rate, fixed cutting entry cost per acre, and net stumpage value per tree by diameter class. Both examples assume that the manager's primary objective is the ...
Optimum Stand Prescriptions
T
For Ponderosa
Pine
E
V
E SO N
David W. Hann, J. DouglasBrodie, and
THONAS ADJUSTNENT-•'•ELK USE Kurt
NILES
H. Riitters
OF ROAD PER SOUARE NILE
Ftgure3. Compositeroad densitymodel showingactual elk useat densitiesgreaterthantwomilesper section.
remainashigh as20 percentof potentialwith five anda half miles of road per squaremile, it must be recognizedthat the full impactof a roaddoesnot occuruntil at least the third year after construction.Thus I have assumedthat the best estimateof habitatpotentialfor elk as influencedby traveledroadsis represented by the averageelk use in habitat with roads more than two years old. In the sevenareas with an averageroad densityof five anda half milesper squaremile, elk use was 18.8 percentof potential. Figure 3 showsa compositemodel of the Montana datausingthe no-overlapassumption for roaddensities undertwo milesper squaremile andthe table2 projections for higher road densities.In addition,I haveused the Thomaset al. (1979) adjustmentto producea projectionof the no-overlap calculations. The agreement betweenthis roaddensitymodeland the adjustment is coincidental,but the similaritydoessuggestthat this approachmay be valid in the absenceof data taken in areaswith high road densities.
ABSTRACT--Twoexamples for a northernArizonaponderosa pine stand illustratethe usefulnessof dynamicprogramming in makingsilviculturaldecisions.Thefirst exampleanalyzes the optimalplanting densityfor bare land, while the second examinesthe optimalprecommercialthinningintensityfor a 43-year-oldstand.Both examplesassumethat the manager's primary objective is maximizationof the soil expectation value. A numberof near-optimalsolutionsare also provided by the program,and may be preferablewhen the manager takes account of noneconomicconsiderations.The optimal solution then provides a standardfor cost comparisonof these noneconomic considerations.
anagement of an even-aged standrequiresdecisions aboutplantingdensity,timing and intensityof thinning (bothprecommercial and commercial)and of fertilization, and rotationlength. Becausethese decisionsare interrelatedandcomplex,considerableresearchhasbeen devotedto developingmethodsto assistthe forestmanager in making them. One such managementmethod which has receivedsubstantialrecent attentionis dynamic programming(Hann and Brodie 1980, Martin and Ek 1981, and Riitters et al. 1982).
ManagementApplication Oncea graphicdisplaysuchas the solidline infigure 3 is developed,it canbe directlyappliedto management
In this article, the use of dynamicprogrammingin determiningoptimumand near optimumdecisionswill be demonstratedwith two examples for a ponderosa pine stand (with Arizona fescue understory)on site
of elk habitat. An evaluation area should be at least
index 88 land in northern Arizona.
3,000 acres;mileageof open roadscan be determined from mapsor aerial photographs. Roadsthat dead-end in lessthanhalf a mile neednot be countedunlessthey receive unusuallyheavy traffic. The calculatedroad density--milesper section--isenteredon the horizontal axis to predicthabitateffectiveness on the verticalaxis. Avoidanceof roadsis Presumedto be a behavioral response conditioned by vehiculartraffic. Otherfactors, includingbetterhidingcoverand lowerroad standards, can be expectedpartially to mitigatethe negativeresponseby elk. However,the best methodfor attaining full use of habitat appears to be effective road
the optimumplantingdensityon bare land. The second addresses the intensityof precommercial thinningin an overstocked stand.In both examples,the analysisalso determinesthe optimum thinning schemeand rotation length.
closures.
ß
Literature
Cited
HERSHEY, T. J., andT. A. LEEGE.1976.Influences of loggingonelk summer rangein north-central Idaho.P. 73-80 in Proc.Elk-Logging-Roads Symp., Univ. Idaho, Moscow.
LYON,L. J. 1979a.Habitateffectiveness for elk as influenced by roadsand cover. J. For. 77:658-
660.
LYON, L. J. 1979b. Influencesof loggingand weatheron elk distributionin westernMontana.USDA For. Serv.Res. Pap. INT-236• 11 p.
(Continuedon page 613)
The first concerns
Dynamic Programming
Optimizationof standgrowthundera wide arrayof silvicultural treatments can be readily accomplished with dynamicprogramming.Analysisof silvicultural treatmentis complex becauseof the high degree of interdependency between stand treatmentsover time. For example, an array of planting density alternatives would create an array of standsfor first commercial thinning. Each of these standscan be thinned to a numberof densities,each of which createsa slightly differentstandfor considerationat secondthinning.The types of standsand possible sequencesof treatments multiply with each successive set of possibledecisions. Additionaltreatmentoptions, such as precommercial thinning,typesof thinning(high, low, mechanical),and fertilization, further increasethe number.of potential treatmentschedules.There are literally millions of pos•1983
SOCIETY OF AMERICAN FORESTERS
September1983/JOURNAL OF FORESTRY/595
s•blesfivlculturalsequences for a s•nglestand. Dynamic programmingpermits a managerto solve thesepotentiallylargeproblemsby reducingthe rangeof alternativesto a workablenumberthroughclassification and eliminationof similar standconditionsand through efficient searchingof the set of possible treatment sequences (Hann and Brodie 1980). Its generalstructure canincorporatea wide arrayof primaryobjectiveswhile the solutionprocesscan provide not only the optimal stand treatment scheme but also a number of alternative
schemesthat might better meet secondarymanagement objectives.The primary advantageof a dynamicprogramminganalysisoversimulationanalysisis the ability to identifythe optimalmanagement schemefor the set of assumptions made in the analysis.Only by knowing the optimalpolicy canthe managerassess the costto the primary objectiveof choosingalternative,suboptimal solutions.A simulationanalysisin which the manager choosesalternative schemesby trial and error cannot guaranteethat the optimalpolicy will be identified. An integralpart of any dynamicprogrammingalgorithm developedto aid in making standdecisionsis a standgrowthmodel. The limits to usefulnessof the dynamic programmingalgorithm are defined by the limits of the growthmodelto predictstanddevelopment under the full range of treatmentschemesto be examined. While the growthmodel mustbe carefullydeveloped,manytypesof growthmodelshavebeensuccessfully integratedwith dynamicprogramming(Hann and Brodie 1980, Martin and Ek 1981,.Riitters et al. 1982).
The algorithmusedto makethe followinganalyses is calledpPOl, Z for ponderosa pine optimizer(Riitterset al. 1982). It incorporatesthe whole stand diameter-class growthmodel,developedby Hann (1980). Data needed include the stand's site index, initial stand age, and initial numberof treesper acre in each 1-inchdiameter class,and the manager'schoiceof cuttingcyclelength and thinning type. In addition, economicanalysesrequire the manager'schoice of real alternativeinterest rate,fixedcuttingentrycostperacre,andnetstumpage valueper tree by diameterclass. Both examplesassumethat the manager'sprimary objectiveis the maximizationof the soil expectation value. Additionalassumptions includea 3-percentinterestrate,a $5 peracrefixedentrycost,a 20-yearcutting cycle after first thinning, a minimumvolumecut of 10 percent,and a silviculturalprescriptioncallingfor mechanical thinning. Net stumpagevalues per tree are givenin table 1. It shouldbe emphasized thatPPOPT can be appliedto a rangeof othersiteindicesand to any set of economicand silviculturalchoicesthat the manager wishes to examine, and that the decisions made can be sensitive to these choices.
Planting Density
Four plantingdensities(880, 680, 480, and 280 trees per acre) were analyzed to determine which would maximize the soil expectationvalue. These particular densitieswere chosenbecausethey bracketedthe 680 treesper acre recommendedby Schubert(1974). To obtaininitial diameterdistributions for eachplanting density,it was assumedthat 15 yearswererequired
for all plantedtreesto reachor exceedbreastheight (Minor 1964), that only 50 percentof the treeswould surviveoverthat period (Schubert1974), and that approximately60 and40 percentof the treeswouldfall in 596/JOURNAL OF FORESTRY/September 1983
Table 1. Net stumpagevalues per tree for both examples. D•ameter
Net stumpage
D•ameter
Net stumpage
class
value per tree
class
value per tree
•ches 7 8 9 10 11 12 13 14 15
Dolla• 0.20 .81 3.85 8.55 14.77 22.49 33.35 45.86 62.60
•ches 16 17 18 19 20 21 22 23 24
Do/la• 81.33 101.09 122.87 148.80 177.04 216.84 260.04 301.79 346.41
Table 2. Ten largest soil expectation values, by planting density and rotation length. Planting density
Maximum per acre Rotation soilexpectation Rank Trees 280 480
680
880
Yea• 90
Change in maximum soil expectahon per acre from
optimalsoluhon
Dolla• 553.52
6
Percent -5.14
11'0
547.62
8
-6.15
90 110 130 90 110 130 110 130
583.50 575.78 562.69 558.76 562.07 551.11 532.74 525.56
1 2 3 5 4 7 9 10
.00 -1.32 -3.57 -4.24 -3.67 - 5.55 -8.70 -9.93
the 1- and 2-inch diameterclasses,respectively.It was further assumedthat planting costs would be $300, $250, $200, and $150 per acre for the four densit]es, andthatthe first thinningwouldoccurat age30. A separatePPOPTrun was made for each planting density,andthe 10 treatmentschemes thatproducedthe highest soil expectationvalues are listed in table 2 From this analysis,it can be concludedthat a planting densityaround480 trees per acre would maximizethe soil expectationvalueunderthe statedassumptions. The resultingoptimal standtreatmentschemecan be found in table 3. The analysisprescribedremovalof 27 trees per acre at age 30•probably an indicationthat 420 treesper acrewould be evenbetterthan the 480. While the treatmentschemein table 3 represents the bestthat couldbe foundin termsof soil expectation,it is also useful for the forest manager to examine suboptimalschemesthat may bettermeetothersecondary objectives.In the nine alternativetreatmentschemes foundin table 2, the soil expectationvaluesare within 10 percentof the optimal scheme,an indicationthat none of them would
cause a severe loss in maximum
soil expectationvalues. The three schemeswith the highestsoil expectationsare all for the plantingdensity of 480 treesper acre, further substantiating this density as the best of those analyzed.Becausethe fourth and fifth "best" schemesare for the 680 trees per acre plantingdensity,a few more than480 treesappearless harmful to the primary objectivethan a few lesstrees Details concerningthe secondbest treatmentscheme are found in table 4. This scheme is of interest for four
reasons. First, it avoids a light thinning at age 30 Second, the rotation length comes closer to the 120 years that is often found in the literature(Schubert 1974, Alexanderand Edminster1980). Third, the hght residual stand at age 90 looks very much like a shelterwoodcut, which has also been recommendedfor
Table 3. Optimal stand treatment scheme for planting density of 480 trees and rotation of 90 years. Valuea are per acre.
Total
REMDVALS
RESIDUAL
stand
Basal
age
area
Years
Square•et
30 50 70 90
32.6 56.1 37.7 .0
Basal
Trees
Number
Totalvolume
area
Cubic•et
Square•et
199 626 573 0
4.2 40.3 60.9 61.6
210 120 45 0
Trees
Total volume
Number
Cubic•et
27 66 73 44
25 449 925 1,203
Table4. Suboptimalstandtreatmentschemefor plantingdensityof 480 trees and rotationof 110 years.Valuesare per acre.
Total
RESIDUAL
stand
Basal
age
area
Trees
Years
Square•et
Number
30 50 70 90 110
36.7 85.0 52.7 17.1 .0
REMOVALS Basal
area
Trees
Total volume
Cub• •et
Square•et
Number
Cubic•et
224 931 765 324 0
0.0 16.5 81.5 66.7 28.2
Totalvolume
237 195 75 15 0
ponderosa pine (Schubert1974). The growthmodelin PPOPT doesnot incorPorate a naturalregeneration componentfor even-agedstands,and thereforethis partial cut is not the result of silviculturalor economicgains dueto naturalregeneration produced by the shelterwood. F•nally,the gainsin silviculturalflexibilityproducedby this schemecome at the small cost of a 1.32-percent reductionin the soil expectation values.
Basal area
ITL
four would best meet the primary objective for the stand. They also demonstratethe added value that an existingstand,even an overstocked one, has over bare land(i.e., theexistingstandis worth$1,890.06peracre while an acre of bare land is worth $583.50). The corresponding optimal standtreatmentschemecan be found in table 7.
An examinationof the nine near optimal treatment schemes found in table 6 illustrates the existence of a
w•dearrayof alternatives thatdo not appreciably reduce the primary objective. For example, the fourth best solution (ITL of 4 with rotation length of 103) has a
Trees
diameter
per acre
Sq. •
•ches
Number
21.2 36.5 44.6 52.8 59.9 75.6
6.0 5.2 4.8 4.6 4.4 4.2
100 227 314 403 494 688
Table 6. Ten largest soil expectation values by initial thinning level (ITL) and rotation length. Changein maximum
Maximumsoil
Rotation ITL
2
3
4
5
The 10 treatmentschemesthat producedthe highest soil expectationvaluesfrom the six PPOPT analysesare found in table 6. These values indicate that ITL number
Mean
per acre
1 2 3 4 5 6
trees for each of Schubert's (1971) ITL's are found in table 5.
0 181 1,184 1,261 667
Table 5. After-thinning basal area, mean diameter, and number of trees for each of Schubert'a Initial thinning levels (ITL).
Precommercial Thinning
In this example, the problem is to decide which •ntensityof thinningto initially applyto an overstocked stand43 yearsold. To solvethe problemsix alternative •mt•al thinning levels (ITL's) were analyzedin PPOPT tO determinewhich initial stocking,and resultantthinning schemeand rotation length, would maximize the soil expectationvalue. It was assumedthat, once the stand was harvested,the optimal bare land scheme previouslydiscussedwould be appliedin perPetuity.It was also assumedthat the initial thinningswould cost $90 per acre. The six ITL's were based on the initial thinnings applied to Schubert's(1971) study of Taylor Woods growingstock levels. With these data as a guide, six after-thinningdiameter distributionswere constructed. The resultingbasalarea, mean diameter,and numberof
0 38 116 58 15
length
expectation per acre
Years
Dollars
103 123 103 123 143 103 123 143 123 143
1,851.32 1,845.79 1,869.71 1,878.91 1,853.29 1,672.92 1,890.06 1,672.75 1,875.09 1,666.76
soil
expectation
per acrefrom Rank
optimalsolution Percent
9 10 6 2 8 4 1 5 3 7
-
2.05 2.34 1.08 .59 1.95 .91 .00 - .92 - .79 - 1.23
treatmentschemeidentical.to the optimalsolutionbut with all treesbeing removedat age 103 (insteadof the shelterwoodlikecut at that age recommendedin the optimalsolution).Discretionaryimplementation of this clearcut solution to better meet secondaryobjectives wouldcostlessthan 1 percentin reducedsoil expectation value.
As a final observation,the fact that the top three treatment
schemes in table 6 have different.ITL's
but
commonrotationlengthsindicatesthat the solutionis more sensitiveto changesin rotation length than in initial thinningintensity.The inferenceis that quality controlon the initial thinningneednot to be too exact September1983/JOURNAL OF FORESTRY/597
Table 7. Optimal stand treatment scheme for initiel thinning levei (ITL) of 4 end rotation length of 123 years. Values are per acre.
Total
REMOVALS
RESIDUAL
stand
Basal
age
area
Basal
Trees
Total volume
Number
Cubic Net
Yea•
Square•et
43
52.8
403
63 83
77.5 53.4
103 123
area
Square•et
Trees
Total volume
Number
Cubic Net
508
0.0
0
0
225 90
1,005 862
58.7 77.5
170 131
762 1,250
14.9
15
297
72.6
73
1,447
.0
0
0
25.9
15
637
aslongasthe a•r-thinning diameterdistribution canbe analyzedto determinethe subsequent optimalthinning
MARTIN,G. L., and A. R. E]c. 1981. A dynamicprogramming analysisot silvicultural alternatives for red pineplantations in Wisconsin.Can. J. For
scheme. This is useful because, in a dense stand of small trees, it is often difficult to make an initial
MINOR,C. O. 1964. Site-indexcurvesfor young-growth ponderosa pine in
thinningto exactingstandards. ß
Res. 11:370-379.
northernArizona. USDA For. Serv.Res. Note RM-37, 18 p. RUTTERS, K. H., J. D. 'BRODIE,and D. W. HANN. 1982. Dynamic program-
mingfor optimization of timberproduction andgrazingin ponderosa pine For. Sci. 28:517-526.
Literature Cited ALEXANDER, R. R., andC. B. EDMINSTER. 1980. Management of ponderosa pine in even-agedstandsin the Southwest.USDA For. Serv. Res. Pap. RM-225, 11 p. HANN,D. W. 1980. Development andevaluationof an even-anduneven-aged ponderosa pine/Arizonafescuestandsimulator.USDA For. Serv.Res.Pap. INT-267, 95 p.
•HANN, D. W., and J. D. BRODIE.1980. Even-aged management: basic managerial questions andavailable or potential techniques for answering
SCHUBERT, G. H. 1971.Growthresponse of even-aged ponderosa pinerelated to standdensitylevels.J. For.69:857-860. SCHUBERT, G. H. 1974. Silvicultureof southwestern ponderosapine: the statusof ourknowledge. USDA For.Serv.Res.Pap.RM-123, 71 p.
THE AUTHORS---DavidW. Hann and J. Douglas Brodie are assistantand associateprofessors,Departmentof ForestManagement, and Kurt H. Riittersis graduateresearchassistant,Departmentof ForestScience,OregonStateUniversity,Corvallis97331
them. USDA For. Serv.Gen. Tech. Bull. INT-83, 29 p.
Catfaceson LodgepolePine--Fire Scars or Strip Kills by the Mountain Pine Beetle? R. G. Mitchell, R. E. Martin, and John Stuart ABSTRACT--Basalscarson lodgepolepine, Pinus contorta, are commonin centralOregonforests.Althoughforestershave generallycalled themfire scars,manyresultfrom old stripattacksby the mountainpine beetle,Dendroctonus ponderosae ---attacksthat kill only one side of the stem. Strip-kill scars are usuallywide at the bottomand narrowat the top, less than4 m long, and on the north and eastsidesof the stem.
Datingthescarsshowedthat centralOregonsuffereda beetle outbreak between 1920 and 1925 and another between 1900
and 1905. Observations of ring widthsin stemsectionsshow that a currentoutbreakand the previousone startedwhen stand growth was very slow. The mountainpine beetle is apparentlyan importantthinningagentthat relievescompetition in overstocked stands.
that leaves a catface-like scar on the lower bole. The trees
can survive for years with no obvious changesin the crown,evenwhenlessthan 20 percentof the bole'slower circumference hasliving cambiumandxylem. This article presentsobservationsshowingthat attacks by the mountainpine beetle often leavelodgepolepines with scarsthat can be confusedwith thosemadeby fire We describethe patternof the scarsandtheir historicaland ecologicalsignificance.Our informationis from two independentstudiesin centralOregon. Origin of Strip-Kills
Strip-killingoccurswhen the mountainpine beetleattacks and kills one or more sides of the stem but leaves
enoughundamaged cambiumfor the treeto survive.Some-
Catfaces onthe lower bole oflodgepole pine are oftentimesthe dead strip is only 6-10 cm wide; a more severe
referredto as fire scars.That is logicalbecausetheylook like the fire scarson fire-tolerantspeciessuchas ponderosa pine, P. ponderosa.But we cannothelp being skeptical aboutthe numberof scarson lodgepole pine--thereare too manyfor a speciesthatis generallyconsidered sensitive to fire (Marlin and Dell 1978).
In centralOregon,the chief sourceof scarson lodgepole pineis the mountainpinebeetle,a pestwith a longhistory of killing lodgepolepine in the West(Cole and Amman 1980). Althoughstrip-attacks are seldommentionedin the literature,we have found that attacksby the beetle commonlykil'l only one sideof the stem,usuallyin a pattern 598/JouRN^L OFFORESTRY/September 1983
attackwill nearlygirdle the tree, leavinglessthan 10 cm of living cambium.Recentlystrip-killedtreeslook at first glancelike "pitch-outs"--trees that forceattackingbeetles out with a copiousflow of resin. While pitch-outsfrequentlyoccurin outbreaks,closeexaminationof suchtrees in centralOregonshowedthatmanywerein factstrip-kills For example,whenchecking139 treesheavilyattackedin 1980and 1981on a 0.5-ha researchplot, we foundthat79' werekilled and 60 strip-killed.Somestrip-killedtreesare reattackedand killed in the same outbreakepisode,but stem analysesshow that many infestedtrees surviveand live for 60 or more yearsafter beingattacked.
