. 82. 116. 158. 207. 256. 309. 362.

12.

149. 109. 140. 170. 201. 12. 90. 90. 91. 91. 90. 21. 52. 83. 114. 0. 122. 118. 114.

4 5

6 7 8

9 1

2 3

4 5

6 7 8

9

215 10 216 216 216 216 216 216 216 216 216

1

2 3

4 5

6 7 8

9

216 10

424. 22. 35. 55. 79. 110. 149. 186. 228. 271. 321.

31. 59. 88. 116. 143. 171. 197. 223. 249. 0.

21. 46. 71. 96. 122. 147. 169. 191. 212.

18.

1.

34. 78.

3

15.

0. 0. 0. 0.

22. 25.

69. 114. 175. 252. 340.

1

2

0. 12.

Shelterwood

110. 106. 0. 29. 59. 88.

1.

1.

1.

7. 14.

21. 28. 35. 42. 49. 60. 71. 82.

12.

7.

395. 509. 623. 737. 850. 599. 693. 787. 881.

11.

0.

341. 452. 563. 674. 785. 576. 665. 754. 842.

16.

21. 26. 31. 36.

43. 49. 56. 5. 9.

14. 18.

23. 27. 31. 36. 41. 46.

181



1

2 3

4 5

6 7 8

9

217 10 218 218 218 218 218 218

114. 157.

203. 255. 304. 354. 406. 460.

Shelterwood

13.

13.

13.

26. 46. 67. 87. 107. 127. 146. 164. 183.

38. 39. 40. 42. 43.

318. 400. 482. 564. 646. 436. 504. 572. 640.

21. 25. 29. 34. 39. 44.

16.

39. 61. 84.

7. 10. 14. 18.

1

14.

1.

1.

1.

6.

2

22. 34. 47. 64. 85.

13.

67. 65. 63. 62. 60.

179.

9. 12. 16. 19.

3

4 5

6

21W 7 218 218

51. 79.


8

9

218 10

106. 128. 151. 179.

27. 40. 54. 68. 82. 94. 106. 118.

5.

21. 37. 53.

238. 296. 355. 414. 306. 353. 400. 447.

22. 26. 29. 33. 37.

182

Table 8: Yields for Uneven-Aged Prescriptions in Mbf per Unit:

Unit Time

Individual Tree Selection First Second Third Fourth 0. 0. 0.

1. 1.

3

0. 0. 0.

1.

1.

1

4

1.

2.

1

5

2.

3.

1

6 7

4.

4.

3. 4. 5.

1 1

8

1

9 10

5. 6. 7. 9.

5. 7. 8. 9.

34. 58. 90. 125. 163. 203. 244.

163.

2. 3. 5. 6. 7. 8. 9. 328. 372.

1

1

1

2

1

1

2 2 2 2 2 2 2 2 2 2

9 10

286. 328. 372.

3

1

12.

3

2

3

3

3

4

3

5

3

3

6 7 8 9

3

10

22. 33. 50. 67. 89. 112. 137. 164. 193. 70. 107. 159.

3 3

4 4 4 4 4 4 4 4

4 4

1

2 3

4 5

6 7 8

1

2 3

4 5

6 7 8

9 10

223. 292. 366. 446. 530. 607. 688.

203. 244. 286. 328. 372. 411. 452. 491. 530. 65. 86. 110. 135. 162. 191.

218. 248. 278. 310. 292. 366. 446. 530. 607. 688. 770. 855. 929. 1003.

411. 452. 491. 530. 571. 611. 646. 684. 160. 188.

216. 246. 276. 308. 339. 367. 397. 427. 607. 688. 770. 855. 929. 1003. 1073. 1147. 1210. 1271.

1. 1.

6.

7. 9. 10.

819. 902. 982. 1062. 1137. 1214. 1291. 1368. 1432. 1507. 275. 307. 338. 367. 397. 426. 457. 484. 517. 540. 930. 1004. 1074. 1148. 1211. 1273. 1337. 1392. 1448. 1501.

Group Selection First Second Third Fourth 0. 0. 0.

0. 0. 3.

1.

4.

3. 4. 5. 6. 7. 9.

87. 105. 123. 141. 159. 177. 195.

213. 231. 249. 32. 48. 63. 80. 97. 114. 130. 147. 164. 180. 157. 237. 317. 397. 477. 557. 637. 717. 797. 877.

0. 0. 7.

6. 7. 9. 10. 12. 13.

0. 0. 5. 7. 9. 10. 12. 14. 15. 17.

10. 11. 13. 15. 16. 18.

219. 228. 238. 247. 256. 265. 274. 283. 292. 301.

297. 300. 303. 306. 309. 312. 315. 318. 321. 324.

394. 397. 399. 402. 404. 407. 409. 412. 415. 417.

113. 124. 136. 148. 160. 172. 184. 195.

177. 168. 162. 153. 145. 136. 128. 119. 111. 102.

121. 114. 112. 106. 101. 95. 89.

207. 219. 449. 507. 565. 623. 680. 738. 796. 854. 912. 970.

673. 706. 738. 771. 804. 836. 869. 902. 934. 967.

8.

83. 78. 72. 700. 712. 724. 736. 748. 760. 772. 784. 796. 808.

183

Table 8: Yields for Uneven-Aged Prescriptions in Mbf per Unit: (Continued)

Unit Time 5

1

5

2

5

3

5

4

5

5

5

5 5

6 7 8 9 10

6

1

6 6 6 6 6 6 6 6 6 7 7 7 7 7

2

5 5

3

4 5

6

Individual Tree Selection First Second Third Fourth 8. 13.

20. 37. 55. 77. 102. 127. 154. 183. 14. 22. 34. 66. 105. 149.

.199. 8 249. 9 299. 7

10 1

2

351. 2.

4

3. 5. 7.

5

29..

7

6

7 7 7

7 8 9 10

57. 90. 127. 164.

7 8 8 8 8 8 8 8 8 8 8

3

1

2 3

4 5

6 7 8

9 10

203. 45. 69. 100. 152.

214. 281. 355. 428. 502. 577.

52. 74. 98. 124. 151. 179. 205. 234. 262. 291. 100. 144. 193. 243. 294. 345. 394. 441. 489. 536. 28. 54. 85. 121. 158. 197. 236. 272. 308. 345. 206. 272. 344. 417. 491. 566. 637. 709. 778. 844.

148. 176.

202. 230. 258. 288. 315. 340. 367. 393. 289. 340. 388. 436. 484. 531. 572. 612. 654. 693. 157. 194.

232. 266. 302. 339. 373. 403. 433. 464. 483. 557. 627. 698. 767. 834. 894. 951. 1011. 1065.

256. 284. 311. 337. 363. 389. 416. 440. 466. 487. 480. 527. 568. 609. 651. 690. 731. 768. 803. 837. 301. 336. 369. 398. 428. 458. 487. 517. 542. 567. 759. 825. 884. 941. 1000. 1055. 1112. 1164. 1211. 1258.

Group Selection First Second Third Fourth 19.

29. 39. 58. 77. 96. 115. 134. 153. 172. 27. 34. 40. 78. 116. 154. 192. 230. 267. 305. 5.

7. 9. 12.

44. 76. 108. 141. 173.

205. 87. 126. 166.

236. 305. 374. 443. 512. 581. 650.

69. 75. 101. 119. 137. 155. 174. 192.

210. 228. 71. 75. 141. 184. 227. 270. 313. 356. 398. 441. 13. 14. 16.

78. 116. 155. 194.

233. 272. 310. 252. 281. 369. 434. 500. 565. 631. 696. 762. 827.

108. 102. 138. 144. 151. 158. 165. 171. 178. 185. 97. 99.

238. 282. 326. 370. 414. 458. 502. 546. 19.

20. 21. 153. 194.

236. 277. 318. 359. 401. 395. 410. 552. 606. 659. 713. 766. 820. 874. 927.

74. 69. 115. 124. 132. 141. 149. 157. 166. 174. 91. 95. 266. 312. 358. 404. 450. 495. 541. 587. 20. 20. 21. 180. 220. 261. 301. 341. 382. 422. 404. 411. 573. 618. 663. 709. 754. 800. 845. 891.

184


Unit Time 9 9 9 9 9 9 9 9 9 9 10

1

2 3

4 5

6 7 8 9 10 1

10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10

Individual Tree Selection First Second Third Fourth 28. 46. 68. 92. 124. 157. 191. 227. 268. 305. 34. 57. 89. 122. 159. 196. 232. 272. 308. 344.

11

1

1.

11 11 11 11 11

2

2. 4. 43. 94. 153.

11

11 11

11

3

4 5

6 7 8 9 10

12 1 12 2 12 3 12 4 12 5 12 6 12 7 12 8 12 9 12 10

222. 290. 362. 435. 0. 1.

2.

43. 96. 157. 228. 297. 371. 445.

121. 154. 187.

222. 263. 300. 337. 377. 412. 450. 159. 196.

232. 272. 308. 344. 384. 419. 453. 490. 94. 153.

222. 290. 362. 435. 502. 568. 637. 701. 87. 144.

211. 281. 354. 428. 496. 563. 633. 699.

260. 297. 332. 372. 407. 445. 483. 523. 557. 595. 308. 344. 384. 419. 453. 490. 526. 558. 594. 625. 362. 435. 502. 568. 637. 701. 756. 811. 867. 920. 345. 415. 479. 547. 616. 682. 738. 795. 853. 908.

404. 441. 478. 519. 552. 590. 625. 660. 692. 727. 454. 490. 527. 559. 594. 625. 657. 693. 725. 752. 645. 711. 767. 824. 882. 937. 993. 1040. 1087. 1135. 609. 671. 724. 781. 839. 894. 951. 999. 1046. 1096.

Group Selection First Second Third Fourth 63. 79. 95. 111. 129. 147. 165. 183. 201. 219. 76. 93. 110. 127. 145. 162. 179. 196. 214. 231. 4. 7. 10.

69. 128. 187. 246.

305. 364. 422. 0. 1.

2. 62. 123. 183. 244. 304. 365. 425.

130. 202. 273. 345. 417. 488. 560. 632.

214. 219. 224. 236. 243. 250. 257. 264. 271. 278. 269. 274. 279. 284. 289. 294. 299. 304. 309. 314. 23. 23. 270. 347. 423. 499. 575. 651. 727. 804.

233. 237. 241. 254. 260. 267. 273. 279. 285. 292. 253. 264. 276. 288. 300. 312. 323. 335. 347. 359. 22. 21. 321. 396. 471. 546. 621. 696. 771. 846.

2. 2.

2. 2.

1.

122. 197.

265. 346. 427. 508. 589. 670. 751. 832.

321. 401. 482. 562. 642. 723. 803. 883.

143. 154. 166. 181. 194.

208. 221. 235. 248. 262. 197.

207. 217. 227. 238. 248. 258. 268. 278. 288. 14. 15.

272. 347. 422. 497. 571. 646.

1.

185


Unit Time 13 13

2

13

3

13

4

13

5

13

6 7 8 9 10

13 13 13 13

1

14 1 14 2 14 3 14 4 14 5 14 6 14 7 14 8 14 9 14 10 15 15 15 15 15 15 15 15 15 15

16 16 16 16 16 16 16 16 16 16

1

2 3

4 5

6 7 8

9 10 1

2 3

4 5

6 7 8 9 10

Individual Tree Selection First Second Third Fourth 73. 304. 632. 111. 381. 717. 166. 464. 802. 232. 552. 890. 304. 632. 968. 381. 717. 1045. 464. 802. 1117. 552. 890. 1195. 632. 968. 1259. 717. 1045. 1323. 29. 105. 211. 44. 131. 238. 64. 159. 265. 85. 187. 293. 109. 214. 318. 134. 241. 344. 368. 162. 268. 190. 296. 389. 217. 321. 412. 244. 347. 433. 79. 304. 595. 375. 670. 121. 178. 449. 742. 238. 523. 817. 305. 596. 884. 376. 670. 951. 450. 743. 1017. 524. 818. 1075. 597. 885. 1137. 671. 952. 1192. 13. 57. 109. 21. 70. 122. 32. 83. 136. 44. 97. 148. 57. 161. 109. 70. 173. 122. 83. 136. 186. 97. 149. 198. 110. 161. 210. 174. 221. 123.

970. 1047. 1121. 1198. 1263. 1328. 1395. 1453. 1510. 1566. 320. 346. 371. 393. 417. 438. 460. 483. 502. 519. 999. 1085. 1167. 1243. 1321. 1393. 1470. 1543. 1609. 1674. 160. 173. 186. 197.

210. 221. 232. 245. 256. 266.


469. 529. 589. 649. 709. 769. 829. 890. 950.

247. 330. 414. 497. 580. 664. 747. 830. 914. 1010. 54. 81. 108. 135. 161. 188.

215. 241. 268. 295. 165.

235. 306. 376. 446. 516. 587. 657. 727. 798. 27. 33. 40. 46. 52. 58. 64. 70. 77. 83.

165. 186.

207. 227. 248. 269. 290. 310. 331. 352. 468. 518. 568. 618. 668. 717. 767. 817. 867. 917. 71. 74. 78. 82. 85. 89. 93. 96. 100. 103.

702. 736. 770. 803. 837. 871. 905. 939. 973. 1006. 258. 266. 274. 282. 290. 298. 307. 315. 323. 331. 723. 747. 772. 797. 821. 846. 871. 895. 920. 944. 97. 98. 100. 102. 104. 105. 107. 109. 111. 112.

730. 743. 755. 767. 779. 792. 804. 816. 828. 841. 264. 269. 274. 278. 283. 288. 293. 297. 302. 307. 745. 755. 765. 775. 785. 795. 805. 815. 825. 835. 91. 95. 99. 103. 108. 112. 116. 120. 124. 129.

186


Unit Time 17 1 17 2 17 3 17 4 17 5 17 6 17 7 17 8 17 9 17 10 18 1 18 2 18 3 18 4 18 5 18 6 18 7 18 8 18 9 18 10 19 1 19 2 19 3 19 4 19 5 19 6 19 7 19 8 19 9 19 10

20 20 20 20 20 20 20 20 20

Individual Tree Selection First Second Third Fourth 54. 86. 126. 174. 227. 284. 342. 406. 466. 527. 26. 43. 67. 92. 120. 148. 175.

205. 232. 259. 15.

3

25. 38. 52. 69. 87. 106. 125. 147. 168. 2. 4. 6.

4

8.

5

13. 19.

1

2

6

9

26. 34. 42.

20 10

51.

7 8

203. 260. 318. 382. 442. 502. 562. 620. 677. 733. 120. 148. 175.

205. 232. 259. 289. 315. 341. 369. 69. 87. 105. 124. 147. 167. 187.

209. 228. 249. 10. 17.

24. 32. 40. 49. 57. 66. 74. 84.

418. 632. 478. 688. 538. 740. 595. 795. 653. 847. 708. 894. 761. 944. 815. 989. 866. 1031. 913. 1081. 232. 352. 259. 380. 289. 409. 315. 434. 341. 462. 369. 487. 396. 511. 420. 539. 447. 565. 470. 586. 146. 228. 167. 249. 186. 270. 208. 293. 228. 312. 248. 333. 269. 353. 292. 372. 310. 390. 332. 410. 38. 77. 88. 46. 98. 54. 63. 107. 71. 117. 81. 126. 90. 135. 98. 146. 107. 154. 162. 115.


247. 301. 355. 409. 462. 516. 570. 57. 70. 83. 96. 109. 122. 135. 148. 161. 174. 36.

44. 53. 61. 69. 78. 86. 95. 103. 112. 4. 9. 14. 18.

23. 28. 32. 37. 42. 46.

279. 322. 366. 409. 453. 497. 540. 584. 627. 671. 148. 156. 164. 171. 179. 187. 194. 202. 209. 217. 79. 85. 91. 97. 103. 109. 115. 121. 127. 133. 22. 28. 33. 38. 43. 49. 54. 59. 64. 70.

422. 446. 471. 496. 520. 545. 570. 594. 619. 644. 203. 207. 210. 214. 218. 221. 225. 229. 232. 236.

454. 467. 481. 495. 508. 522.

119. 121. 123. 126. 128. 130. 133. 135. 137. 140. 29.

130. 132. 134. 136. 138. 140. 143. 145. 147. 149.

28. 27. 26. 25. 24. 23. 22. 21. 20.

535. 549. 56.3.

576. 191. 199. 208. 217. 226. 235. 243. 252. 261. 270.

31. 33. 34. 36. 37. 39. 40. 42. 43. 45.

187


Unit Time 21 21 21 21 21 21 21 21 21 21

22 22 22 22 22 22 22 22 22

9 10

31. 52. 80. 114. 155. 198. 246. 295. 346. 396.

1

1.

2

1.

3

3.

4 5

43. 94.

6 7

155. 226.

8

295. 369. 444.

1

2 3

4 5

6 7 8

9

22 10 23 23 23 23 23 23 23 23 23 23

24 24 24 24 24 24 24 24 24

Individual Tree Selection First Second Third Fourth

1

2 3

4 5

6 7 8 9

10 1

2 3

4 5

6 7 8 9

24 10

12. 19. 29. 43. 60. 79. 101. 123. 148. 171. 17. 27. 42.

63. 90. 122. 156. 189. 227. 265.

140. 183. 231.

280. 331. 381. 433. 481. 532. 581. 94. 155. 226. 295. 369. 444. 512. 580. 650. 715. 57. 76. 98. 120. 145. 168. 194.

219. 246. 275. 90. 122. 156. 189. 227. 265. 303. 342. 378. 413.

316. 366. 418. 466. 517. 566. 616. 659. 702. 745. 369. 444. 512. 580. 650. 715. 771. 828. 885. 939. 142. 165. 191. 216. 243. 272. 298. 321. 345. 371. 227. 265. 303. 342. 378. 413. 450.

482. 513. 546.

517. 567. 619. 664. 709. 754. 799. 842. 885. 922. 658. 726. 783. 841. 899. 955. 1013. 1061. 1108. 1157. 375. 425. 477. 522. 572. 624. 677. 725. 774. 822. 378. 413. 450. 482. 514. 546. 578. 610. 638. 666.

Group Selection First Second Third Fourth 62. 106. 150. 193. 237. 281. 324. 368. 411. 455.

226. 259. 293. 327. 360. 394. 428. 461. 495. 529.

312. 330. 349. 368. 387. 405. 424. 443. 462. 480.

300. 311. 322. 333. 344. 355. 366. 377. 388. 399.

3. 4. 7.

9.

15. 15.

14. 14.

270. 350. 429. 508. 587. 666. 745. 824.

323. 402. 481. 559. 637. 715. 793. 871.

184.

146. 145. 145. 145. 144. 144. 144. 143. 143. 143. 297.

202. 225. 248. 271. 294. 316. 339. 361. 384.

297. 305. 312. 316. 320. 324. 327. 331. 335.

95. 96. 97. 97. 98. 99. 100. 100. 101. 102. 283. 276.

67. 127. 187. 247. 307. 368. 428. 39. 60. 81. 102. 123. 144. 165. 186. 207.

228. 58. 88. 119. 151. 185.

218. 252. 286. 319. 353.

10. 127.

201. 275. 349. 423. 497. 571. 644. 140. 148. 156. 164. 172. 180. 188. 196.

205. 213.

280. 282. 279. 277. 274. 272. 269. 267.

188


Unit Time 25 25 25 25 25 25 25 25 25 25

26 26 26 26 26 26 26 26 26 26

27 27 27 27 27 27 27 27 27

1

2 3

4 5

6 7 8 9 10 1

2 3

4 5

6 7 8 9 10 1

2 3

4 5

6

7 8 9

27 10 28 28 28 28 28 28 28 28 28

1

2 3

4 5 6

7 8 9

28 10

Individual Tree Selection Group Selection First Second Third Fourth First Second Third Fourth 51. 78. 114. 152. 193.

234. 275. 319. 359. 401. 60. 115. 186.

268. 357. 450. 545. 646. 738. 830. 55. 87. 127. 174.

223. 275. 328. 386. 440. 494. 12. 19.

28. 38. 51. 65. 81. 98. 115. 133.

305. 206. 346. 247. 390. 292. 430. 332. 469. 373. 510. 417. 551. 457. 588. 497. 627. 538. 663. 347. 718. 439. 810. 534. 902. 636. 989. 728. 1070. 820. 1149. 912. 1224. 999. 1300. 1080. 1374. 1159. 1434. 211. 415. 263. 469. 316. 523. 374. 574. 428. 626. 482. 674. 535. 721. 586. 767. 638. 812. 686. 851. 47. 107. 61. 125. 77. 143. 94. 161. 111. 178. 166.

129. 146. 165. 182.

200.

196.

214. 231. 248. 264.

452. 494. 536. 574. 615. 651. 689. 729. 766. 799. 1067. 1147. 1223. 1300. 1374. 1436. 1502. 1565. 1620. 1681. 625. 675. 723. 771. 818. 859. 904. 943. 980. 1022. 207. 230. 252. 274. 296. 316. 339. 360. 380. 400.

90. 237. 115. 254. 141. 270. 166. 286. 192. 303. 217. 319. 243. 335. 268. 352. 294. 368. 319. 384. 91. 336. 177. 423. 263. 509. 349. 596. 434. 682. 520. 768. 606. 855. 692. 941. 777. 1028. 863. 1114. 94. 270. 139. 307. 344. 184. 229. 380. 275. 417. 320. 454. 365. 491. 410. 528. 456. 565. 501. 602. 27. 80. 90. 40. 100. 52. 64. 109. 76. 119. 129. 88. 100. 113. 125. 137.

138. 148. 158. 167.

331. 340. 348. 357. 365. 374. 382. 391. 399. 407. 549. 626. 703. 779. 856. 933. 1010. 1087. 1163. 1240. 412. 436. 459. 482. 505. 529. 552. 575. 598. 621. 114.

320. 332. 344. 357. 369. 382. 394. 406. 419. 431. 629. 694. 759. 824. 889. 955. 1020. 1085. 1150. 1215. 456. 472. 487. 503. 519. 534. 550. 566. 581. 597. 114. 116. 116. 119. 117. 121. 119. 121. 123. 126. 122. 128. 124. 126. 131. 133. 128. 136. 129.

189


Unit Time 29 29 29 29 29 29 29 29 29

1

2 3

4 5

6 7 8

9

29 10 30 30 30 30 30 30 30 30 30

21. 32. 47. 64. 84. 104. 125. 146. 168. 190.

1

6.

2

23. 45. 71. 101. 130. 161. 193. 222. 251. 33. 51. 73. 100. 127. 157. 187. 220. 250. 281.

3

4 5

6 7 8

9

30 10 31 31


1

2

31 31 31 31 31 31 31 31 32 32 32 32 32 32

9 10

32 32 32

8

3

4 5

6 7 8

1

12.

2

20. 31. 52. 77. 104. 135. 165. 197. 228.

3

4 5

6 7

9

32 10

84. 104. 125. 146. 168. 190.

211. 233. 253. 273. 101. 130. 161. 193. 222. 251. 280. 308. 332. 356. 108. 137. 168.

201. 231. 262. 293. 325. 354. 382. 64. 90. 118. 149. 181.

212. 243. 272. 303. 331.

168. 190.

211. 233. 253. 273. 293. 313. 332. 350. 222. 251. 280. 308. 332. 356. 380. 404. 427. 447. 211. 243. 274. 305. 334. 363. 390. 418. 443. 467. 168. 198. 227.

256. 287. 315. 342. 368. 394. 418.

328. 356. 384. 411. 437. 462. 487. 509. 532. 556. 508. 555. 603. 649. 692. 730. 770. 809. 845. 879. 325. 354. 383. 412. 439..

463. 490. 513. 536. 559. 377. 419. 460. 499. 540. 577. 616. 650. 685. 717.

Group Selection First Second Third Fourth 49. 66. 83. 100. 117. 134. 151. 168. 185. 202. 10.

36. 62. 88. 114. 140. 166. 192. 219. 245. 58. 88. 119. 150. 180. 211. 242. 272. 303. 334. 19.

34. 49. 76. 103. 129. 156. 183. 210. 237.

121. 133. 144. 156. 167. 179. 190.

202. 213. 225. 69. 99. 130. 160. 190. 221. 251. 281. 312. 342. 167. 191. 214. 237. 261.

284. 308. 331. 355. 378. 70. 83. 120. 149. 177. 205. 233. 262. 290. 318.

175. 181. 188. 195.

201. 208. 214. 221. 228. 234. 132. 163. 194. 225.

256. 287. 318. 349. 381. 412. 250. 264. 279. 293. 308. 322. 336. 351. 365. 379. 107. 116. 176.

201. 226. 250. 275. 299. 324. 349.

185. 188. 190. 192. 194. 196. 198.

200. 202. 204. 156. 186. 216. 245. 275. 304. 334. 363. 393. 422. 267. 273. 280. 287. 294. 300. 307. 314. 320. 327. 114. 119. 186. 207. 228. 248. 269. 290. 311. 331.

190


Unit Time 33 33 33 33 33 33 33 33 33 33

34 34 34 34 34 34 34 34 34

1

2 3

4 5

6 7 8 9 10 1

2 3

4

Individual Tree Selection First Second Third Fourth 42. 70. 109. 163.

227. 293. 367. 445. 522. 599. 45. 75. 116. 171.

34 10

235. 301. 375. 453. 529. 606.

35 35 35 35 35 35 35 35 35 35

23. 38. 57. 83. 114. 146. 181. 218. 255. 292.

36 36 36 36 36 36 36 36 36

5

6 7 8

9 1

2 3

4 5

6 7 8 9 10 1

2 3

4 5

6 7 8

9

36 10

6. 10. 16.

25. 67. 122. 184. 255. 327. 402.

227. 522. 1314. 293. 599. 1461. 367. 680. 1603. 445. 759. 1741. 522. 836. 1875. 599. 912. 2006. 680. 982. 2128. 759. 1048. 2245. 836. 1114. 2362. 912. 1177. 2472. 223. 504. 801. 289. 581. 874. 362. 660. 944. 440. 737. 1009. 516. 813. 1074. 593. 886. 1137. 957. 1196. 673. 750. 1022. 1253. 826. 1087. 1310. 900. 1149. 1363. 106. 239. 382. 138. 276. 418. 173. 315. 452. 210. 352. 484. 247. 389. 516. 284. 426. 547. 323. 460. 577. 360. 492. 605. 397. 524. 634. 434. 555. 661. 327. 618. 67. 402. 689. 122. 184. 478. 757. 255. 548. 815. 327. 618. 873. 402. 689. 932. 478. 757. 989. 548. 815. 1047. 618. 873. 1096. 932. 1144. 689.

Group Selection First Second Third Fourth 100. 167.

235. 302. 369. 436. 503: 571. 638. 705. 95. 161.

227. 294. 361. 428. 495. 561. 628. 695. 50. 82. 115. 147. 180. 212. 244. 277. 309. 342. 22. 34. 45. 58. 120. 182. 244. 307. 369. 431.

334. 383. 433. 482. 532. 581. 630. 680. 729. 779. 322. 374. 427. 480. 532. 585. 637. 690. 743. 795. 165. 189. 212. 236. 259. 282. 306. 329. 353. 376. 70. 77. 84. 192.

262. 332. 402. 472. 542. 612.

486. 504. 522. 541. 559. 577. 595. 613. 631. 649. 479. 502. 527. 551. 575. 599. 623. 647. 671. 695. 237. 246. 254. 263. 271. 279. 288. 296. 305. 313.

430. 440. 450. 460. 470. 481. 491. 501. 511. 521. 446. 459. 474. 488. 502. 515. 529. 543. 556. 570. 208. 213. 217. 222. 226. 231. 236. 240. 245. 250.

114. 113. 113.

108. 106. 103.

334. 402. 470. 538. 606. 674. 741.

369. 433. 498. 563. 628. 693. 758.

191


Unit Time 37 37 37 37 37 37 37 37 37

1

2 3

4 5

6 7 8

9

37 10 38 38 38 38 38 38 38 38 38

2

30. 45. 66. 91.

4 5

6 7 8

9 1

2 3

4 5

6 7 8

9

39 10 40 40 40 40 40 40 40 40 40

28. 40. 55. 71. 89. 107. 127. 148. 19.

3.

125. 175.

229. 289. 349. 412. 473. 536. 598.

3

s;

5

6 7 8

9

40 10

.

213. 247. 83.

2 4

211. 234.

120. 150. 180.

2. 3.

1

55. 71. 89. 107. 127. 148. 168. 190.

11. 18.

1

38 10 39 39 39 39 39 39 39 39 39


45. 96. 155. 223.

290. 361. 432.

.

91. 120. 150. 180.

127. 148. 168. 190.

211. 234. 256. 276. 297. 318. 213. 247. 280. 314. 346. 377. 409. 438. 466. 494. 528. 589. 651. 708. 765. 820. 871. 922. 972.

216. 239. 262. 283. 305. 326. 348. 368. 390. 408. 522. 581. 643. 701. 756. 811. 867. 919. 968. 1017. 761. 816. 867. 918. 968. 1014. 1060. 1101. 1147. 1187. 597. 657. 708. 764. 820. 873. 928. 975.

213. 247. 280. 314. 346. 377. 285. 345. 408. 469. 532. 593. 655. 712. 769. 825. 1018. 88. 339. 407. 144. 208. 469. 276. 534. 346. 602. 418. 665. 483. 719. 549. 774. 616. 830. 1020. 679. 883. 1068.

Group Selection First Second Third Fourth 29. 41. 53. 66. 78. 90. 103. 115. 127. 139. 56. 86. 116. 146. 176. 206. 236. 266. 296. 325. 153. 215. 278. 341. 403. 466. 529. 592. 654. 717.

93. 101. 109. 117. 125. 133. 140. 148. 156. 164. 177. 196. 216. 235. 254.

3. 5. 9.

11. 13. 126. 198..

67. 125. 184. 242. 300. 359. 417.

274. 293. 313. 332. 351. 387. 436. 485. 534. 583. 632. 681. 730. 779. 829.

269. 341. 412. 483. 555. 626.

148. 143. 138. 133. 128. 123. 118. 113. 108. 103.

120. 116. 112. 109. 105. 101. 98. 94. 90. 86.

284. 286. 287. 289. 291. 293. 295. 296. 298. 300. 577. 601. 625. 649. 673. 697. 721. 745. 769. 793.

274. 270. 266. 261. 257. 253. 249. 244. 240. 236. 578. 587. 596. 605. 615. 624. 633. 643. 652. 661.

16. 17.

15. 16.

264. 340. 416. 492. 569. 645. 721. 798.

314. 389. 465. 540. 615. 690. 766. 841.

192


Unit Time 41 1 41 2 41 3 41 4 41 5 41 6 41 7 41 8 41 9 41 10 42 1

42 42 42 42 42 42 42 42

2 3

4 5

6 7 8

9

42 10 43 43 43 43 43 43 43 43 43 43


29. 66. 109. 159. 209. 261. 49. 73. 102. 135. 171. 208. 246. 281. 319. 355.

2

8. 13.

3

19.

4

6 7 8 9

27. 38. 52. 66. 84. 104. 124. 24. 40. 62. 92. 128. 165. 206. 250. 293.

44 10

336.

44 44 44 44 44 44 44 44 44

1

5

6 7 8

9 10 1

2 3

4 5

29. 66. 109. 159. 209. 261. 314. 362. 410. 460. 171. 208. 246. 281. 319. 355. 390. 422. 454.. 486. 37. 51. 66. 84. 103. 124. 144. 167. 189. 212. 128. 165.

209. 261. 314. 362. 410. 460. 506. 545. 586. 626. 319. 355. 390. 422. 454. 486. 513. 540. 567. 591.

206. 250. 293. 336. 380. 424. 466. 507.

380. 424. 466. 507. 545. 581. 617. 651.

103. 124. 144. 167. 189. 212. 235. 258. 282. 305. 293. 336.

411. 461. 508. 548. 588. 629. 667. 707. 741. 773. 758. 821. 881. 937. 993. 1046. 1094. 1141. 1189. 1230. 292. 335. 378. 424. 471. 516. 561. 609. 655. 700. 758. 843. 924. 1005. 1083. 1158. 1227. 1294. 1360. 1423.


0. 0. 0.

0. 0. 0.

0. 0. 0.

1.

85. 138. 191.

187. 244. 301. 359.

226. 283. 340. 397. 454. 511. 568. 340. 346. 366. 375. 385. 394. 404. 414. 423. 433.

43. 86. 129. 171. 214. 256. 86. 122. 159. 198. 237. 276. 315. 354. 393. 432. 23. 55. 87. 119. 152. 184.

216. 249. 281. 313. 54. 91. 129. 166.

203. 240. 277. 315. 352. 389.

244. 297. 350. 403. 217. 246. 280. 312. 344. 376. 408. 440. 472. 504. 101. 118. 134. 151. 167. 184. 200. 217. 233. 250. 178. 207. 236. 265. 293. 322. 351. 380. 409. 437.

416. 474. 531. 330. 345. 371. 388. 406. 424. 442. 460. 478. 496. 179. 179. 179. 178. 178. 178. 177. 177. 177. 176.

183. 175. 166. 158. 150. 141. 133. 125. 116. 108.

271. 282. 293. 304. 315. 327. 338. 349. 360. 371.

246. 252. 258. 264. 270. 276. 282. 288. 294. 300.

193


Unit Time 45 1 45 2 45 3 45 4 45 5 45 6 45 7 45 8 45 9 45 10

46 46 46 46 46 46 46 4 46

2 3

142.

4

204. 274. 355. 441. 531. 625. 715.

1

5

6 7 8 9

3

7. 12. 18.

4

.27.

5

37. 50. 63. 75. 90. 105. 48. 74. 110. 149. 198. 247. 298. 348. 400. 449.

1

2

6 7 8 9

47 10 48 48 48 48 48 48 48 48 48

16.

29. 48. 79. 117. 162. 208. 257. 310. 361. 57. 94.

46 10 47 47 47 47 47 47 47 47 47


1

2 3

4 5

6 7 8 9

48 10

101. 146. 192.

241. 294. 345. 395. 448. 497. 548. 264. 344. 431. 521. 615. 704. 802. 896. 988. 1073. 37. 50. 63. 75. 90. 105. 120. 135. 149. 163. 198.

247. 298. 348. 400. 449. 501. 551. 601. 645.

278. 329. 379. 432. 481. 532. 576. 620. 665. 704. 605. 694. 792. 885. 977. 1063. 1158. 1237. 1318. 1397. 90. 105. 120. 135. 149. 163. 177. 190.

202. 215. 400. 449. 501. 551. 601. 645. 686. 728. 767. 807.

474. 526.

57. 617. 663. 705. 744. 785. 820. 856. 967. 1053. 1148. 1227. 1308. 1387. 1458. 1532. 1601. 1667. 236. 264. 293. 321. 347. 373. 399. 424. 447. 471. 1001. 1094. 1187. 1279. 1368. 1452. 1526. 1602. 1674. 1744.

Group Selection First Second Third Fourth 25. 106. 56. 136. 86. 184. 126. 225. 165. 266. 205. 307. 245. 348. 284. 389. 324. 430. 363. 471. 119. 387. 205. 462. 292. 537. 378. 612. 464. 686. 551. 761. 637. 836. 723. 911. 810. 986. 896. 1060. 79. 25. 38. 87. 51. 95. 64. 103. 77. 111. 90. 119. 103. 127. 116. 135. 141 129. 151. 142. 76. 230. 123. 269. 169. 309. 216. 348. 263. 387. 309. 426. 356. 465. 402. 504. 449. 544. 496. 583.

181.

201. 261. 293. 325. 357. 389. 421. 453. 486. 629. 666. 704. 741. 778. 816. 853. 891. 928. 965. 127. 127. 127. 126. 126. 125. 125. 125. 124. 124.

371. 394. 418. 442. 466. 489. 513. 537. 561. 584.

185. 193.

.

250. 270. 290. 311. 331. 351. 371. 392. 596. 616. 636. 656. 676. 696. 716. 736. 756. 776. 120. 117. 114. 111. 109. 106. 103. 100. 97. 94. 393. 406. 419. 432. 445. 458. 471. 485. 498. 511.

194


Unit Time 49 1 49 2 49 3 49 4 49 5 49 6 49 7 49 8 49 9 49 10 50 50 50 50 50 50 50 50 50 50 51 51 51 51 51 51 51 51 51 51

1

2 3

4 5

6 7 8

9 10 1

2 3

4 5

6 7 8 9 10

52 1 52 2 52 3 52 4 52 5 52 6 52 7 52 8 52 9 52 10


23. 32. 43. 55. 68. 80. 48. 74. 108. 150. 195. 243. 295. 349. 400. 453. 71. 107. 150. 198.

252. 306. 364. 420. 479. 535. 76. 113. 159.

215. 280. 346. 415. 482. 552. 618.

68. 23. 32. 80. 43. 93. 55. 107. 68. 125. 80. 138. 154. 93. 107. 169. 125. 184. 138. 199. 178. 366. 227. 420. 278. 473. 332. 528. 383. 577. 436. 626. 490. 673. 545. 721. 594. 763. 643. 805. 250. 476. 305. 533. 363. 591. 418. 644. 478. 697. 534. 750. 592. 797. 645. 845. 698. 891. 751. 934. 280. 552. 346. 618. 415. 684. 482. 745. 552. 805. 618. 864. 684. 916. 745. 966. 805. 1018. 864. 1063.

125. 138. 154. 169. 184. 199.

214. 229. 241. 256. 561. 609. 656. 705. 747. 789. 832. 870. 908. 944. 1094. 1189. 1279. 1365. 1449. 1529. 1605. 1677. 1752. 1817. 874. 947. 1012. 1075. 1139. 1197. 1252. 1305. 1358. 1407.


2. 3. 3.

54. 95. 137. 178. 220. 262. 102. 153. 205. 257. 309. 361. 413. 464. 516. 568. 130. 187. 244. 301. 358. 415. 472. 529. 586. 643. 133. 191. 249.

319. 388. 457. 527. 596. 665. 735.

5. 5. 5.

6. 50.

44. 38. 32. 27. 21. 293. 330. 367. 404. 441. 478.

sis; 552. 589. 626. 347. 389. 431. 473. 515. 558. 600. 642. 684. 726. 340. 386. 455. 515. 575. 636. 696. 757. 817. 877.

7. 7. 6. 6. 85. 73. 61. 50. 38. 26.

443. 462. 481. 500. 519. 538. 557. 576. 595. 614. 519. 538. 558. 577. 596. 615. 634. 653. 672. 691. 519. 542. 615. 654. 692. 731. 770. 808. 847. 886.

5. 5. 4. 4. 97. 83.

70. 56. 43. 29. 457. 463. 469. 475. 480. 486. 492. 498. 504. 510. 525. 531. 537. 543. 549. 555. 562. 568. 574. 580. 533. 543. 613. 638. 663. 688. 713. 738. 763. 788.

195


Unit Time 53 53 53 53 53 53 53 53 53 53

54 54 54 54 54 54 54 54 54

2

33. 56. 86. 129. 178. 229. 286. 346. 405. 464. 0. 0.

3

1.

4

27. 61.

1

2 3

4 5

6 7 8 9 10 1

5

6 7 8

9

54 10 55 55 55 55 55 55 55 55 55 55


1

2 3

4 5

6 7 8

9 10

101. 147. 193.

241. 290. 21. 31. 44. 61. 80. 102. 127. 155. 183.

5

213. 27. 43. 64. 90. 118.

6 7

149. 182.

8

215. 250. 285.

56 56

2

.56

3

56 56 56 56 56 56

4

1

9

56 10

176.

227. 283. 343. 402. 462. 523. 583. 641. 698. 59. 97. 142. 188. 236. 285. 329. 373. 419. 462. 71. 94. 118. 147. 175. 205. 237. 272. 302. 335. 111. 141. 174.

208. 243. 277. 311. 346. 378. 410.

400. 638. 459. 696. 520. 748. 580. 799. 638. 848. 695. 896. 747. 940. 798. 982. 847. 1025. 894. 1065. 233. 418. 281. 461. 324. 497. 368. 536. 414. 574. 457. 611. 493. 649. 530. 681. 568. 712. 604. 745. 167. 450. 197. 510. 229. 573. 263. 639. 703. 294. 327. 770. 360. 833. 393. 896. 429. 964. 465. 1027. 236. 364. 270. 396. 303. 428. 338. 457. 370. 486. 403. 514. 435. 542. 463. 569. 492. 591. 521. 617.

Group Selection First Second Third Fourth 75. 126. 177. 229. 280. 331. 383. 434. 486. 537. 0. 0 1.

40. 79. 119. 158. 198. 237. 277. 66. 117. 169.

220. 271. 323. 374. 426. 477. 528. 57. 91. 124. 158. 193.

227. 261. 295. 330. 364.

246. 286. 325. 365. 405. 445. 484. 524 564. 603. 0. 0. 79. 128. 177.

226. 275. 323. 372. 421. 242. 263. 285. 306. 328. 350. 371. 393. 414. 436. 184.

208. 233. 257. 282. 306. 331. 355. 380. 404.

373. 389. 404. 420. 435. 451. 466. 482. 497. 512.

339. 347. 356. 364. 373. 381. 389. 398. 406. 414.

0. 0.

0. 0.

173. 226. 279. 332. 385. 438. 491. 544. 420. 412. 405. 398. 391.

209. 262. 315. 367. 420. 472. 525. 578. 330. 316. 302. 288. 274. 259. 245. 231. 217. 203. 297. 301. 309. 314. 319. 324. 330. 335. 340. 345.

383. 376. 369. 362. 355. 307. 315. 326. 335. 344. 354. 363. 372. 381. 390.

196


Unit Time 57 57 57 57 57 57 57 57 57

1

2 3

4 5

6 7 8

9

57 10 58 1 58 2 58 3 58 4 58 5 58 6 58 7 58 8 58 9 58 10 59 1 59 2 59 3 59 4 59 5 59 6 59 7 59 8 59 9 59 10 60 1 60 2 60 3 60 4 60 5 60 6 60 7 60 8 60 9

60 10

Individual Tree Selection Group Selection First Second Third Fourth First Second Third Fourth 11. 19.

28. 40. 56. 76. 97. 122. 150. 178. 79. 121. 179. 250. 326. 407. 495. 588. 673. 763. 26. 44. 67. 101. 140. 180. 224. 271. 317. 364. 30. 55. 95. 155. 228. 316. 404. 501. 606. 706.

52. 72. 93. 118. 146. 174. 202. 235. 267. 298. 315. 396.

484; 577. 662. 752. 842. 935. 1018. 1100. 136. 176. 220. 267. 313. 360. 408. 455. 500. 545. 221. 309. 398. 494. 599. 700. 799. 905. 1001. 1103.

142. 170. 198.

231. 263. 294. 327. 359. 392. 425. 651. 741. 831. 924. 1007. 1089. 1167. 1250. 1320. 1389. 310. 356. 404. 451. 496. 541. 582. 621. 660. 697. 592. 693. 792. 898. 994. 1096. 1185. 1271. 1360. 1437.

259. 290. 323. 355. 389. 422. 452. 487. 518. 549. 997. 1079. 1157. 1239. 1309. 1378. 1451. 1513. 1575. 1636. 494.

539. 579. 619. 658. 695. 730. 763. 796. 828. 994. 1097. 1187. 1274. 1364. 1442. 1516. 1596. 1661. 1729.

31. 141. 250. 164. 249. 76. 121. 187. 249. 166. 210. 248. 211. 233. 248. 256. 256. 248. 301. 279. 247. 346. 302. 247. 391. 325. 246. 436. 348. 246. 171. 489. 733. 258. 552. 768. 345. 615. 803. 432. 677. 838. 524. 745. 882. 615. 807. 916. 707. 869. 950. 798. 931. 983. 889. 993. 1017. 981. 1055. 1051. 58. 191. 290. 98. 222. 302. 253. 316. 138. 178. 285. 328. 218. 316. 341. 259. 348. 354. 299. 379. 366. 339. 410. 379. 380. 442. 392. 420. 473. 404. 55. 237. 406. 124. 305. 452. 193. 384. 522. 268. 459. 576. 343. 534. 629. 418. 609. 682. 493. 684. 735. 568. 759. 788. 643. 834. 841. 717. 909. 894.

255. 243. 232. 220. 208. 197. 185. 174. 162. 150.

762. 774. 787. 800. 823. 834. 845. 856. 867. 879. 263. 270. 279. 286. 293. 300. 307. 314. 321. 329. 415. 433. 482. 508. 534. 560. 586. 612. 638. 664.

197


Unit Time 61 61 61 61 61 61 61 61 61 61

1

2 3

29. 49. 76.

5

117. 166.

6 7 8 9 10

218. 275. 337. 398. 460.

62 1 62 2 62 3 62 4 62 5 62 6 62 7 62 8 62 9 62 10

14.

63 63 63 63 63 63 63 63 63 63

4


1

2 3

4 5

6 7 8

9 10

64 1 64 2 64 3 64 4 64 5 64 6 64 7 64 8 64 9 64 10

23. 35. 52. 73. 99. 128. 159. 192. 226. 36. 59. 89. 128. 173. 223. 278. 334. 394. 450. 45. 67. 95. 132. 176.

221. 270. 318. 369. 418.

149. 198.

251. 312. 374. 435. 497. 559. 622. 681. 67. 92. 122. 152. 186.

220. 256. 291. 326. 363. 172.

222. 277. 333. 393. 449. 510. 569. 627. 681. 176.

221. 270. 318. 369. 418. 467. 512. 558. 603.

357. 414. 472. 534. 597. 657. 713. 768. 822. 873. 179. 213. 249. 284. 320. 356. 390. 426. 458. 491. 392. 448. 509. 568. 626. 680. 739. 788. 839. 888. 369. 418. 467. 512. 558. 603. 643. 683. 722. 758.

595. 653. 708. 765. 821. 874. 928. 975. 1025. 1074. 326. 365. 401. 439. 474. 509. 544. 579. 615. 646. 626. 680. 740. 789. 840. 889. 934. 981. 1023. 1064. 600. 653. 701. 748. 796. 840. 884. 926. 968. 1007.

Group Selection First Second Third Fourth 60. 107. 154. 207. 260. 313. 366. 420. 473. 526. 34. 55. 75. 98. 120. 143. 165. 188.

211. 233. 77. 132. 187.

242. 297. 352. 406. 461. 516. 571. 81. 118. 155.

202. 249. 296. 344. 391. 438. 485.

213. 251. 302. 348. 394. 440. 486. 532. 578. 624.

356. 370. 412. 435. 458. 481. 504. 527. 550. 573.

136. 144. 156. 166. 176. 187. 197.

193. 192.

207. 217. 228. 251. 298. 344. 391. 438. 485. 532. 579. 625. 672. 220. 247. 295. 335. 375. 415. 454. 494. 534. 574.

200. 201. 202. 204. 205. 206. 208. 209. 410. 432. 455. 478. 501. 524. 547. 570. 593. 616. 331. 343. 401. 428. 454. 480. 507. 533. 559. 586.

311. 317. 356. 371. 385. 399. 414. 428. 443. 457. 190. 184. 189. 187. 184. 181. 178. 175. 172. 169.

389. 401. 414. 426. 438. 451. 463. 476. 488 501. 337. 341. 401. 419. 437. 455. 473. 491. 509. 527.

198


Unit Time 1 65 65 2 65 3 65 4 65 5 65 6 65 7 65 8 65 9 65 10 66 1 66 2 66 3 66 4 66 5 66 6 66 7 66 8 66 9 66 10 67 1

67 67 67 67

2

67 67 67 67

6 7

3

4 5

8

9

67 10 68 68 68 68 68 68 68 68 68

1

2 3

4 5


31. 70. 116. 168.

219. 274. 328. 29. 46. 70. 99. 129. 163. 199.

235. 273. 310. 32. 53. 81. 117. 160.

203. 251. 301. 351. 400. 23. 37. 55. 77. 100.

9

126. 152. 180. 209.

68 10

238.

6 7 8

64. 106. 155. 207. 261.

316. 366. 416. 468. 516. 129. 163. 199.

235. 273. 310. 346. 384. 418. 452. 142. 186. 233.

284. 333. 383. 434. 485. 533. 582. 99. 125. 152. 179.

209. 237. 268. 298. 326. 356.

255. 307. 353. 404. 455. 504. 545. 587. 630. 671. 273. 310. 346. 384. 418. 452. 487. 516. 547. 576. 316. 366. 417. 467. 516. 564. 608. 651. 693. 733. 208. 237. 267. 297. 326. 355. 385. 414. 443. 473.

475. 525. 569. 616. 663. 709. 754. 794. 833. 873. 418. 453. 487. 516. 547. 576. 605. 634. 655. 681. 499. 547. 591. 634. 676. 716. 754. 790. 827. 862. 489. 539. 591. 642. 692. 743. 793. 840. 887. 933.


0. 0.

1.

89. 145. 200. 256.

45. 90. 135. 180.

224. 269. 314. 65. 103. 141. 180. 218. 256. 295. 333. 371.

410. 64. 108. 151. 195.

239. 282. 326. 370. 413. 457. 60. 83. 106. 128. 151. 174. 196.

219. 241. 264.

312. 367. 423. 478. 204. 233. 262. 290. 319. 347. 376. 404. 433. 462. 210. 244. 278. 312. 345. 379. 413. 447. 480. 514. 175. 188.

201. 214. 227. 241. 254. 267. 280. 293.

0. 0. 196.

256. 316. 377. 437. 497. 557. 618. 348. 359. 370. 381. 392. 403. 414. 425. 436. 447. 319. 333. 346. 359. 372. 385. 399. 412. 425. 438. 292. 295. 297. 300. 302. 305. 307. 310. 312. 315.

0. 0.

238. 297. 357. 417. 476. 536. 596. 655. 336. 343. 350. 357. 364. 371. 377. 384. 391. 398. 292. 299. 306. 313. 320. 327. 334. 341. 348. 355. 318. 311. 304. 297. 290. 282. 275. 268. 261. 254.

199


Unit Time 69 69 69 69 69 69 69 69 69

1

2 3

4 5

6 7 8

9

69 10 70 1 70 2 70 3 70 4 70 5 70 6 70 7

70 70

8

9

70 10 71 71 71 71 71 71 71 71 71 71

1

2 3

4 5

6 7 8

9 10

72 1 72 2 72 3 72 4 72 5 72 6 72 7 72 8 72 9 72 10

Individual Tree Selection First Second Third Fourth 21. 39. 64. 94. 130. 172. 213.

258. 306. 353. 43. 67. 99. 135. 178. 223. 269. 314. 361. 405. 6. 10. 15.

21. 29. 40. 52. 66. 82. 98. 82. 127. 185.

252. 330. 412. 498. 585. 675. 765.

100. 141. 183.

228. 276. 322. 368. 417. 462. 509. 178.

222. 268. 314. 360. 405. 452. 497. 542. 582. 29. 40. 52. 66. 82. 98. 114. 132. 150. 168.

245. 292. 338. 387. 431. 479. 521. 562. 604. 641. 360. 404. 452. 496. 541. 582. 618. 656. 691. 727. 82. 98. 114. 132. 150. 168. 186.

204. 223. 242. 666. 756. 843. 929. 1015. 1098. 1176. 1249.

326. 407. 493. 580. 671. 760. 848. 934. 1019. 1326. 1102. 1391.

412. 461. 505. 547. 591. 629. 666. 706. 739. 774. 542. 583. 619. 658. 693. 729. 760. 790. 821. 848. 231. 265. 299. 335. 372. 408. 444. 481. 517. 553. 1113. 1207. 1297. 1380. 1466. 1541. 1616. 1688. 1759. 1826.

Group Selection First Second Third Fourth 33. 70. 106. 143. 179.

216. 252. 289. 325. 361. 69. 111. 153. 195.

237. 279. 321. 363. 405. 448. 18.

43. 68. 94. 119. 145. 170. 196.

221. 247.

133. 168. 203. 238.

272. 307. 342. 377. 412. 446. 208. 243. 278. 314. 349. 385. 420. 455. 491. 526. 80. 93. 106. 118. 132. 145. 158. 171. 184. 197.

442. 514. 324. 586. 412. 659. 500. 731. 588. 803. 676. 875. 763. 947. 851. 1019. 939. 1092. 149. 237.

224. 247. 270. 293. 316. 339. .362. 385. 408. 431. 334. 356. 377. 399. 420. 442. 463. 484. 506. 527. 141. 141. 140. 140. 141. 140. 140. 140. 140. 140. 670. 711. 753. 794. 836. 877. 918. 960. 1001. 1043.

229. 238. 248. 257. 266. 275. 284. 293. 302. 311. 355. 366. 378. 390. 402. 413. 425. 437. 449. 461. 144. 137. 131. 124. 118. 112. 106. 99. 93. 87. 656.

680. 704. 728. 752. 776. 800. 824. 848. 872.

200 Table 8: Yields for Uneven-Aged Prescriptions in Mbf per Unit: (Continued)

Unit Time 73 73 73 73 73 73 73 73 73 73

1

2 3

4


9 10

228. 295. 368. 447. 524. 602.

1

16.

2

9

27. 40. 58. 78. 101. 126. 151. 178.

74 10

205.

74 74 74 74 74 74 74

74 74 75 75 75 75 75 75 75 75 75 75 76 76 76 76 76 76 76 76

76

5

6 7 8

3

4 5

6 7 8

1

2 3

4 5

6 7 8

9 10 1

2 3

4 5

6 7 8

9

76 10

6. 11.

20. 31. 46. 63. 80. 99. 120. 139. 45. 68. 102. 143. 187.

234. 285. 338. 388. 440.

228. 524. 1324. 295. 602. 1470. 368. 682. 1612. 447. 761. 1751. 524. 838. 1886. 602. 912. 2016. 682. 981. 2137. 761. 1047. 2253. 838. 1112. 2368. 912. 1174. 2478. 78. 178. 308. 101. 205. 336. 126. 231. 363. 151. 258. 389. 178. 285. 415. 205. 311. 438. 231. 336. 462. 258. 359. 484. 285. 384. 505. 311. 405. 526. 46. 120. 201. 63. 139. 221. 80. 159. 239. 99. 180. 257. 120. 199. 275. 139. 219. 290. 159. 237. 305. 321. 180. 254. 199. 272. 334. 219. 287. 347. 187. 388. 630. 234. 440. 682. 285. 492. 732. 338. 546. 784. 388. 594. 828. 440. 641. 872. 492. 686. 917. 546. 733. 957. 594. 773. 996. 641. 812. 1033.


229. 296. 363. 430. 497. 564. 631. 697. 32. 56. 81. 106. 130. 155. 180. 204. 229. 254. 12.

26. 41. 56. 71. 85. 100. 115. 129. 144. 100. 152.

203. 254. 305. 356. 407. 458. 509. 561.

318. 370. 422. 474. 526. 579. 631. 683. 735. 787.

489. 509. 529. 549. 570. 590. 610. 630. 650. 671.

441. 452. 462. 473. 483. 494. 504. 514. 525. 535.

111. 131. 152. 173. 193.

166. 179. 191. 204. 217. 230. 243.

155. 163. 172. 180. 189. 197.

214. 235. 255. 276. 297. 51. 65. 79. 94. 108. 122. 137. 151. 165. 180. 287. 324. 361. 398. 435. 472. 509. 546. 583. 620.

255. 268. 281. 86. 96. 105. 115. 125. 134. 144. 153. 163. 172.

431. 451. 472. 493. 514. 535. 555. 576. 597. 618.

206. 214. 223. 231. 87. 91. 95. 99. 103. 107. 111. 115. 119. 123.

448. 456. 463. 471. 478. 486. 493. 501. 508. 516.

201


Unit Time 77 77 77 77 77 77 77 77 77

Individual Tree Selection Group Selection First Second Third Fourth First Second Third Fourth

1

17.

2

27. 41. 70. 105. 146. 192. 239. 288. 338. 78. 124. 188.

3

4 5

6 7 8

9

77 10 78 1 78 2 78 3 78 4 78 5 78 6 78 7 78 8 78 9 78 10 79 1 79 2 79 3 79 4 79 5 79 6 79 7 79 8 79 9 79 10 80 1 80 2 80 3 80 4 80 5 80 6 80 7 80 8 80 9 80 10

263. 344. 433. 530. 626. 727. 827. 2. 3. 5.

25. 51. 82. 117. 152. 188. 226. 21. 39. 66. 103. 149. 202. 255.

315. 378. 439.

95. 136. 182. 229. 279. 328.

377. 425. 474. 522. 344. 433. 530. 626. 727. 827. 923. 1023. 1114. 1206. 51. 81. 116. 151. 188. 225. 259. 294. 329. 363. 142. 195.

249. 308. 371. 432. 492. 557. 614. 677.

269. 461. 318. 511. 367. 555. 416. 601. 464. 644. 512. 686. 555. 729. 599. 769. 641. 808. 682. 846. 727. 1841.

827. 2033. 923. 2220. 1023. 2398. 1114. 2570. 1206. 2741. 1297. 2908. 1375. 3063. 1457. 3201. 1535. 3350. 187. 224.

259. 293. 329. 363. 391. 421. 450. 479. 364. 425. 485. 550. 608. 670. 725. 778. 831. 879.

329. 363. 392. 422. 451. 480. 510. 535. 559. 586. 902. 1014. 1119. 1225. 1326. 1426. 1514. 1606. 1690. 1770.

32. 53. 75. 114. 153. 191. 230. 269. 308. 347. 173. 275. 377. 479. 581.

122. 135. 182. 216. 251. 285. 319. 353. 388. 422. 545. 621. 697. 773. 849. 683. 926. 786. 1002. 888. 1078. 990. 1154. 1092. 1230. 7. 33. 10. 32. 13. 83. 42. 114. 72. 146. 101. 177. 130. 209. 160. 240. 189. 272. 218. 303. 160. 37. 84. 205. 131. 251. 296. 178. 225. 342. 272. 387. 319. 433. 366. 478. 413. 523. 460. 569.

184. 188.

268. 294. 321. 348. 375. 402. 429. 456. 927. 956. 985.

182. 182. 274. 296. 319. 342. 364. 387.

410. 432. 895. 914. 932. 1015. 951. 1044. 969. 1074. 987. 1103. 1006. 1132. 1024. 1162. 1043. 1191. 1061. 37. 28. 34. 27. 146. 178.

164. 198.

210. 242. 275. 307. 339. 371. 276. 306. 337. 367. 398. 428. 459. 490. 520. 551.

232. 265. 299. 333. 366. 400. 276. 290. 303. 317. 331. 345. 359. 372. 386. 400.

202


Unit Time 81 81 81 81 81 81 81 81 81 81

82 82 82 82 82 82 82 82 82


1

1.

2

1.

3

1.

4

2. 2. 3. 3. 4. 4.

5

6 7 8

9 10 1

2 3

4 5

6 7 8 9

82 10

5. 18.

30. 46. 66. 92. 120. 150. 183. 216. 250.

83

1

83 83 83 83 83 83 83 83 83

2

1.

3

2. 15.

4 5

6 7 8

9 10

84 1 84 2 84 3 84 4 84 5 84 6 84 7 84 8 84 9 84 10

1.

30. 49. 69. 90. 111. 133. 61. 101. 151.

212. 277. 346. 420. 495. 568. 641.

2. 3. 3. 4. 4. 5.

6. 6. 7. 7. 92. 120. 150. 183.

216. 250. 283. 317. 351. 384. 26. 42. 61. 82. 103. 125. 145. 165. 185. 204. 256.

325. 399. 474. 548. 621. 690. 763. 830. 898.

4. 5. 6. 6. 7. 7. 8. 8. 8.

9.

216. 250. 283. 317. 351. 384. 416. 445. 477. 503. 99. 119. 136. 156. 177. 196.

213. 230. 247. 264. 527. 600. 670. 743. 810. 878. 940. 997. 1056. 1110.

7. 7. 8. 8. 8. 9. 9. 10. 10. 10.

361. 395. 428. 459. 492. 520. 549. 576. 602. 628. 267. 303. 335. 370. 405. 438. 469. 498. 527. 555. 802. 871. 935. 994. 1054. 1109. 1163. 1213. 1261. 1309.

1. 1.

2. 2. 3. 3. 4. 4. 5. 5.

35. 65. 95. 126. 156. 187.

217. 248. 278. 308. 2. 2. 3.

20. 38. 56. 73. 91. 108. 126. 98. 164.

231. 297. 363. 429. 496. 562. 628. 694.

3. 3. 3.

4. 4. 5. 5. 6. 6.

6. 130. 155. 182.

208. 233. 259. 285. 311. 337. 363. 4. 4. 39. 61. 83. 105. 126. 148. 170. 192. 304. 364.

425. 485. 546. 606. 667. 727. 788. 848.

4. 4.

4. 4.

5. 5. 5. 5. 6. 6. 6.

5. 5. 5. 5. 5. 5. 5. 6.

6. 195.

210. 229. 245. 262. 278. 295. 311. 328. 345.

179. 190.

204. 215. 227. 238. 250. 261. 273. 284.

7. 7. 83. 106. 130. 153. 177.

100. 123. 146. 169. 192.

200. 224. 247. 507. 545. 582. 620. 657. 694. 732. 769. 807. 844.

215. 238. 261. 549. 567. 586. 604. 623. 641. 659. 678. 696. 715.

9. 8.

203


Unit Time 85 85 85 85 85 85 85 85 85 85 86 86 86 86 86 86 86


6 7 8 9 10

3. 5. 7. 10. 13. 34. 60. 91. 125. 160.

29. 54. 84. 118. 152. 189. 225. 259. 293.

1

1.

3.

2 4

2. 3. 3.

26. 57. 93.

5

5.

6 7 8 9 10

29. 61. 97. 140. 182. 40. 64. 94.

135. 177.

1

2 3

4 5

3

86 86 86 87 1 87 2 87 3 87 4 87 5 87 6 87 7 87 8 87 9 87 10 88 1 88 2 88 3 88 4 88 5 88 6 88 7 88 8 88 9 88 10

131. 171.

218. 268. 319. 373. 428. 60. 95. 139. 189. 243. 299. 357. 416. 476.

532.

9.

221. 266. 307. 347. 162.

209. 260. 310. 365. 419. 476. 533. 586. 640. 232. 288. 347. 406. 465. 522. 579. 637. 691. 743.

113. 147. 183.

218. 252. 286. 321. 354. 383. 413. 132. 174.

217. 262. 301. 342. 384. 424. 458. 492. 356. 411. 467. 525. 577. 631. 685. 736. 788. 838. 455. 511. 569. 627. 680. 733. 785. 833. 879. 928.

248. 281. 315. 347. 376. 406. 436. 465. 494. 520. 301. 341. 383. 422. 456. 490. 525. 559. 593. 622. 569. 623. 677. 729. 781. 831. 884. 934. 980. 1028. 670. 722. 775. 823. 869. 917. 963. 1008. 1049. 1092.


23. 29. 59. 88. 118. 148. 178. 1.

2. 3. 4. 6. 42. 78. 114. 151. 187. 99. 130. 162. 194.

226. 266. 305. 345. 384. 424. 115. 162. 209. 256. 302. 349. 396. 443. 490. 537.

32. 34. 35. 37. 87. 119. 150. 182. 214. 245.

48. 45. 42. 39. 142. 171. 200. 230. 259. 289.

42. 40. 39. 37. 164. 195. 225. 256. 287. 317.

6. 7.

8.

8. 8. 8. 162.

8. 8. 7. 6. 194.

210. 257. 305. 352. 400. 411. 415. 418. 421. 458. 471. 484. 498. 511. 525. 516. 535. 553. 572. 590. 608. 627. 645. 663. 682.

240. 287. 334. 380. 427. 493. 490. 487. 484. 521. 528. 534. 541. 548. 555. 590. 593. 597. 601. 604. 608. 611. 615. 619. 622.

7. 8. 79. 124. 168.

213. 257. 301. 278. 296. 314. 332. 365. 392. 420. 447. 474. 502. 331. 368. 405. 441. 478. 515. 551. 588. 625. 661.

204


Unit Time 89 89 89 89 89 89 89 89 89

1

2 3

4 5

6 7 8

9

89 10 90 90 90 90 90 90 90 90 90

1

2 3

4 5

6 7 8 9

90 10 91 91 91 91 91 91 91 91 91 91

92 92 92 92 92 92 92 92 92

1

2 3

4 5

6 7 8

9 10 1

2 3

4 5

6 7 8 9

92 10

Individual Tree Selection First Second Third Fourth 60. 93. 135. 184. 235. 288. 345. 401. 457. 509. 40. 62. 91. 124. 160. 196. 235. 274. 313. 349. 12. 20. 32. 73. 123. 179.

243. 307. 373. 438. 43. 72. 113. 164.

226. 292. 363. 444. 523. 604.

225. 436. 632. 278. 488. 678. 334. 540. 725. 391. 593. 764. 446. 642. 803. 499. 687. 844. 550. 734. 878. 604. 773. 918. 652. 811. 951. 698. 852. 987. 160. 313. 767. 834. 196. 349. 235. 384. 901. 274. 421. 964. 313. 454. 1023. 349. 485. 1082. 384. 517. 1137. 421. 543. 1190. 454. 569. 1237. 485. 597. 1289. 114. 345. 792. 890. 165. 405. 462. 977. 224. 288. 524. 1069. 354. 585. 1161. 420. 644. 1248. 481. 696. 1331. 748. 1407. 543. 604. 799. 1483. 663. 848. 1559. 226. 523. 837. 292. 604. 916. 363. 680. 991. 444. 759. 1061. 523. 836. 1127. 604. 914. 1197. 680. 989. 1257. 759. 1059. 1315. 836. 1125. 1372. 914. 1194. 1429.

Group Selection First Second Third Fourth 104. 160. 216. 272. 328. 384. 440. 496. 551.

607. 72. 111. 149. 188.

227. 265. 304. 343. 381. 420. 20. 36. 53. 109. 165. 221. 277. 334. 390. 446. 71. 145. 218. 292. 365. 439. 512. 586.

659. 733.

319. 362. 406. 449. 493. 536. 579. 623. 666. 710. 220. 250. 280. 310. 340. 370. 400. 430. 460.

490. 69. 84. 179.

243. 308. 372. 437. 501. 565. 630. 274. 338. 401. 465. 528. 592. 655. 719. 782. 846.

484. 505. 526. 547. 568. 589. 611. 632. 653. 674. 334. 349. 364. 379. 393. 408. 423. 437. 452. 467. 119. 128. 311. 373. 435. 497. 559. 621. 683. 745. 451. 494. 537. 580. 623. 666. 709. 752. 795. 838.

515. 526. 538. 550. 562. 574. 585. 597. 609. 621. 356. 364. 372. 381. 389. 398. 406. 414. 423. 431. 120. 125. 344. 403. 462. 521. 580. 639. 699. 758. 413. 443. 473. 503. 533. 564. 594. 624. 654. 684.

205


Unit Time 93 93 93 93 93 93 93 93 93 93 94 94 94 94 94 94

1

2 3

4 5

6 7 8

9 10 1

2 3

4 5

6 7

94 94 8 94 9 94 10 95 1 95 2 95 3 95 4 95 5 95 6 95 7 95 8 95 9 95 10 96 1 96 2 96 3 96 4 96 5 96 6 96 7 96 8 96 9

96 10

Individual Tree Selection First Second Third Fourth 35. 63. 106. 161. 229. 305. 384. 470. 562. 651. 4. 7. 13. 45. 87. 136. 192.

248. 306. 364. 39. 59. 83. 112. 145. 179.

214. 250. 287. 324. 2. 6. 11. 18.

27. 35. 44. 54. 62. 71.

213. 290. 368. 455. 546. 636. 722. 814. 898. 988. 87. 136. 192. 248. 306. 364. 417. 471. 526. 578. 125. 159. 193. 229. 266. 302. 340. 377. 413. 449. 24. 33. 42. 51. 60. 69. 78. 87. 95. 104.

531. 620. 707. 799. 883. 973. 1053. 1131. 1207. 1279. 306. 364. 417. 471. 526. 578. 622. 666. 711. 754. 247. 282. 319. 356. 391. 428. 462. 497. 530. 564. 58. 66. 76. 85. 93. 101. 109. 118. 125. 133.

1055. 1173. 1280. 1385. 1488. 1588. 1678. 1772. 1854. 1940. 526. 578. 622. 666. 711.

754. 798. 834. 871. 908. 447. 493. 538. 584. 627. 672. 715. 754. 794. 833. 92. 100. 109. 117. 125. 133. 141. 148. 155. 163.

Group Selection First Second Third Fourth 59. 130. 202. 274. 345. 417.

488. 560. 631. 703. 7. 12. 18.

65. 113. 160.

207. 255. 302. 349. 71. 94. 117. 140. 164. 188.

212. 235. 259. 283. 5.

12. 19. 27. 34. 41. 48. 55. 62. 70.

246. 313. 381. 449. 516. 584. 652. 719. 787. 854. 23. 29. 117. 174. 232.

289. 346. 403. 460. 517. 195.

213. 233. 252. 271. 291. 310. 329. 348. 368. 34. 40. 45. 50. 55. 60. 66. 71. 76. 81.

423. 469. 514. 560. 606. 652. 698. 743. 789. 835. 38. 42. 229. 289. 349. 409. 469. 529. 590. 650. 313. 322. 335. 345. 355. 365. 375. 385. 395. 405. 49. 53. 58. 62. 66. 70. 74. 79. 83. 87.

415. 438. 461. 484. 508. 531. 554. 577. 600. 624. 42. 44. 269. 327. 386. 444. 503. 561. 619. 678. 369. 366. 368. 367. 365. 364. 362. 361. 359. 358. 47. 52. 58. 63. 69. 74. 80. 85. 91. 96.

206


Unit Time 97 97 97 97 97 97 97 97 97 97 98 98 98 98 98 98 98 98 98 98 99 99 99 99 99 99 99 99 99 99 100 100 100 100 100 100 100 100 100

1

2 3

4 5

6 7 8

9 10 1

2 3

4 5

6 7 8

9 10 1

2 3

4 5

6 7 8

9 10 1

2 3

4 5

6 7 8

9

100 10

Individual Tree Selection First Second Third Fourth 32. 54. 84. 128. 182. 240. 304. 369. 436. 500. 36. 62. 96. 138. 187.

242. 302. 364. 428. 495. 22. 38. 58. 84. 116. 150. 187. 226. 266. 306. 43. 65. 95. 131. 169.

210. 253. 299. 341. 385.

181.

239. 302. 367. 435. 498. 559. 623. 682. 740. 168. 223. 283. 345. 409. 476. 539. 605. 671. 734. 116. 150. 187.

226. 266. 306. 345. 385. 424. 462. 151. 192. 235. 281. 323. 367. 411. 457. 498. 538.

434. 497. 558. 622. 680. 738. 790. 843. 891. 936. 390. 457. 520. 586. 652. 715. 778. 835. 896. 949. 266. 306. 345. 385. 424. 462. 499. 533. 568. 598. 305. 349. 393. 439. 480. 520. 559. 599. 634. 669.

773. 850. 918. 989. 1054. 1115. 1177. 1233. 1287. 1342. 657. 724. 790. 851. 916. 972. 1030. 1085. 1138. 1190. 440. 480. 519. 556. 593. 626. 660. 691. 722. 752. 463. 504. 543. 583. 618. 653. 689. 720. 752. 782.

Group Selection First Second Third Fourth 52. 95. 138. 197. 255. 314. 372. 431. 490. 548. 67. 127. 186.

245. 304. 363. 422. 481. 541. 600. 42. 78. 114. 150. 187. 223. 259. 296. 332. 369. 85. 129. 172. 216.

259. 303. 346. 390. 433. 477.

182.

222. 293. 352. 411. 470. 529. 588. 647. 706. 253. 303. 353. 403. 453. 503. 553. 603. 653. 703. 154. 185.

217. 249. 281. 312. 344. 376. 408. 439. 244. 275. 307. 338. 370. 401. 433. 464. 496. 527.

315. 337. 428. 471. 515. 558. 602. 645. 688. 732. 379. 411. 443. 475. 506. 538. 570. 601. 633. 665. 241. 260. 281. 300. 320. 340. 359. 379. 398. 418. 366. 384. 401. 419. 437. 455. 472. 490. 508. 526.

316. 332. 431. 468. 504. 541. 578. 615. 652. 688. 348. 370. 391. 413. 435. 457. 479. 501. 523. 544. 227. 241. 256. 270. 284. 298. 311. 325. 339. 353. 381. 387. 394. 400. 407. 413. 420. 426. 433. 439.


Unit Time 101 101 101 101 101 101 101 101 101

1

2 3

4 5

6 7 8

9

101 10 102 102 102 102 102 102 102 102 102

1

2 3

4 5

6 7 8 9

102 10 103 103 103 103 103 103 103 103 103

1

2 3

4 5

6 7 8

9

103 10 104 104 104 104 104 104 104 104 104

1

2 3

4 5

6 7 8

9

104 10

Individual Tree Selection Group Selection First Second Third Fourth First Second Third Fourth 30. 48. 73. 103. 134. 169. 207. 244. 284. 323. 20. 34. 51. 71. 92. 115. 139. 162. 187. 211. 37. 60. 90. 127. 166. 208. 255. 301. 350. 398. 31. 67. 112. 167. 227. 290. 356. 423. 487. 551.

134. 169.

207. 244. 284. 323. 360. 399. 435. 470. 92. 115. 138. 162. 187. 211. 237. 261. 285. 309. 166.

208. 255. 301. 350. 398. 444. 492. 536. 580. 207. 269. 335. 403. 467. 530. 593. 656. 713. 770.

284. 323. 360. 399. 435. 470. 506. 537. 568. 599. 187. 210. 236. 261. 284. 309. 332. 356. 379. 402. 350. 398. 444. 492. 536. 580. 624. 661. 701. 738. 447. 510. 572. 635. 692. 750. 803. 855. 906. 953.

441. 478. 514. 546. 578. 610. 640. 671. 693. 722. 294. 320. 345. 370. 394. 418. 444. 466. 489. 510. 539. 584. 628. 666. 706. 744. 781. 818. 846. 880. 686. 745. 800. 853. 907. 954. 1001. 1046. 1090. 1131.

67. 107. 147. 187. 227. 267. 307. 346. 386. 426. 49. 60. 71. 81. 92. 103. 114. 125. 135. 146. 83. 132. 181.

230. 280. 329. 378. 427. 476. 525. 46. 99. 152. 207. 261. 316.

371. 425. 480. 535.

213. 242. 272. 302. 331. 361. 391. 421. 450. 480. 128. 136. 145. 154. 162. 171. 180. 189. 197.

206. 262. 299. 335. 372. 409. 445. 482. 518. 555. 592. 183.

241. 302. 362. 421. 481. 541. 601. 661. 720.

362. 373. 384. 396. 407. 419. 430. 442. 453. 465. 209. 214. 219. 224. 229. 234. 239. 244. 249. 254. 446. 460. 474. 488. 502. 516. 530. 545. 559. 573. 327. 378. 437. 490. 543. 596. 649. 702. 755. 808.

349. 357. 364. 371. 378. 385. 392. 400. 407. 414. 265. 261. 257. 253. 249. 245. 241. 237. 233. 229. 431. 439. 448. 457. 466. 475. 484. 493. 501. 510. 384. 423. 471. 512. 554. 595. 636. 678. 719. 760.

208


Unit Time 105 105 105 105 105 105 105 105 105

1

16.

2

25. 36. 52. 71. 95.

3

4 5

6 7 8

9

105 10 106 106 106 106 106 106 106 106 106

1

2 3

4 5

6 7 8 9

106 10 107 107 107 107 107 107 107 107 107

1

2 3

4 5

6 7 8

9

107 10 108 108 108 108 108 108 108 108 108


1

2 3

4 5

6 7 8

9

108 10

121. 151. 180.

210. 6. 9. 13. 19.

26. 33. 41. 51. 60. 69. 23. 36. 54. 73. 97. 121. 146. 170. 196.

220. 78. 122. 178. 242. 311. 382. 457. 533. 607. 677.

61. 152. 83. 181. 107. 211. 135. 244. 162. 274. 193. 307. 225. 345. 260. 376. 292. 410. 325. 444. 48. 20. 58. 27. 68. 36. 45. 79. 54. 89. 64. 100. 74. 112. 85. 122. 95. 132. 143. 105. 97. 196. 121. 220. 146. 246. 170. 270. 196. 294. 220. 316. 246. 336. 270. 356. 294. 376. 316. 395. 288. 560. 359. 631. 434. 701. 510. 773. 584. 839. 654. 901. 724. 964. 796. 1018. 862. 1071. 925. 1126.

267. 298. 334. 364. 397. 431. 466. 500. 532. 564. 84. 95. 107. 117. 128. 138. 150. 160. 171. 181. 490. 536. 581. 626. 670. 711. 747. 784. 820. 854. 846. 912. 978. 1036. 1093. 1151. 1202. 1258. 1306. 1357.


20. 27. 34. 41. 48. 56. 63. 70. 77. 37. 60. 83. 106. 129. 151. 174. 197.

220. 243. 133.

207. 280. 354. 428. 502. 575. 649. 723. 796.

154. 168. 182. 196. 213. 229. 245. 261. 277.

294. 54. 58. 63. 68. 72. 77. 81. 86. 91. 95. 113. 132. 151. 170. 189.

209. 228. 247. 266. 285. 407. 466. 525. 583. 642. 701. 760. 819. 878. 936.

199. 196. 193. 190. 196. 195. 195. 194. 194. 194. 69. 68. 66. 65. 64. 62. 61. 60. 58. 57. 181. 193.

205. 216. 228. 240. 251. 263. 274. 286. 622. 652. 683. 713. 744. 775. 805. 836. 867. 897.

195. 183. 171. 158. 156. 146. 136. 127. 117. 107. 67. 63. 58. 54. 49. 44. 40.

35. 31. 26. 192. 199. 205. 212. 218. 224. 231. 237. 244. 250. 665. 681. 697. 712. 728. 744. 760. 776. 792. 807.

209


Unit Time 109 109 109 109 109 109 109 109 109

1

2 3

4 5

6 7 8

9

109 10 110 110 110 110 110 110 110 110 110

19.

2

31. 46. 63. 82. 102. 123. 143. 165. 186.

3

4 5

6 7 8 9

112. 157.

207. 260. 318. 375. 432. 490. 549. 605. 80. 100. 120. 140. 162. 183.

205. 226. 247. 268.

1

3.

11.

2

4.

3

6. 8. 11. 57. 114. 179.

49. 97.

4 5

6 7 8

9

111 10 112 112 112 112 112 112 112 112 112

32. 54. 81. 116. 160. 209. 262. 318. 376. 433.

1

110 10 111 111 111 111 111 111 111 111 111


1

2 3

4 5

6 7 8

9

112 10

252. 325. 28. 44. 65. 90. 141. 200. 264. 336. 405. 476.

154.

220. 293. 369. 446. 517. 588. 135. 189.

248. 315. 385. 456. 528. 594. 660. 726.

270. 324. 377. 432. 491. 547. 602. 655. 706. 756. 159. 180.

203. 224. 244. 265. 286. 307. 326. 347. 220. 285. 353. 422. 485. 555. 628. 696. 756. 816. 379. 445. 512. 574. 640. 706. 768. 826. 883. 936.

455. 511. 565. 619. 673. 726. 780. 832. 883. 932. 242. 264. 284. 305. 325. 345. 367. 385. 403. 421. 684. 809. 939. 1066. 1177. 1298. 1420. 1537. 1646. 1747. 675. 742. 805. 863.

925. 984. 1044. 1103. 1154. 1208.

Group Selection First Second Third Fourth 49. 89. 130. 174.

223. 272. 321. 370. 419. 468. 44. 53. 63. 73. 82. 92. 102. 111. 121. 131. 4. 6. 9. 11. 14. 78. 142.

206. 270. 334. 48.

185.

217. 256. 302. 345. 387. 430. 472. 515. 557. 113. 121. 129. 137. 145. 153. 160. 168. 176. 184. 12. 14. 16. 18. 143.

221. 299. 378. 456. 535.

72. 96. 121. 181.

138. 159. 180. 272. 338.

241. 302. 362. 422. 483.

404. 469. 535. 601. 666.

302. 313. 340. 378. 401. 424. 447. 470. 493. 516. 185. 190. 194. 199.

203. 208. 212. 217. 221. 226. 19.

20. 22. 23. 293. 377. 461. 545. 629. 713. 211. 225. 240. 413. 476. 539. 602. 665. 728. 791.

291. 292. 311. 342. 354. 366. 378. 390. 402. 414. 235. 232. 228. 225. 221. 218. 214. 211. 207. 204. 20. 21. 22. 22. 349. 432. 515. 598. 680. 763. 244. 252. 259. 459. 514. 570. 626. 682. 737. 793.

210


Unit Time 113 113 113 113 113 113 113 113 113

1

2 3

4 5 6

7 8 9

Individual Tree Selection First Second Third Fourth 0. 0. 0. 0. 1.

25. 55. 88.

115 10

127. 165. 62. 102. 149. 206. 266. 334. 406. 481. 555. 627. 24. 44. 77. 122. 177. 243. 308. 381. 460. 535.

116 116 116 116 116 116 116 116 116

1

13.

2

6 7 8 9

22. 34. 52. 74. 97. 123. 149. 176.

116 10

202.

113 10 114 114 114 114 114 114 114 114 114

1

2 3

4 5

6

7 8

9

114 10 115 115 115 115 115 115 115 115 115

1

2 3

4 5

6 7 8 9

3

4 5

1.

18.

42. 69. 101. 139. 179.

219. 255. 292. 229. 297. 369. 444. 518. 590. 661. 734. 801. 870. 177.

243. 308. 381. 460. 535. 609. 689. 761. 838. 69. 90. 114. 140. 168. 194. 219. 246. 271. 296.

330. 393. 457. 520. 230. 576. 267. 638. 305. 702. 341. 762. 372. 819. 404. 871. 481. 729. 553. 798. 624. 861. 697. 920. 764. 978. 833. 1032. 896. 1085. 955. 1134. 1013. 1185. 1067. 1231. 460. 1160. 535. 1303. 609. 1436. 689. 1572. 761. 1701. 838. 1828. 905. 1940. 970. 2057. 1036. 2164. 1095. 2265. 163. 263. 187. 286. 210. 309. 237. 333. 262. 355. 287. 376. 310. 398. 333. 418. 354. 438. 374. 457. 101. 132. 166. 199.


34. 67. 101. 134. 168. 85. 142. 200. 257. 315. 378. 442. 506. 569. 633. 45. 102. 159.

216. 274. 331. 388. 445. 502. 559. 23. 42. 61. 85. 109. 132. 156. 179.

203. 227.

0. 0. 0. 0. 67. 108. 150. 191. 233.

275. 257. 313. 368. 424. 491. 555. 618. 681. 744. 807. 194. 250. 305. 360. 416. 471. 526. 582. 637. 693. 84. 101. 126. 148. 170. 192.

213. 235. 257. 279.

0. 0. 0. 0. 147. 192.

237. 282. 327. 372. 420. 458. 496. 534. 598. 644. 690. 736. 782. 828. 334. 372. 409. 446. 483. 521. 558. 595. 632. 670. 143. 151. 177. 190. 204. 217. 230. 244. 257. 270.

0. 0. 0. 0. 178.

222. 267. 312. 356. 401. 475. 493. 511. 530. 580. 607. 633. 660. 686. 712. 336. 352. 369. 385. 402. 418. 435. 451. 468. 484. 138. 142. 169. 179. 189. 199. 209. 219. 229.

239.

211


Unit Time 117 117 117 117 117 117 117 117 117

1

2 3

4 5

6 7 8

9

117 10 118 118 118 118 118 118 118 118 118

1

2 3

4 5

6 7 8

9

118 10 119 119 119 119 119 119 119 119 119

6. 10. 15.

22. 33. 46. 61. 78. 96. 114. 35. 59. 91. 130. 176. 227.

281. 339. 397. 456.

1

13.

2

24. 37. 56. 82. 113. 150. 191.

3

4 5

6 7 8 9

119 10 120 120 120 120 120 120 120 120 120


1

2 3

4 5

6 7 8

9

120 10

234. 279. 34. 58. 89. 128. 175.

227. 283. 343. 403. 467.

31. 45. 59. 76. 94. 112. 130. 150. 170. 189. 163. 214. 268. 325. 384. 443. 500. 560. 618. 673. 73. 104. 141. 182. 225.

270. 315. 362. 412. 457. 161.

214. 270. 329. 390. 453. 513. 576. 639. 699.

92. 110. 129. 149. 168. 187.

208. 226. 245. 264. 371. 430. 487. 546. 605. 660. 715. 766. 819. 864. 216. 261. 306. 353. 402. 447. 497. 540. 584. 629. 376. 440. 500. 562. 626. 685. 745. 799. 858. 907.

Group Selection First Second Third Fourth

184.

17.

207. 232. 253. 277. 299. 323. 345. 367. 388. 593. 649. 704. 755. 807. 853. 901. 945. 988.

29. 42. 54. 69. 84. 98. 113. 127. 142. 62. 116. 170. 224. 277. 331. 385. 438. 492. 546. 36. 68.

1031.

411. 459. 512. 559. 607. 655. 704. 752. 799. 843. 984. 1104. 1221. 1334. 1452. 1558. 1666. 1765. 1867. 1960.

100. 133. 165. 198.

230. 262. 295. 327. 64. 120. 176. 233. 289. 345. 401. 457. 513. 569.

76. 83. 91. 103. 113. 123. 134. 144. 154. 164. 230. 277. 323. 369. 416. 462. 508. 555. 601. 647. 171. 188. 206. 224. 242. 259. 277. 295. 313. 330. 241. 289. 336. 383. 430. 478. 525. 572. 620. 667.

109. 106. 104. 110. 110. 110. 111. 111. 111. 111.

356. 385. 413. 442. 470. 499. 527. 556. 584. 613. 259. 252. 246. 239. 232. 226. 219. 213. 206. 200. 360. 390. 420. 450. 480. 510. 540. 570. 600. 630.

99. 92. 85. 89. 85. 80. 76. 72. 67. 63. 335. 354. 374. 394. 414. 433. 453. 473. 493. 513. 211. 196. 180. 165. 150. 135. 119. 104. 89. 73. 330. 351. 372. 392. 413. 433. 454. 475. 495. 516.

212


Unit Time 121 121 121 121

121 121 121 121 121

1

2 3

4 5

6 7 8 9

121 10 122 122 122 122 122 122 122 122 122

1

2 3

4 5

6 7 8 9

122 10 123 123 123 123 123 123 123 123 123

1

2 3

4 5

6 7 8

9

123 10 124 124 124 124 124 124 124 124 124

1

2 3

4 5

6 7 8

9

124 10


21. 30. 40. 51. 65. 78. 91. 30. 50. 78. 119. 169.

223. 283. 345. 408. 469. 3. 6. 8.

12. 16. 22. 27. 34. 41. 48. 46. 76. 113. 159.

208. 260. 316. 372. 427. 482.

29. 39. 51. 64. 77. 91. 105. 121. 136. 151. 169. 222. 282. 344. 407. 468. 527. 587. 645. 700. 14.

20. 25. 32. 39. 46. 53. 62. 69. 77. 204. 256. 312. 368. 423. 477. 529. 583. 633. 683.

76. 148. 90. 165. 105. 185. 121. 202. 135. 220. 151. 239. 258. 168. 182. 276. 198. 294. 214. 311. 407. 644. 467. 699. 525. 750. 586. 802. 643. 849. 699. 893. 750. 939. 802. 981. 848. 1021. 892. 1061. 37. 65. 44. 73. 51. 82. 60. 89. 67. 97. 75. 105. 84. 113. 91. 121. 99. 129. 107. 136. 419. 625. 473. 676. 525. 720. 579. 762. 629. 804. 679. 843. 724. 880. 766. 914. 808. 949. 846. 981.


26. 36. 46. 56. 65. 75. 85. 95. 104. 50. 93. 135. 190. 245. 300. 355. 410.

465. 520. 8.

14.

20. 25. 31. 37. 42. 48. 54. 59. 76. 125. 174.

223. 272. 321. 370. 419. 468. 517.

73. 79. 85. 92. 98. 104. 110. 116. 123. 129. 182. 220. 282. 336.

93. 92. 90. 88. 86. 84. 82. 80. 79. 77. 311. 330. 405. 441.

389. 442. 495. 549. 602. 655. 37. 41. 44. 48.

477. 514. 550. 586. 622. 659.

52. 55. 59. 62. 66. 69.

233. 278. 323. 367. 412. 457. 502. 547. 591. 636.

51. 50. 49. 48. 47. 46. 44. 43. 42. 41. 371.

400. 429. 458. 488. 517. 546. 575. 604. 633.

91. 85. 78. 72. 66. 60. 53. 47. 41. 34. 305. 318. 398. 427. 456. 486. 515. 544. 574. 603. 48. 45. 42. 38. 35. 31. 28. 25. 21. 18.

409. 423. 437. 451. 465. 478. 492. 506. 520. 534.

213


Unit Time 125 125 125 125 125 125 125 125 125

1

20. 31. 45. 62. 82. 102. 123. 144. 165. 185. 9.

2

17.

3

5

30. 48. 71. 98. 126. 155. 188. 219. 21. 36. 56. 82. 113.

6 7

148. 185.

8

225. 266. 309. 62. 101.

1

2 3

4 5

6 7 8 9

125 10 126 126 126 126 126 126 126 126 126

4 5

6

7 8

9

126 10 127 127 127 127 127 127 127 127 127

1

2 3

4

9

127 10 128 128 128 128 128 128 128 128 128


1

2 3

150.

4

208. 276. 349. 425. 507. 586. 663.

5

6 7 8 9

128 10

82. 102. 123. 144. 165. 185.

207. 227. 248. 267. 71. 98. 126. 155. 188.

219. 250. 284. 313. 345. 113. 148. 185.

225. 266. 309. 350. 392. 435. 475. 276. 348. 425. 507. 585. 662. 740. 816. 889. 961.

165. 185.

207. 227. 248. 267. 283. 301. 317. 333. 188.

219. 250. 284. 313. 345. 373. 400. 428. 452. 266. 309. 350. 392. 435. 475. 516. 552. 591. 624. 585. 662. 739. 816. 888. 960. 1027. 1093. 1156.

413. 452. 490. 528. 565. 600. 630. 661. 691. 720. 501. 565. 623. 684. 741. 797. 847. 899. 946. 991. 701. 784. 866. 944. 1026. 1099.

1174. 1243. 1313. 1377. 919. 995. 1066. 1136. 1203. 1267. 1330. 1390. 1446. 1215. 1505.


41. 64. 86. 109. 132. 155. 178. 201. 224. 43. 81. 119. 156. 194. 232. 269. 307. 345. 382. 115. 167.

219. 271. 332. 393. 453. 514. 575. 636.

95. 111. 127. 144. 160. 176. 192.

208. 225. 241. 77. 100. 123. 145. 168. 190.

213. 236. 258. 281. 162. 194.

226. 258. 289. 321. 353. 385. 416. 448. 335. 378. 420. 481. 534. 588. 642. 695. 749. 803.

153. 163. 173. 182. 192.

202. 212. 222. 231. 241. 133. 149. 164. 179. 194. 209. 224. 239. 255. 270. 242. 262. 282. 303. 323. 343. 363. 383. 403. 423. 519. 547. 575. 643. 683. 723. 764. 804. 844. 885.

162. 168. 173. 179. 184. 189. 195.

200. 206. 211. 136. 142. 148. 154. 160. 167. 173. 179. 185. 191.

222. 236. 250. 264. 277. 291. 305. 319. 333. 347. 577. 592. 607. 669. 696. 723. 750. 777. 804. 831.

214


Unit Time 129 129 129 129 129 129 129 129 129

1

4.

15.

2

6. 8. 11. 15.

33. 56. 82. 113. 143. 174. 206. 234. 263. 311. 388. 470. 550. 632. 712. 791. 868. 945. 1017. 40. 56. 75. 96. 117. 139. 161. 183. 206. 227. 417. 508. 607. 701. 795. 890. 979. 1070. 1157. 1235.

3

4 5

6 7 8

9

129 10 130 130 130 130 130 130 130 130 130

1

2 3

4 5

6 7 8

9

130 10 131 131 131 131 131 131 131 131 131


1

2 3

4

33. 56. 83. 113. 143. 74. 116. 172. 238. 311. 388. 470. 551. 632. 713. 7. 11. 18.

9

26. 40. 56. 75. 96. 117. 139. 114. 177. 252. 336. 430. 521. 620. 714. 807.

132 10

903.

5

6 7 8

9

131 10 132 132 132 132 132 132 132 132 132

1

2 3

4 5

6 7 8

112. 142. 174. 205. 234. 263. 293. 321. 345. 370. 632. 712. 790. 868. 945. 1017. 1085. 1149. 1211. 1270. 117. 139. 161. 183. 206. 227. 249. 269. 288.

307. 782. 877. 966. 1057. 1144. 1222. 1295. 1366. 1434. 1500.


254. 11. 286. 13. 318. 16. 348. 19. 375. 22. 402. 47. 430. 73. 456. 98. 483. 123. 506. 148. 945. 150. 1017. 231. 1085. 312. 1149. 393. 1211. 474. 1271. 555. 1328. 636. 1384. 716. 1437. 797. 1485. 878. 227. 18. 253. 32. 280. 45. 305. 59. 329. 76. 353. 94. 377. 111. 400. 129. 422. 147. 442. 164. 169. 1132. 1210. 261. 1283. 354. 1354. 447. 1422. 539. 1488. 632. 1554. 725. 1607. 817. 1668. 910. 1724. 1003.

29. 30. 32. 34. 80. 110. 140. 169. 199. 229. 469. 531. 593. 655. 717. 779. 841. 902. 964. 1026. 70. 78. 86. 103. 116. 129. 142. 156. 169. 182.

494. 574. 653. 733. 812. 892. 971. 1051. 1131. 1210.

38. 39. 40. 40. 140. 171. 202. 233. 264. 295. 699. 730. 762. 793. 825. 857. 888. 920. 951. 983. 107. 108. 108. 126. 132. 138. 144. 150. 155. 161. 762. 810. 857. 904. 951. 998. 1045. 1092. 1139. 1186.

37. 38. 39. 40. 160. 191. 222. 253. 284. 315. 718. 732. 747. 762. 777. 792. 806. 821. 836. 851. 95. 92. 88. 107. 110. 112. 115. 117. 119. 122. 786. 814. 842. 871. 899. 927. 955. 983. 1012. 1040.

215


Unit Time 133 133 133 133 133 133 133 133 133

1

2 3

4 5

6 7 8 9

133 10 134 134 134 134 134 134 134 134 134

228. 298. 373. 452. 533. 612. 689. 2.

2

3. 5. 7. 18.

3

4 5

6 7 8

9 1

2 3

4 5

6 7 8 9

135 10 136 136 136 136 136 136 136 136 136

65. 109. 163.

1

134 10 135 135 135 135 135 135 135 135 135


1

2 3

4 5

6 7 8

9

136 10

33. 51. 71. 92. 113. 23. 40. 60. 85. 114. 146. 182.

268. 547. 817. 342. 623. 888. 420. 695. 952. 499. 772. 1012. 577. 843. 1074. 655. 915. 1131. 728. 980. 1186. 806. 1041. 1236. 877. 1103. 1289. 950. 1159. 1337. 18. 33. 51. 71. 92. 113. 135. 156. 177. 198. 96. 129. 164.

202. 241. 278. 316. 220. 355. 259. 393. 296. 429. 80. 330. 125. 412. 185. 497. 251. 582. 331. 668. 414. 751. 500. 840. 585. 923. 672. 1007. 754. 1082.

92. 113. 135. 156. 177. 198.

219. 237. 255. 273. 223. 260. 298. 337. 375. 411. 447. 482. 515. 546. 667. 749. 837. 920. 1004. 1079. 1147. 1218. 1284. 1351.

181.

203. 224. 243. 262. 281. 300. 319. 336. 352. 358. 394. 430. 465. 498. 529. 562. 593. 623. 653. 1029. 1107. 1178. 1252. 1320. 1390. 1449. 1510. 1569. 1622.


224. 290. 357. 424. 492. 559. 626. 694. 5. 14.

23. 32. 54. 76. 98.

281. 346. 411. 479. 545. 612. 678. 745. 811. 878. 22. 28. 34.

127.

66. 89. 112. 134. 157. 180. 202. 152. 178. 203. 229. 255. 281. 306. 332. 358. 384. 385.

205. 283. 361. 440. 518. 597. 675. 754. 832.

451. 517. 582. 649. 715. 781. 847. 914. 980.

121. 143. 165. 39. 72. 105. 138. 171. 204.

237. 270. 303. 336.

467. 512. 556. 607. 654. 701. 747. 794. 841. 888. 60. 58. 56. 114. 130. 147. 163. 179. 196. 212. 250. 259. 267. 276. 284. 293. 301. 310. 319. 327. 620. 660.

700. 740. 782. 822. 863. 903. 943. 984.

533. 555. 576. 604. 627. 650. 673. 696. 719. 742. 47. 44. 41. 110. 125. 140. 155. 170. 185. 200. 232. 234. 237. 239. 242. 245. 247. 250. 252. 255. 658.

680. 702. 724. 748. 771. 793. 816. 839. 861.

216


Unit Time 137 137 137 137 137 137 137 137 137

1

2 3

4 5

6 7 8 9

137 10 138 138 138 138 138 138 138 138 138

1

2 3

4 5

6

7 8

9

138 10 139 139 139 139 139 139 139 139 139

1

2 3

4 5

6 7 8

9

139 10 140 140 140 140 140 140 140 140 140

1

2 3

4 5

6

7 8 9

140 10

Individual Tree Selection First Second Third Fourth 37. 61. 92. 130. 171. 215. 262. 309. 356. 401. 56. 82. 118. 161. 206. 257. 309. 364. 415. 468. 39. 59. 86. 119. 152. 189. 227. 267. 303. 342. 21. 32. 48. 67. 87. 109. 133. 158. 181. 206.

171.

215. 262. 309. 356. 401. 444. 490. 531. 574. 192.

244. 295. 350. 401. 454. 507. 556. 607. 654. 134. 171. 209.

248. 284. 323. 361. 396. 432. 466. 87. 109. 133. 158. 181. 206. 230. 256. 278. 300.

356. 591. 401. 641. 444. 686. 490. 728. 531. 770. 574. 809. 611. 845. 645. 879. 681. 913. 712. 944. 387. 612. 441. 664. 493. 714. 542. 763. 593. 808. 640. 854. 686. 899. 731. 941. 772. 979. 813. 1021. 267. 396. 305. 430. 343. 463. 377. 495. 413. 524. 447. 554. 481. 584. 513. 611. 542. 635. 572. 663. 181. 278. 206. 300. 230. 321. 256. 343. 278. 362. 300. 380. 321. 399. 343. 416. 362. 432. 380. 448.


210. 249. 288. 326. 365. 404. 109. 162. 215. 268. 321. 375. 430. 484. 538. 592. 73. 113. 153. 192. 232. 272. 313. 353. 393. 433. 47. 71. 95.

166.

204. 242. 281. 319. 357. 395. 434. 472. 510. 339. 375. 411. 447. 486. 523. 561. 598. 636. 673. 235. 263. 290. 318. 346. 374. 402. 430. 458. 486.

119. 143. 167. 190.

135. 152. 169. 186. 204. 221. 238.

214. 238. 262.

255. 273. 290.

275. 302. 328. 355. 381. 408. 434. 461. 487. 514. 526. 539. 551. 564. 582. 597. 611. 626. 640. 655. 375. 385. 395. 405. 416. 427. 437. 448. 458. 469. 202. 211. 221. 231. 240. 250. 260. 270. 279. 289.

314. 327. 340. 352. 365. 377. 390. 402. 415. 427. 506. 513. 520. 527. 541. 550. 558. 567. 576. 585. 362. 366. 371. 375. 382. 387. 392. 397. 403. 408. 210. 213. 217. 220. 224. 227. 231. 234. 238. 241.

217


Unit Time 141 141 141 141 141 141 141 141 141

1

5. 8. 11. 16. 20. 25. 30. 36. 41. 47. 0.

23. 28. 34. 39. 45. 50. 56. 62. 2.

2

1.

14.

1

2 3

4 5

6 7 8 9

141 10 142 142 142 142 142 142 142 142 142

3

1.

4

1.

5

2. 14.

6

7 8 9

142 10 143 143 143 143 143 143 143 143 143

1

2 3

4 5

6

7 8

9

143 10 144 144 144 144 144 144 144 144 144


1

2 3

4 5

6 7 8 9

144 10

31. 50. 73. 95. 29. 50. 74. 105. 137. 174. 213. 254. 297. 341. 63. 107. 161. 224. 294. 367. 446. 526. 608. 684.

13. 18.

26. 32. 37. 43. 49. 54. 59. 64. 70. 74. 73. 95. 119. 142. 164. 185.

62. 71. 80. 88. 97. 105. 113. 121. 128. 136. 165. 187.

31. 210. 50. 231. 73. 249. 95. 268. 119. 208. 286. 142. 228. 304. 164. 246. 322. 185. 264. 337. 111. 244. 395. 147. 288. 442. 187. 330. 487. 228. 376. 529. 270. 420. 572. 314. 467. 615. 357. 512. 657. 402. 554. 696. 447. 597. 741. 494. 639. 775. 245. 509. 765. 318. 585. 838. 396. 662. 906. 476. 740. 975. 558. 813. 1037. 634. 885. 1096. 711. 952. 1157. 790. 1021. 1214. 862. 1083. 1269. 934. 1142. 1325.


22. 27. 33. 38. 43. 49. 54. 1. 1.

1. 1.

2. 21. 40. 59. 78. 97. 52. 83. 114. 144. 175. 206. 237. 268. 299. 330. 98. 171. 243. 316. 388. 461. 533. 605. 678. 750.

24. 28. 32. 37. 41. 45. 50. 54. 58. 63.

36. 39. 41. 44. 47. 49. 52. 54. 57. 59.

2. 2. 2. 2.

2. 3. 3. 3. 85. 111. 136. 162. 187.

40. 63. 87. 110. 134. 157. 176. 201. 227. 252. 278.

303. 329. 355. 380. 406. 333. 398. 464. 529. 594. 659. 725. 790. 855. 921.

212. 281. 282. 283. 284. 285. 286. 287. 289. 290. 291. 564. 600. 636. 671. 707. 743. 779. 815. 851. 886.

34. 35. 37. 39. 41. 42. 44. 46. 48. 49. 2. 2. 2. 2. 102. 127. 153. 178.

203. 228. 241. 239. 237. 235. 235. 233. 232. 230. 228. 227. 567. 592. 617. 642. 667. 691. 716. 741. 766. 790.

218


Unit Time 145 145 145 145 145 145 145 145 145

1

2 3

4 5

6 7 8

9

145 10 146 146 146 146 146 146 146 146 146

1

2 3

4 5

6 7 8 9

146 10 147 147 147 147 147 147 147 147 147

1

2 3

4 5

6 7 8

9

147 10 148 148 148 148 148 148 148 148 148

1

2 3

4 5

6 7 8

9

148 10

Individual Tree Selection First Second Third Fourth 5. 8. 12. 17. 23. 51. 86. 127. 173.

218. 37. 57. 81. 109. 141. 172.

205. 239. 273. 306. 8. 11. 14. 18.

23. 29. 36. 43. 51. 60. 57. 81. 110. 151. 199.

251. 301. 354. 410. 465.

23. 49. 83. 121. 165. 211. 258. 306. 350. 394. 129. 160. 193. 228. 262. 294. 329. 363. 395. 428. 18. 24. 32. 39. 47. 55. 63. 72. 80. 88. 199. 251. 301. 354. 410. 465. 516. 568. 620. 670.

165.

209. 254. 300. 342. 386. 431. 474. 511. 548. 251. 283. 317. 352. 384. 417. 449. 481. 511. 543. 42. 51. 59. 67. 76. 84. 92. 102. 111. 119. 410. 465. 516. 568. 620. 670. 722. 774. 823. 873.

344. 387. 431. 472. 508. 546. 584. 621. 658. 690. 380. 414. 447. 480. 511. 544. 574. 604. 634. 663. 75. 83. 92. 102. 111. 120. 130. 139. 147. 158. 650. 704. 759. 815. 868. 922. 976. 1031. 1083. 1135.


22. 59. 96. 133. 170. 207. 76. 96. 117. 137. 157. 177. 197. 217. 237. 258. 18.

26. 34. 43. 51. 59. 67. 75. 84. 92. 156. 194.

233. 271. 309. 348. 386. 425. 463. 501.

31. 33. 35. 37. 107. 152. 197. 241. 286. 331. 220. 232. 245. 257. 269. 282. 294. 306. 319. 331. 63. 63. 62. 62. 62. 62. 61. 61. 61. 61. 421. 443. 465. 487. 509. 531. 553. 575. 597. 619.

41. 42. 44. 45. 197.

245. 293. 341. 389. 437. 346. 353. 359. 365. 372. 378. 385. 391. 398. 404. 81. 76. 71. 66. 61. 56. 51. 46. 42. 37. 556. 564. 573. 581. 589. 598. 606. 614. 623. 631.

34. 35. 37. 38. 222. 269. 317. 364. 411. 459. 362. 364. 365. 367. 369. 370. 372. 374. 376. 377. 57. 56. 54. 52. 51. 49. 47. 46. 44. 43. 529. 542. 555. 569. 582. 596. 609. 622. 636. 649.

219


Unit Time 149 149 149 149 149 149 149 149 149

1

2 3

4 5

6 7 8 9

149 10 150 150 150 150 150 150 150 150 150

1

2 3

4 5

6 7 8

9

150 10 151 151 151 151 151 151 151 151 151

1

2 3

4 5

6 7 8

9

151 10 152 152 152 152 152 152 152 152 152

1

2 3

4 5

6 7 8 9

152 10

Individual Tree Selection First Second Third Fourth 34. 56. 84. 119. 157. 197. 240. 283. 326. 367. 3. 5. 7.

11. 36. 71. 111. 157.

203. 253. 45. 76. 113. 159.

207. 259. 313. 369. 423. 476. 28. 47. 71. 100. 132. 166. 202. 239. 274. 309.

157. 197.

240. 283. 326. 367. 407. 449. 486. 525. 36. 71. 111. 157. 203. 253. 302. 350. 396. 444. 190.

242. 297. 352. 406. 460. 510. 564. 613. 663. 132. 166. 202. 239. 274. 309. 342. 377. 409. 442.

326. 367. 407. 449. 486. 525. 559. 591. 623. 652. 203. 252. 302. 350. 396. 444. 491. 531. 571. 612. 390. 443. 494. 547. 596. 646. 691. 732. 774. 812. 274. 309. 342. 377. 409. 442. 471. 497. 525. 549.

812. 893. 966. 1040. 1110. 1177. 1239. 1296. 1355. 1407. 406. 457. 506. 548. 591. 634. 677. 720. 757. 794. 844. 928. 1004. 1079. 1152. 1222. 1287. 1346. 1407. 1463. 436. 473. 504. 535. 565. 592. 619. 642. 667. 690.


228. 263. 299. 335. 370. 9.

25. 41. 58. 107. 156.

206. 255. 304. 354. 64. 110. 157.

203. 249. 295. 341. 387. 433. 480. 42. 72. 102. 132. 162. 192. 222. 252. 282. 312.

152. 187.

222. 257. 292. 327. 362. 397. 432. 467. 38. 48. 59. 135. 187.

239. 291. 342. 394. 446. 197.

242. 287. 333. 378. 424. 469. 514. 560. 605. 128. 157. 187.

216. 246. 275. 305. 334. 364. 393.

252. 276. 300. 325. 349. 373. 398. 422. 446. 470. 111. 107. 103.

243. 284. 324. 365. 405. 446. 486. 326. 358. 389. 421. 452. 484. 515. 546. 578. 609. 212. 232. 253. 273. 294. 314. 335. 355. 375. 396.

288. 299. 311. 322. 334. 345. 357. 368. 380. 391. 85. 79. 73. 243. 281. 319. 357. 395. 433. 471. 373. 388. 403. 418. 433. 447. 462. 477. 492. 507. 242. 252. 262. 271. 281. 291. 300. 310. 320. 329.

220


Unit Time 153 153 153 153 153 153 153 153 153

1

2 3

4 5

6 7 8

9

153 10 154 154 154 154 154 154 154 154 154

1

2 3

0. 0. 0. 1.

5

33. 76. 125. 183.

6 7 8 9

241. 301.

1

0.

2

1.

3

1.

4

1.

5 6

2. 11. 22. 36. 51. 67. 19. 29. 43. 60. 79. 99. 120. 142. 163. 184.

7 8 9

155 10 156 156 156 156 156 156 156 156 156

35. 58. 87. 118. 156. 202. 249. 298. 349. 398.

4

154 10 155 155 155 155 155 155 155 155 155


1

2 3

4 5

6

7 8

9

156 10

151. 192. 234.

278. 324. 373. 424. 474. 523. 571. 33. 76. 125. 183.

241. 301. 362. 417. 473. 530. 2. 11.

22. 36. 51. 67. 83. 100. 115. 130. 78. 97. 119. 141. 162. 183.

205. 227. 247. 267.

319. 363. 409. 454. 498. 546. 594. 641. 690. 733. 241. 301. 362. 417. 473. 530. 584. 629. 675. 722. 51. 67. 83. 100. 115. 130. 145. 160. 172. 185. 161. 182. 204. 226. 246. 266. 285. 304. 322. 339.

497. 539. 583. 626. 670. 714. 759. 803. 847. 889. 713. 831. 946. 1046. 1148. 1252. 1350. 1441. 1526. 1610. 115. 131. 146. 161. 173. 186. 199. 211. 224. 234. 259. 281. 302. 323. 342. 361. 380. 397. 414. 430.

80. 100. 120. 139. 159. 188. 217. 246. 275. 305.

220. 234. 249. 263. 297. 323. 349. 376. 402. 428.

291. 302. 313. 323. 376. 399. 423. 447. 470. 494.

242. 251. 261. 270. 330. 352. 374. 396. 418. 440.

0. 0. 0.

0. 0. 0.

0. 0. 0.

0. 0. 0.

1.

98. 159.

220. 281. 342. 403. 464.

215. 282. 348. 414. 480. 546. 612.

261. 327. 392. 458. 523. 589. 655.

2. 2. 2. 3.

3. 3. 3. 3.

2. 3. 3. 3.

29. 45. 61. 77. 94. 110. 120. 134. 148. 162. 176. 191.

60. 78. 95. 113. 130. 148. 182. 190. 198.

72. 89. 106. 124. 141. 159. 192. 195. 198.

206. 214. 222. 230. 238. 246. 254.

201. 204. 207. 210. 214. 217. 220.

50. 99. 148. 197. 247. 296. 1. 1.

1. 1.

2. 15.

28. 41. 54. 68. 42. 61. 81. 100. 119. 139. 158. 177. 197. 216.

205. 219. 233. 248.

221


Unit Time 157 157 157 157 157 157 157 157 157

1

2 3

4


9

26. 36. 47. 60. 73. 87.

157 10

102.

158 158 158 158 158 158 158 158 158

5

6 7 8

1

2 3

4 5

6 7 8

9

158 10 159 159 159 159 159 159 159 159 159

1

2 3

4 5

6 7 8 9

159 10 160 160 160 160 160 160 160 160 160

1

2 3

4 5

6 7 8

9

160 10

8. 13.

20. 27. 35. 44. 52. 61. 70. 78. 24. 40. 59. 82. 106. 132. 159. 187. 216. 245. 51. 80. 116. 156. 199. 242.

285. 330. 372. 415.

27. 38. 51. 64. 79. 94. 108. 126. 141. 157. 31. 39. 48. 57. 66. 74. 82. 91. 99. 107. 81. 107. 134. 163. 191. 220. 248. 277. 306. 335. 195. 238. 281. 326. 368. 411. 456. 495. 536. 575.

70. 85. 100. 117. 133. 149. 166. 181. 197. 213. 61. 70. 78. 87. 95. 103. 111. 118. 126. 133. 166. 195. 223. 252. 281. 310. 338. 364. 391. 416. 364. 406. 451. 491. 531. 571. 611.

646. 685. 719.

140. 158. 178. 195.

212. 230. 249. 267. 284. 300. 104. 114. 123. 132. 141. 150. 159. 166. 174. 182.

272. 303. 333. 361. 390. 417. 445. 470. 498. 522. 528. 567. 608. 643. 681. 715. 749. 787. 821. 849.


39. 64. 88. 112. 137. 161. 186. 210. 234. 14.

20. 25. 31. 37. 43. 49. 54. 60. 66. 37. 59. 81. 103. 126. 148. 170. 192. 214. 236. 95. 121. 148. 174. 201. 227. 254. 280. 306. 333.

61. 77. 94. 111. 127. 144. 161. 178. 194. 211. 40. 45. 50. 54. 59. 64. 69. 74. 78. 83. 118. 138. 157. 177. 197. 217. 236. 256. 276. 296. 241. 259. 276. 294. 311. 328. 346. 363. 380. 398.

167. 163. 159. 155. 151. 147. 142. 138. 134. 130. 63. 66. 70. 73. 76. 79. 82. 85. 88. 91. 188. 196.

203. 211. 218. 226. 233. 241. 248. 256. 328. 337. 345. 354. 362. 371. 379. 388. 397. 405.

134. 127. 119. 111. 104. 96. 88. 81. 73. 65. 72. 73. 74. 76. 77. 78. 80. 81. 83. 84. 181. 184. 187. 190. 193. 196. 198.

201. 204. 207. 306. 319. 331. 343. 356. 368. 380. 393. 405. 417.

222


Unit Time 161 161 161 161 161 161 161 161 161

1

2 3

4 5

6 7 8 9

161 10 162 162 162 162 162 162 162 162 162

1

2 3

4 5

6 7 8

9

162 10 163 163 163 163 163 163 163 163 163

1

2 3

4 5

6 7 8

9

163 10 164 164 164 164 164 164 164 164 164

1

2 3

4 5

6 7 8 9

164 10

Individual Tree Selection First Second Third Fourth 29. 50. 75. 102. 134. 166. 197. 231. 264. 297. 29. 47. 71. 102. 133. 168. 204. 241. 277. 313. 27. 44. 64. 91. 121. 154. 191.

227. 265. 304. 59. 82. 110. 148. 192. 242. 291. 344. 399. 454.

121. 153. 185.

219. 252. 285. 318. 351. 383. 414. 133. 167. 204. 241. 277. 312. 346. 382. 414. 447. 121. 154. 191.

227. 265. 304. 343. 381. 419. 456. 182.

231. 281. 333. 389. 444. 495. 548. 600. 651.

240. 272. 306. 339. 371. 402. 433. 465. 497. 525. 277. 312. 346. 381. 414. 447. 476. 503. 530. 555. 265. 304. 343. 381. 419. 456. 491. 527. 567. 605. 379. 434. 485. 538. 590. 641. 693. 744. 793. 843.

359. 390. 421. 452. 485. 512. 542. 570. 599. 626. 691. 759. 822. 884. 944. 1001. 1054. 1102. 1152. 1197. 419. 456. 492. 527. 568. 606. 640. 673. 705. 739. 593. 648. 705. 761. 814. 868. 923. 977. 1029. 1080.

Group Selection First Second Third Fourth 64. 81. 99. 117. 135. 152. 170. 188. 206. 223. 42. 73. 103. 133. 164. 194.

224. 254. 285. 315. 78. 105. 132. 159. 186. 213. 241. 268. 295. 322. 144. 180. 215. 251. 287. 327. 367. 406. 446. 486.

176. 189.

203. 217. 231. 245. 259. 273. 286. 300. 129. 159. 189.

219. 249. 278. 308. 338. 368. 398. 227. 241. 254. 268. 281. 295. 308. 322. 335. 349. 390. 410. 430. 451. 480. 506. 531. 557. 583. 608.

241. 251. 260. 269. 278. 287. 297. 306. 315. 324. 214. 235. 256. 276. 297. 318. 338. 359. 380. 400. 319. 317. 315. 313. 311. 309. 307. 305. 303. 301. 515. 522. 530. 538. 564. 578. 591. 604. 618. 631.

205. 212. 220. 227. 235. 242. 250. 257. 265. 272. 245. 255. 265. 274. 284. 294. 304. 314. 323. 333. 298. 292. 286. 280. 274. 268. 263. 257. 251. 245. 489. 501. 514. 526. 561. 579. 597. 614. 632. 650.

224


Unit Time 169 169 169 169 169 169 169 169 169

1

13.

2

21. 31. 44. 58. 73. 89.

3

4 5

6 7 8

9

169 10 170 170 170 170 170 170 170 170 170

1

2 3

4 5

6 7 8

9

170 10 171 171 171 171 171 171 171 171 171

1

2 3

4 5

6 7 8

9

171 10 172 172 172 172 172 172 172 172 172


1

2 3

4 5

6 7 8

9

172 10

105. 121. 136. 26. 45. 94. 154.

225. 302. 379. 461. 544. 619. 0. 0. 0. 2.

41. 92. 153. 223. 293. 366. 34. 64. 102. 147. 197. 246. 300. 352. 403. 454.

58. 121. 182. 73. 136. 196. 89. 151. 209. 105. 167. 221. 121. 233. 181. 244. 136. 195. 151. 208. 255. 167. 220. 264. 231 274. 181. 195. 242. 283. 225. 544. 1128. 302. 619. 1237. 379. 696. 1346. 461. 775. 1456. 544. 850. 1561. 619. 916. 1661. 696. 982. 1755. 775. 1049. 1845. 850. 1112. 1938. 916. 1178. 2025. 41. 292. 665. 92. 365. 757. 152. 439. 846. 222. 506. 922. 292. 573. 999. 365. 643. 1078. 439. 708. 1152. 507. 763. 1226. 574. 820. 1290. 644. 876. 1353. 197. 403. 599. 246. 454. 642. 300. 503. 683. 352. 553. 723. 403. 598. 763. 454. 641. 800. 503. 682. 836. 553. 721. 868. 598. 762. 901. 641. 798. 934.


32. 45. 58. 71. 85. 98. 111. 124. 137. 58. 77. 136. 194. 254. 314. 374. 433. 493. 553. 0. 1.

2. 3. 63. 123. 183.

243. 303. 363. 56. 102. 148. 194. 240. 286. 332. 378.

424. 470.

56. 69. 82. 95. 108. 121. 134. 147. 160. 174. 160. 255. 319. 386. 451. 517. 583. 649. 714. 780.

94. 103. 112. 121. 130. 139. 148. 157. 166. 175. 226.

410. 473. 541. 605. 670. 734. 799. 863. 927.

202. 422. 482. 548. 610. 672. 734. 795. 857. 919.

2. 2. 3.

4. 4. 4.

4. 4. 3.

122. 196.

264. 344. 424. 504. 584. 664. 743. 332. 369. 405. 442. 478. 514. 550. 587. 623. 659.

318. 397. 476. 556. 635. 714. 793. 358. 389. 418. 448. 478. 508. 538. 568. 598. 627.

270. 345. 419. 493. 567. 199. 244. 290. 335. 380. 426. 471. 517. 562. 607.

107. 111. 115. 120. 124. 128. 133. 137. 141. 145.

225


Unit Time 173 173 173 173 173 173 173 173 173

1

2 3

4 5

6 7 8 9

173 10 174 174 174 174 174 174 174 174 174

1

2 3

4 5

6 7 8 9

174 10 175 175 175 175 175 175 175 175 175

1

2 3

3. 4. 6. 15.

27. 41. 57. 73. 91. 109. 6. 30. 73. 126. 188. 252. 320. 388.

454. 518. 23. 38. 59. 82. 110. 138. 168. 200. 230. 260.

25. 39. 55. 72. 90. 108. 125. 143. 161. 178. 188. 252. 320. 388.

454. 518. 582. 645. 701. 755. 110. 138. 168.

1

13.

200. 230. 260. 293. 322. 350. 381. 48.

2

21. 30. 42. 57. 73. 90. 109. 129. 149.

64. 81. 100. 120. 140. 160. 181. 201. 222.

4 5

6 7 8

9

175 10 176 176 176 176 176 176 176 176 176


3

4 5

6 7 8

9

176 10

88. 106. 123. 141. 159. 176. 193.

161. 180. 197.

213. 230. 247. 264. 280. 294. 310. 703. 756. 810. 862. 915. 963. 1008. 1053. 1095. 1135. 555. 610. 666. 715. 767. 816. 866. 915. 964.

208. 224. 240. 454. 518. 582. 645. 701. 755. 808. 860. 913. 961. 230. 260. 293. 322. 350. 381. 410. 436. 465. 490. 1007. 203. 111. 131. 227. 151. 252. 172. 274. 192. 297. 213. 323. 235. 345. 254. 368. 273. 392. 295. 414.


27. 48. 69. 89. 110. 131. 151. 172. 12.

49. 105. 161.

217. 273. 329. 385. 441. 496. 51. 62. 74. 85. 102. 118. 134. 151. 167. 184. 32.

47. 62. 77. 92. 106. 121. 136. 151. 166.

25. 33. 60. 79. 99. 118. 138. 157. 177. 196. 99. 180.

246. 312. 378. 444. 510. 575. 641. 707. 131. 138. 145. 162. 175. 188. 201. 214. 227. 240. 102. 109. 115. 122. 129. 135. 142. 149. 156. 162.

73. 71. 112. 123. 134. 145. 157. 168. 179. 190. 188. 315. 384. 452. 520. 589. 657. 726.

57. 54. 103. 112. 122. 132. 141. 151. 160. 170. 212. 356.

794. 862.

424. 491. 558. 625. 692. 760. 827. 894.

179. 183. 186.

169. 176. 184.

211. 221. 231. 241. 251. 261. 271.

219. 233. 248. 262. 277. 291. 306.

139. 140. 140. 141. 141. 141. 142. 142. 143. 143.

112. 108. 105. 101. 98. 94. 90. 87. 83. 80.

226


Unit Time 177 177 177 177 177 177 177 177 177

1

2 3

4 5

6 7 8 9

177 10 178 178 178 178 178 178 178 178 178

1

2

8.

4

12. 17.

5

6 7 8 9 1

2 3

4 5

6 7 8

9

179 10 180 180 180 180 180 180 180 180 180

33. 54. 82. 114. 151. 193. 234. 279. 326. 370. 4. 6.

3

178 10 179 179 179 179 179 179 179 179 179


1

2 3

4 5

6 7 8

9

180 10

23. 30. 37. 45. 53. 41. 69. 103. 145. 191. 238. 291. 343. 393. 445. 22. 31. 42. 56. 73. 91. 109. 127. 147. 167.

151. 193.

234. 279. 326. 370. 416. 462. 506. 550. 17.

23. 30. 37. 45. 53. 61. 70. 78. 86. 190. 238. 290. 342. 393. 444. 493. 542. 590. 632. 65. 83. 101. 120. 140. 159. 178. 197. 215.

234.

326. 370. 416. 462. 506. 550. 594. 637. 680. 720. 45. 53. 61. 70. 78. 86. 95. 103. 112. 120. 392. 443. 492. 541. 589. 632. 674. 712. 753. 789. 132. 152. 170. 189. 208. 226. 245. 264. 282. 300.

561. 613. 668. 723. 776. 826. 879. 929. 977. 1027. 110. 123. 139. 153. 168. 182. 197.

212. 226. 241. 946. 1035. 1122. 1204. 1289. 1363. 1434. 1499. 1568. 1629.

203. 222. 242. 261. 279. 298. 317. 336. 354. 372.


209. 236. 263. 289. 316. 11. 17.

23. 30. 36. 43. 49. 55. 62. 68. 59. 102. 146. 189. 232. 276. 319. 363. 406. 449. 51. 65. 79. 93. 108. 122. 136. 150. 164. 178.

223. 240. 258. 276. 294. 312. 330. 348. 366. 384. 43. 45. 48. 50. 53. 56. 58. 61. 63. 66. 202. 239. 276. 313. 349. 386. 423. 460. 496. 533.

305. 314. 324. 333. 342. 352. 361. 370. 380. 389. 59. 57. 58. 57. 56. 56. 55. 54. 53. 53. 318. 346. 373. 400. 427. 454. 481. 507. 534. 561.

274. 278. 283. 288. 292. 297. 301. 306. 310. 315. 43. 41. 41. 39. 37. 35. 33. 32. 30. 28. 314. 335. 356. 376. 396. 417. 437. 457. 478. 498.

142. 149. 157. 164. 172. 180. 187. 195.

187. 190. 192. 195. 197.

173. 176. 179. 181. 184. 187. 190. 193. 196. 199.

202. 210.

200. 202. 205. 207. 210.

227


Unit Time 181 181 181 181 181 181 181 181 181

1

3.

2

5. 8. 11.

3

4 5

6 7 8

9

181 10 182 182 182 182 182 182 182 182 182

24. 42. 63. 86. 110.

3

136. 0. 0. 0.

4

8.

1

2

5

18.

6 7

30. 44. 57. 72. 86.

8

9

182 10 183 183 183 183 183 183 183 183 183


1

3.

2

6 7 8 9

5. 9. 30. 57. 89. 125. 161. 199.

183 10

238.

184 184 184 184 184 184 184 184 184

3

4 5

1

12.

2

20. 31. 44. 82. 129. 183. 244. 303. 365.

3

4 5

6 7 8

9

184 10

24. 42. 63. 86. 110. 136. 162. 188.

212. 239. 18.

30. 44. 57. 72. 86. 99. 113. 126. 139. 51. 81. 115. 151. 189. 228.

264. 300. 336. 372. 82. 129. 183.

244. 303. 365. 429. 487. 546. 606.

110. 136. 162. 188.

212. 239. 263. 286. 309. 332. 72. 86. 99. 113. 126. 139. 150. 161. 172. 183. 184. 220. 254. 290. 327. 362. 393. 424. 455.

485. 303. 365. 429. 487. 546. 606. 663. 712. 763. 813.


256. 291. 325. 357. 390. 424. 456. 489. 521. 552.

9. 23. 37. 52. 79. 107. 135. 163. 191. 219.

38. 50. 61. 100. 129. 157. 186. 214. 242. 271.

92. 90. 88. 146. 162. 179. 195. 211. 228. 244.

126. 139. 150. 161. 172. 183. 194.

0. 0. 0. 12.

1. 1.

1. 1.

1.

24. 38. 53. 67. 82. 96.

52. 67. 83. 98. 114. 130. 145. 161. 47. 47. 159. 193. 228. 262. 297. 331. 366. 400. 116. 117. 118.

62. 78. 93. 109. 124. 139. 155. 170. 42. 41. 175. 208. 241. 273. 306. 339.

289. 342. 395. 449. 502. 555. 609.

321. 375. 428. 482. 536. 589. 643.

203. 212. 221. 325. 358. 388. 420. 452. 483. 514. 541. 568. 596. 633. 704. 772. 831. 892. 953. 1011. 1071. 1126. 1176.

24. 36. 47. 59. 71. 82. 7. 13. 19.

50. 82. 113. 145. 176. 207.

239. 27. 37. 47. 58. 107. 156.

205. 254. 302. 351.

110. 125. 25. 29. 85. 120. 156. 192.

228. 264. 300. 336. 75. 82. 89. 174. 229. 284. 339. 395. 450. 505.

87. 81. 75. 141. 153. 165. 177. 189.

201. 213. 0.

372. 405. 109. 111. 113.

228


Unit Time 185 185 185 185 185 185 185 185 185

1

13.

2

25. 41. 66. 98. 138. 179. 224. 273. 322.

3

4 5

6 7 8

9

185 10 186 186 186 186 186 186 186 186 186

1

2 3

4 5

6 7 8

9

186 10 187 187 187 187 187 187 187 187 187

1

2 3

4 5

6 7 8

9

187 10 188 188 188 188 188 188 188 188 188


1

2 3

4 5

6 7 8

9

188 10

9. 12. 17.

22. 28. 35. 41. 49. 56. 65. 46. 64. 86. 116. 150. 187. 224. 262. 302. 342. 33. 55. 86. 118. 154. 189. 224. 263. 298. 333.

95. 135. 175. 221. 270. 318. 368.

416. 465. 514. 23. 30. 37. 44. 52. 60. 68. 76. 85. 92. 140. 177.

213. 251. 292. 331. 368. 406. 444. 480. 154. 189.

224. 263. 298. 333. 371. 405. 439. 474.

266. 315. 364. 412. 461. 511. 559. 604. 648. 691. 47. 56. 63. 72. 80. 88. 96. 103. 111. 120. 281. 321. 358. 396.

433. 470. 508. 545. 581. 618. 298. 333. 371. 405. 439. 474. 509. 540. 574. 604.


459. 508. 557. 602. 646. 689. 727. 769. 808. 845.

38. 72. 106. 140. 173. 207. 241. 275. 309.

85. 94. 104. 113. 122. 133. 142. 151. 160. 169.

19.

672. 742. 811. 880. 947. 1015. 1083. 1151. 1217. 1283. 439. 474. 510. 540. 575. 605. 635. 670. 701. 727.

343. 26. 33. 40. 48. 55. 62. 69. 77. 84. 111. 139. 167. 196. 224. 252. 281. 309. 337. 366. 73. 90. 107. 123. 140. 156. 173. 190. 207. 223.

160. 184.

209. 234. 258. 283. 308. 332. 357. 382. 47. 50. 54. 57. 60. 64. 67. 70. 73. 77. 301. 317. 333. 349. 365. 381. 397. 413. 429. 445. 190. 200. 210. 220. 230. 240. 249. 259. 269. 279.

256. 262. 267. 273. 279. 284. 290. 295. 301. 306. 61. 61. 61. 60. 60. 60. 59. 59. 59. 58. 398. 404. 410. 415. 421. 427. 433. 438. 444. 450. 260. 265. 269. 275. 279. 284. 289. 294. 299. 304.

224. 219. 214. 209. 204. 199. 194. 189. 184. 179. 47. 45. 43. 42. 40. 38. 36. 34. 32. 30. 375. 383. 392.

400. 409. 417. 425. 434. 442. 451. 244. 256. 267. 279. 290. 301. 313. 324. 336. 347.


Unit Time 189 189 189 189 189 189 189 189 189

1

2 3

4 5

6 7 8

9

189 10 190 190 190 190 190 190 190 190 190

1

2 3

4 5

6 7 8

9

190 10 191 191 191 191 191 191 191 191 191

1

2 3

4 5

6 7 8

9

191 10 192 192 192 192 192 192 192 192 192

1

2 3

4 5

6 7 8

9

192 10

Individual Tree Selection First Second Third Fourth 22. 36. 61. 93. 129. 169. 208. 249. 290. 331. 26. 40. 60. 84. 111. 142. 175. 210. 247. 283. 11. 19.

29. 39. 53. 67. 81. 96. 113. 129. 11. 18.

27. 37. 49. 63. 76. 90. 106. 121.

126. 166. 205. 246. 288. 328. 368.

409. 447. 481. 111. 142. 175. 210. 247. 283. 322. 360. 398. 434. 53. 67. 81. 96. 113. 129. 144. 161. 176. 192. 49. 63. 76. 90. 106. 121. 135. 151. 165. 180.

285. 579. 325. 632. 365. 688. 406. 742. 444. 791. 843. 478. 516. 894. 553. 944. 585. 989. 622. 1038. 247. 409. 283. 448. 322. 483. 360. 519. 398. 554. 434. 586. 469. 622. 503. 653. 537. 687. 568. 716. 113. 176. 192. 129. 208. 144. 161. 226. 176. 240. 192. 257. 208. 272. 226. 287. 240. 301. 257. 316. 106. 270. 300. 121. 135. 329. 362. 151. 389. 165. 180. 419. 194. 448. 211. 478. 224. 504. 240. 534.

Group Selection First Second Third Fourth 54. 67. 94. 121. 148. 175.

202. 229. 256. 283. 62. 103. 145. 187.

229. 272. 314. 356. 398. 440. 27. 33. 40. 46. 53. 59. 66. 72. 78. 85. 25. 31. 37. 43. 49. 55. 61. 67. 73. 79.

159. 194.

219. 243. 267. 292. 316. 340. 364. 389. 189.

221. 254. 286. 318. 350. 383. 415. 447. 479. 60. 64. 69. 74. 78. 83. 87. 92. 97. 101. 56. 60. 65. 69. 73. 77. 81. 86. 90. 94.

216. 285. 309. 332. 356. 379. 403. 427. 450. 474. 335. 341. 345. 349. 354. 358. 362. 367. 371. 376. 90. 92. 94. 96. 97. 99. 101. 103. 105. 106. 84. 86. 88. 89. 91. 92. 94. 96. 97. 99.

229. 311. 333. 356. 379. 401. 424. 446. 469. 491. 329. 326. 322. 318. 313. 309. 305. 300. 296. 292. 98. 100. 102. 104. 106. 107. 109. 111. 113. 114. 92. 94. 95. 97. 98. 100. 102. 103. 105. 106.

230


Unit Time 193 193 193 193 193 193 193 193 193

1

1.

2

1.

3

2.

4 5

35. 78.

6 7

129. 188.

8

246. 307. 370. 22. 36.

9

193 10 194 194 194 194 194 194 194 194 194

1

2 3

4 5

6 7 8

9

194 10 195 195 195 195 195 195 195 195 195

1

2 3

4 5

6 7 8

9

195 10 196 196 196 196 196 196 196 196 196


1

2 3

4 5

6 7 8

9

196 10

55. 75. 105. 138. 171. 207. 248. 286. 32. 49. 101. 168. 243. 329.

415. 507. 601. 686. 24. 33. 45. 57. 71. 86. 102. 120. 137. 157.

78. 129. 188.

246. 307. 370. 426. 482. 540. 595. 105. 138. 171.

207. 248. 286. 322. 361. 397. 434. 240. 325. 412. 503. 597. 682. 770. 858. 945. 1019. 60. 76. 92. 109. 126. 147. 165. 184.

204. 221.

307. 546. 370. 601. 426. 648. 482. 696. 540. 744. 595. 790. 641. 838. 689. 877. 736. 916. 781. 957. 248. 403. 286. 441. 322. 479. 361. 518. 397. 551. 434. 589. 471. 623. 509. 658. 689. 542. 579. 722. 594. 943. 679. 1018. 767. 1093. 855. 1167. 941. 1238. 1015. 1306. 1090. 1372. 1163. 1431. 1233. 1494. 1301. 1548. 116. 136. 154. 173. 194.

211. 231. 248. 267. 286.

184.

201. 220. 238. 256. 276. 294. 312. 329. 347.


2. 3.

52. 102. 152. 201.

251. 301. 350. 50. 64. 77. 91. 111. 131. 151. 171. 191.

211. 72. 109. 189.

269. 350. 431. 512. 592. 673. 754. 49. 68. 86. 104. 122. 141. 159. 177. 195. 214.

3. 3. 102. 163.

225. 286. 348. 409. 471. 532. 116. 126. 136. 160. 178. 196.

4. 4. 221.

5.

287. 354. 420. 487. 553. 620. 686.

267. 333. 399. 465. 531. 596. 662. 728.

175. 180. 184.

188. 193. 198.

218. 232. 245. 259. 273. 286. 300. 322. 524. 593. 662. 731. 800. 869. 938.

237. 251. 264. 278. 291. 304. 318. 322. 558. 620. 684. 746. 808. 870. 932. 994.

214. 232. 250. 268. 204. 318. 400. 482. 563. 645. 727. 809. 891. 1007. 972. 1076. 118. 126. 135. 143. 152. 160. 169. 177. 186. 194.

5.

153. 151. 150. 149. 148. 147. 146. 144. 143. 142.

1057. 119. 114. 110. 106. 101. 97. 93. 88. 84. 80.

231


Unit Time 197 197 197 197 197 197 197 197 197

1

16.

2

22. 31. 41. 52. 65. 79. 94. 108. 126. 32. 45. 61. 82. 105. 130. 155. 181. 208. 235.

3

4 5

6 7 8

9

197 10 198 198 198 198 198 198 198 198 198

1

2 3

4 5

6 7 8

9

198 10 199 199 199 199 199 199 199 199 199

1

2 3

4 5

6 7 8

9

199 10 200 200 200 200 200 200 200 200 200


1

2 3

4 5

6 7 8 9

200 10

12.

21. 35. 51. 71. 93. 115. 138. 163. 186. 21. 32. 44. 59. 75. 94. 114. 135. 156. 181.

52. 65. 79. 94. 108. 126. 142. 158. 176. 191. 95. 120. 145. 171. 198. 225. 250. 275. 300. 325. 64. 86. 108. 131. 156. 180. 202. 227. 249. 271. 69. 88. 107. 128. 149. 175. 197. 220. 246. 267.

108. 126. 142. 158. 176. 191.

208. 223. 239. 256. 188.

215. 240. 265. 291. 315. 340. 364. 388. 412. 150. 173. 196. 220. 242. 265. 287. 310. 330. 353. 143. 168. 190. 214.

239. 261. 285. 307. 330. 355.

284. 317. 350. 381. 415. 447. 480. 510. 541. 573. 432. 477. 520. 564. 606. 649. 692. 735. 776. 817. 278. 307. 336. 366. 392. 420. 445. 471. 495. 520. 233. 255. 279. 301. 324. 349. 371. 393. 415. 437.

Group Selection First Second Third Fourth 41. 57. 73. 89. 104. 120. 136. 152. 168. 183. 71. 91. 111. 131. 151. 171. 191. 211. 231. 251. 26. 34. 48. 61. 76. 90. 105. 119. 133. 148. 55. 77. 99. 122. 144. 166. 188. 210. 232. 254.

96. 104. 111. 118. 125. 133. 140. 147. 154. 162. 195. 208. 221. 234. 247. 259.

272. 285. 298. 311. 62. 79. 92. 107. 121. 135. 149. 163. 177. 190. 134. 145. 156. 167. 178. 189. 199. 210. 221.

232.

125. 123. 122. 120. 119. 118. 116. 115. 114. 112. 261. 267.

273. 279. 285. 291. 297. 303. 308. 314. 94. 122. 132. 146. 157. 169. 180. 192. 203. 214. 172. 172. 172. 173. 173. 173. 174. 174. 174. 175.

94. 90. 85. 81. 76. 72. 68. 63. 59. 54.

254. 261. 268. 274. 281. 288. 295. 302. 309. 316. 101. 134. 143. 157. 167. 178. 188. 198. 209. 219. 133. 129. 126. 122. 118. 114. 110. 106. 103. 99.

232


Unit Time 201 201 201 201 201 201 201 201 201

1

2 3

4 5

6 7 8 9

201 10 202 202 202 202 202 202 202 202 202

1

2 3

4 5

6 7 8 9

202 10 203 203 203 203 203 203 203 203 203

10. 16.

24. 34. 43. 54. 67. 80. 93. 108. 62. 102. 158.

225. 303. 381. 468. 558. 649. 733.

1

18.

2

38. 66. 99. 168. 248. 337. 436. 533. 632. 40. 76. 127. 184. 249. 314. 384. 456. 527. 596.

3

4 5

6 7 8 9

203 10 204 204 204 204 204 204 204 204 204


1

2 3

4 5

6 7 8

9

204 10

37. 48. 61. 74. 87. 102. 116. 131. 146. 161. 302. 380. 467. 557. 648. 731. 819. 906. 990. 1070. 159. 239. 328. 427. 524. 623. 723. 815. 907. 998. 219. 284. 355. 426. 498. 566. 635. 701. 767. 829.

80. 95. 109. 124. 140. 155. 169. 184. 199.

135. 151. 165. 181. 196.

212. 227. 242. 256. 271. 1007. 1089. 1168. 1244. 1316. 1378. 1453. 1511. 1569. 1626. 899. 992. 1079. 1158. 1236. 1314. 1387. 1463. 1529. 1592. 763. 833. 898. 962. 1021. 1081. 1135.

215. 647. 730. 818. 905. 989. 1069. 1145. 1219. 1288. 1348. 515. 614. 714. 806. 898. 989. 1075. 1153. 1229. 1306. 468. 537. 605. 672. 738. 800. 857. 915. 1191. 967. 1247. 1022.

1293.

Group Selection First Second Third Fourth 30. 43. 55. 68. 80. 93. 105. 118. 130. 142. 111. 183. 257. 331. 405. 479. 552. 626. 700. 774. 34. 68. 102. 137. 220. 303. 386. 470. 553. 636. 75. 138.

201. 263. 326. 389. 452. 515. 577. 640.

83. 89. 95. 101. 107. 113. 119. 125. 130. 136.

363. 429. 494. 559. 623. 688. 753. 818. 883. 947. 134. 169.

204. 337. 434. 530. 626. 722. 819. 915. 271. 333. 396. 458. 520. 583. 645. 707. 770. 832.

96. 99. 102. 105. 108. 111. 114. 117. 120. 123. 548. 590.

628. 667. 706. 744. 783. 821. 860. 898. 219. 248. 277. 523. 618. 714. 810. 906. 1002. 1097. 424. 472. 519. 567. 615. 662. 710. 758. 806. 853.

76. 77. 77. 78. 79. 80. 80. 81. 82. 83. 529. 554. 574. 595. 615. 635. 655. 675. 696. 716. 252. 275. 299. 585. 675. 764. 854. 943. 1033. 1123. 492. 526. 560. 594. 629. 663. 697. 731. 766. 800.

233


Unit Time 205 205 205 205 205 205 205 205 205

1

16.

2

28. 45. 66. 118. 179. 249. 327. 406. 486. 26. 47. 77.

3

4 5

6 7 8

9

205 10 206 206 206 206 206 206 206 206 206

1

2 3

4 5

6 7 8

9

206 10 207 207 207 207 207 207 207 207 207

1

2 3

4 5

6 7 8 9

207 10 208 208 208 208 208 208 208 208 208


114. 158.

207. 260. 315. 373. 428. 50. 84. 128. 181. 245. 311. 385. 455. 527. 600.

1

16.

2

27. 39. 55. 70. 87. 109. 130. 151. 174.

3

4 5

6

7 8

9

208 10

110. 171. 241. 319. 397. 477. 558. 634. 710. 786. 148. 196. 249. 304. 362. 417. 473. 529. 584.

636. 245. 311. 385. 455. 527. 600. 675. 743. 815. 881. 56. 73. 94. 115. 136. 160. 183. 207. 232. 257.

389. 469. 550. 626. 701. 777. 848. 913. 976. 1039. 352. 407. 463. 519. 573. 625. 674. 725. 770. 815. 527. 600. 675. 743. 815. 881. 948. 1014. 1069. 1131. 122. 145. 168. 193.

218. 242. 265. 290. 315. 341.

695. 771. 842. 907. 970. 1034. 1095. 1154. 1209. 1258. 570. 623. 674. 726. 773. 819. 864. 905. 947. 981. 1003. 1093. 1185. 1277. 1355. 1441. 1528. 1601. 1678. 1749. 323. 367. 409. 456. 501. 548. 593. 639. 682. 729.

Group Selection First Second Third Fourth 33. 59. 84. 110. 176. 243. 310. 376. 443. 509. 57. 104. 151. 198. 246. 294. 343. 391. 439. 487. 117. 160. 202. 244. 292. 339. 386.

434. 481. 528. 49. 68. 88.

119. 139. 160.

262. 334. 405. 477. 548. 619. 691. 210. 248. 286. 326. 366. 405. 445. 484. 524. 563. 351. 383. 414. 456. 494. 533. 571. 609. 647. 685.

108. 127. 147. 166. 186.

137. 146. 155. 163. 172. 181. 189. 198.

206. 225.

207. 215.

189.

200. 211. 403. 469. 536. 602. 669. 735. 802. 338. 358. 379. 405. 428. 450. 473. 495. 518. 540. 498. 519. 540. 584. 612. 640. 669. 697. 725. 753. 152. 157. 163. 168. 173. 179. 184. 189. 195.

200.

192. 194. 197.

419. 476. 534. 592. 650. 708. 765. 343. 348. 353. 366. 373. 380. 387. 394. 401. 408. 503. 516. 529. 569. 588. 608. 628. 647. 667. 687. 120. 122. 123. 125. 127. 128. 130. 131. 133. 135.


Unit Time 209 1 209 2 209 3 209 4 209 5 209 6 209 7 209 8 209 9

209 10 210 210 210 210 210 210 210 210 210

1

2 3

4 5

6 7 8

9

210 10 211 211 211 211 211 211 211 211 211

1

2 3

4 5

6 7 8

9

211 10 212 212 212 212 212 212 212 212 212

1

2 3

4 5

6 7 8 9

212 10

Individual Tree Selection First Second Third Fourth 15. 39. 72. 109. 161.

216. 276. 339. 400. 461. 47. 83. 136. 203. 283. 369. 463. 561. 665. 762. 29. 43. 60. 80. 101. 124. 147. 171. 195. 220. 4. 7. 11. 18.

50. 92. 141. 196. 252. 309.

145. 200. 260. 323. 383. 444. 506. 565. 620. 674. 275. 361. 456. 554. 658. 755. 855. 956. 1052. 1145. 89. 112. 135. 159. 183. 208.

233. 257. 282. 306. 50. 92. 141. 196.

252. 309. 368. 421. 475. 529.

367. 428. 490. 548. 603. 658. 710. 760. 808. 855. 650. 748. 848. 948. 1045. 1138. 1224. 1314. 1395. 1474. 171. 196. 221. 245. 270. 294. 317. 342. 365. 389. 252. 309. 368. 421. 475. 529. 580. 625. 669. 714.

698. 768. 835. 899. 962. 1021. 1077. 1134. 1186. 1235. 1047. 1141. 1229. 1320. 1402. 1482. 1560. 1630. 1703. 1761. 260. 284. 307. 332. 355. 379. 403. 426. 448. 470. 530. 592. 652. 704. 757. 809. 859. 910. 954. 995.


249. 303. 356. 409. 463. 106. 192.

277. 363. 448. 534. 620. 705. 791. 877. 64. 81. 98. 115. 132. 149. 166. 183. 200. 217. 9. 16.

23. 31. 78. 125. 173. 220. 267. 315.

128. 170.

212. 283. 344. 404. 464. 525. 585. 646. 386. 454. 523. 592. 661. 730. 799. 867. 936. 1005. 171. 180. 189. 198. 207.

215. 224. 233. 242. 251. 32. 38. 44. 130. 185. 241. 296. 352. 408. 463.

222. 262. 301. 404. 463. 522. 581. 640. 699. 757. 619. 656. 693. 730. 767. 804. 842. 879. 916. 953. 234. 238. 243. 248. 252. 257. 262. 266. 271. 276.

259. 293. 327. 439. 493. 547. 600. 654. 708. 762. 628. 637. 645. 654. 662. 671. 680. 688. 697. 705. 221. 225. 229. 232. 236. 240. 244. 247. 251. 255.

52. 55. 58. 237. 294. 351. 408. 466. 523. 580.

52. 53. 54. 268. 322. 377. 431. 485. 540. 594.

235


Unit Time


213 213

0. 0.

1. 1.

1.

2. 2.

1

2

2133 2134 213 213 213 213 213

5

1.

6 7 8 9

1.

213 10 214 214 214 214 214 214 214 214 214

1

2 3

4 5

6 7 8 9

214 10 215 215 215 215 215 215 215 215 215

1

2 3

4 5

6 7 8

9

215 10 216 216 216 216 216 216 216 216 216

1.

2. 2. 3. 3. 19.

30. 46. 66. 88. 113. 138. 167. 193. 223. 10. 15.

22. 31. 42. 55. 67. 81. 95. 110.

2

5. 9.

3

14.

4

20. 28. 37. 47. 57. 68. 80.

1

5

6 7 8

9

216 10

3. 3. 3.

4. 4. 5.

86. 111. 136. 164. 191.

220. 248. 277. 304. 331. 40. 53. 65. 79. 93. 109. 124. 139. 154. 169. 28. 37. 47. 57. 68. 80. 93. 105. 118. 130.

3. 3. 3. 4. 4. 5. 5. 5.

6. 6. 188.

217. 245. 274. 301. 329. 357. 385. 411. 437. 91. 107. 122. 137. 152. 167. 183. 199.

214. 228. 68. 80. 93. 105. 118. 130. 144. 157. 170. 181.

7. 7. 8. 9. 10. 11. 12.

13. 13. 14.

301. 329. 357. 385. 412. 438. 466. 488. 513. 540. 198. 220. 243. 267. 289. 309. 333. 354. 375. 397. 126. 140. 155. 171. 185. 198.

213. 228. 241. 256.


2. 2. 2. 3. 3. 3. 4. 4. 54. 72. 90. 108. 126. 144. 162. 180. 199.

217. 28. 37. 46. 55. 64. 72. 81. 90. 99. 108. 19.

26. 33. 40. 47. 54. 61. 68. 75. 82.

3. 3. 3. 3. 3. 3. 3. 3. 3. 4. 138. 149. 159. 170. 181. 191.

202. 213. 224. 234. 79. 82. 85. 88. 91. 94. 97. 101. 104. 107. 63. 65. 66. 67. 68. 70. 71. 72. 73. 75.

3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 194.

2. 2. 2. 2. 2. 2. 2. 2. 2. 2.

200. 207. 214. 220. 227. 234. 240. 247. 253.

208. 209. 210. 210. 211. 212. 212. 213. 214. 214.

102. 103. 104. 106. 107. 108. 109. 111. 112. 113. 77. 77. 77. 76. 76. 75. 75. 74. 74. 74.

84. 83. 81. 80. 79. 77. 76. 75. 73. 72. 42. 40. 38. 35. 33. 31. 29. 26. 24. 22.


Unit Time 217 217 217 217 217 217 217 217 217

1

15.

2

23. 32. 43.

3

4 5

6 7 ,8

9

217 10 218 218 218 218 218 218 218 218 218


1

2 3

4 5

6 7 8 9

218 10

56. 69. 82. 96. 109. 123. 6. 9. 12. 16.

22. 28. 33. 40. 47. 54.

52. 66. 79. 92. 105. 120. 134. 147. 161. 174. 17.

23. 29. 36. 42. 50. 58. 65. 72. 80.

102. 116. 130. 144. 158. 171. 184. 198. 210.

167. 183. 198.

223. 38. 46.

215. 230. 245. 261. 276. 290. 304. 67. 75.

53. 61. 68. 76. 84. 92. 100. 107.

83. 92. 100. 108. 116. 125. 132. 141.

Group Selection First Second Third Fourth 35. 43. 52. 60. 68. 77. 85. 94. 102. 111. 13. 18.

22. 27. 32. 36. 41. 46. 50. 55.

95. 99. 103. 107. 111. 115. 118. 122. 126. 130. 43. 44. 44. 45. 46. 47. 48. 48. 49. 50.

133. 134. 136. 138. 139. 141. 142. 144. 145. 147. 52. 52. 51. 51. 51. 50. 50. 50. 49. 49.

121. 122. 123. 124. 126. 127. 128. 129. 130. 131. 28. 26. 24. 23. 21. 20. 18. 17. 15. 14.

237

APPENDIX 3

Transportation Network

238

Table 9: Road Network:

To Node 4 7 15

40

From Node 6 4 7 39

43 50

40

70

69 74

73

70 70 83 91 111 114 117 119 121 126 129 131 132 133 138 143

48

Class 2 2

142

2

596 1099

1

5

1

24 2531 2763 470 1367 2143 1250

2 2 1

73

1

79 69 92

2

112 107 115 114 117

Length Feet

1

2

138

1

405 772 439

1

1191

1

1

129 132

1

768 582 335 459 1128 470 1320

1

1481

39 146

143 138

1

148

43 157 170 148

1

907 2307 1243 943

69 166 171

170 182 186 181

187 186 190 192 187 196 193

1

121

1

15

1

126

1

123 17

1

171 171

182 157 186 188 169 177 193 166 199

2

1

2 2

1251

1

2113

2 2 2

172 1419 301 4895 30 125 4561 1356 302

1 1

1

2 1

2 2 2

6770 627

239

Table 9: Road Network: (Continued)

To Node 199

From Node

Class

Length Feet

185

1

200

83

1

198 85

192

1

1314 2508 1865

83

1

2322

202

196 190 181 198

2 2

90

2 2

203 204 204 193 199 91

211 92

214 216 217 218 218 220 96

91 194

1 1

1

204 212 202

2 2

211

1

214

2

215 96 214 219

1

1

143

1

1556 1368

1

219

1

219 96 222

221

1

221 223 98 225

222 100

237 226 241 242 241 244 244 245 104 105 105

203 221

226 220 235 240 237

509 582 850 844 607 824

1

211

222 218 222 216

1033 1166 1879 1572 1541 1782 1494

1 1 1 1

2 1 1

1 1 1

1

241

1

240

1

243

1

242 244

1

102 102 245

2 2

1

1

2000 532 330 497 1016 1051 1849 641 426 1184 218 3403 1355 67 1375 124 1827 1997 1862 1994 1120

240

Table 9: Road Network: (Continued)

To Node

From Node

Class

4

5

3

8 10 9 19 18

4 9

3

23 26 27 24 30 25 24 35 36 38 42 44 44 28 47

44 50 52 53 54 55 56 48

60 55

62 62 65

66 68 72 75

77 80 81

18 18

3 3

3

22 24 27 23 28 27 32 34 25 30 36 39 36 45 46 45 49

3 3 3 3 3

Length Feet 608 482 217 1714 641 631

276 1232 958 299

3

170

3

3

485 412 539 604

3

166

3

779 438

3 3

3 3

7

3

3

757 358 467

51

3

991

46 52

3

45 52 54 57 54 61 55

3

64 64 62 66

3 3

818 255 860 260 340 906 439 412 615 428 273 592

3 3 3 3 3 3

449 673 360 1437 1616

73

76 76 81

84

3

3 3 3 3 3 3

3

3

114

241

Table 9: Road Network: (Continued) To Node 88 92 109 109 110 3

113 116 111 118 118 122 12 13

124 127 124 128 129 16

135 131 122 21 137 136 23 141 139 25 141 145 146 43

59 152

67 64 151

152 160

From Node

Class

Length Feet

89 93 108 110 112 110 114 117 118

3

177

3

29 4 308 660 417 498 253 1472

9 122 120 121 124

3

14 123

3

128 125 128 126 132

3

20

3

426 246 49 332 309 725

136 133 134 137 131 142 143 136 31 146 147 58 148

3

1311

3

285

3

404

3

155 1106 156

66 152 156 158 159 54

3 3 3 3 3 3 3 3

271 502

3

400

3

157 1051 158 222

3 3 3 3 3 3

3 3 3

409

3

1199 600 484 60 1416 100 267 218 385 295

3 3 3 3 3 3 3 3 3 3

3

103 1226