How Ecosystem Service Provision Can Increase ...

How Ecosystem Service Provision Can Increase Forest Mortality from Insect Outbreaks Charles Sims, David Aadland, David Finnoff, and James Powell ABSTRACT. Climate change is believed to be the root cause of the unprecedented mountain pine beetle (MPB) outbreak currently underway in the western United States. While climate change is undoubtedly a factor, changes in public forest management have resulted in more host trees in MPB habitat. We employ a novel approach to separate the contribution of changing preferences for ecosystem services from the effects of fire suppression and climate change in the current MPB outbreak. Simulations illustrate how an increased emphasis on nontimber ecosystem services induced a shift from a climate-independent disturbance process (timber harvesting) to a climatedependent one (insect outbreaks). (JEL Q23, Q57)

I. INTRODUCTION

In western North America, the native mountain pine beetle (MPB; Dendroctonus ponderosae Hopkins) plays an important role by removing older and less vigorous trees from the forest. Endemic MPB populations periodically surge, creating a natural cycle and periods of considerable forest mortality. The region has experienced four to five significant outbreaks over the last century (Taylor and Carroll 2004) and is in the midst of an outbreak of unparalleled severity. Surveys conducted by the U.S. Department of Agriculture Forest Service (USDA FS) show that while the areal extent of the current outbreak is comparable to previous outbreaks, nearly three times the number of trees have been killed (Figure 1). This forest mortality has resulted in billions of dollars in manufacturing losses (Abbott, Stennes, and van Kooten 2008; Patriquin, Wellstead, and White 2007; Phillips, Breck, and Nickel 2007) and numer-

Land Economics • February 2013 • 89 (1): 154–176 ISSN 0023-7639; E-ISSN 1543-8325 䉷 2013 by the Board of Regents of the University of Wisconsin System

ous less obvious impacts.1 The current outbreak is occurring in new habitats, with unknown ecological consequences (Logan, Re´gnie`re, and Powell 2003), and producing unexpected variations in wildfire type and severity due to alterations of forest fuels (Jenkins et al. 2008). It may also be contributing to global warming, as vast tracts of forest have been converted from a carbon sink to a carbon source (Kurz et al. 2008). While the economic and ecological consequences of the outbreak are not in question, we extend current research to demonstrate the role played by recent changes in forest management practices. A shift in forest management toward nontimber ecosystem services is shown to have significantly amplified the outbreak. In order for endemic MPB populations to transition to a large-scale outbreak, two requirements must be satisfied. The first is a sustained period of favorable weather over several years. Winter temperature influences MPB populations through survival, while summer temperature and drought indirectly impact populations through MPB attack success, which is required for reproduction (Carroll et al. 2004). Conventional wisdom appears to implicate climate change and a recent sequence of abnormally warm years as the root cause of the increase in outbreak severity (Aukema et al. 2008; Carroll, Re´gnie`re, and 1 A transitory economic boom for the forest-products industry is possible as killed trees are removed from the forest.

The authors are, respectively, assistant professor, Department of Applied Economics, Utah State University, Logan; associate professor, Department of Economics and Finance, University of Wyoming, Laramie; associate professor, Department of Economics and Finance, University of Wyoming, Laramie; and professor, Department of Mathematics and Statistics and Department of Biology, Utah State University, Logan.

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Sims et al.: Ecosystem Services and Insect Outbreaks

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FIGURE 1 Public Forestland Management and Climate Change as Primary Drivers of Mountain Pine Beetle (MPB) Outbreaks

Safranyik 2004; Harrington, Fleming, and Woiwod 2001; Logan and Powell 2001, 2009) (Figure 1). The implied argument is that the recent outbreak is abnormally severe because climate change allowed MPBs to successfully attack healthy trees that would have fought off attack in previous outbreaks. However, a second and more fundamental requirement for an outbreak is a sufficient stock of susceptible host trees. Large stocks of susceptible host trees combined with a homogenous forest structure increase the risk and severity of landscape-level MPB outbreaks (Safranyik and Carroll 2006). The vast majority of MPB habitat in the United States is public land administered by the USDA FS. As a result, pub-

lic forest management has played an important role in the current outbreak by regulating the abundance of susceptible host trees. Two changes in public forest management have increased the stock of susceptible host trees in MPB habitat. First, decades of fire suppression activities have caused less frequent but more severe fires (Gibson and Negroń 2009). The decreased frequency of fires created a period during which fewer hectares in the western United States were burned (Figure 1). The result was more host trees in MPB habitat. Increased fire severity led to more stand-replacing fires, which in turn created denser forests that are more susceptible to MPB attack. Second, timber harvesting on

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public forests has declined dramatically. Since 1990, the USDA FS has favored forest management with less timber harvesting (Figure 1), resulting in public forests with more susceptible host trees (Bengston 1994). In the absence of any drastic decline in forest product demand (Wear and Murray 2004) or forest stock inventories (Smith et al. 2009), this indicates a shift in preferences from timber to nontimber ecosystem services. Although economic theory typically holds individual preferences constant (Mas-Colell, Whinston, and Green 1995), there is growing evidence that preferences evolve according to individual and group interaction (see Durlauf and Young 2001, for a review). Changing preferences for ecosystem services of public forests thus provides an alternative economic explanation for the current outbreak. While climate change is undoubtedly a factor in the current outbreak, it is important to quantify the relative contribution of these two public forest management changes in an attempt to mitigate unintended climatic amplifications of MPB outbreaks. This effort is complicated by diverse forest characteristics in MPB habitat, ranging from low-elevation stands of Ponderosa pine to high-elevation forests of lodgepole pine. The influence of climate, fire, and timber harvesting has historically differed across these forest types due to the prevalence of, and adaptations to, these factors.2 To provide general results that may inform public forest management, we employ a novel approach to separate the contribution of changing preferences for ecosystem services from the effects of fire suppression and climate change in the current MPB outbreak on a representative forest in the western United States. Using a bioeconomic model of forest management on USDA FS lands, the effect of timber harvesting and fire suppression are tracked to determine the im2 For example, Ponderosa pine relies on frequent lowintensity fires to create low-density stands. It is primarily in this type of forest where fire suppression has had the greatest impact (Allen et al. 2002) and makes analyses that incorporate fuel load management fitting (Konoshima et al. 2008). In contrast, lodgepole pine relies on infrequent highintensity fires to create dense stands that are not as heavily influenced by fire suppression (Schoennagel, Veblen, and Romme 2004). Lodgepole pine forests have also historically experienced more timber harvesting (Smith et al. 2009).

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plied changes in preferences over forest ecosystem services and quantify the resulting impacts of these changes on forest and MPB dynamics. The framework extends (Sims, Aadland, and Finnoff 2010) to include the effects of wildfire and fire suppression with a thermal response model that links climate to MPB attack success. Much of the existing literature has focused on how forest management responds to climate change policies that encourage carbon sequestration (e.g., Alig et al. 1997; Englin and Callaway 1993; Lubowski, Plantinga, and Stavins 2006; Newell and Stavins 2000; Sohngen and Mendelsohn 2003). To our knowledge, no other study has incorporated the effect of climate change on forest resource growth in an economic framework. The model demonstrates that changes in preferences and subsequent reductions in timber harvesting have exacerbated the MPB disturbance process in western forests. The result is robust when controlling for the influence of fire suppression, and occurs by increasing susceptible hosts and amplifying the effect of climate change on MPB populations. While fire suppression may have played a larger role in certain forest types, it cannot fully explain the extent of the outbreak at a landscape scale without accounting for changes in preferences for ecosystem services. II. BACKGROUND

Stretching from New Mexico to California and north into British Columbia, the majority of MPB habitat in the United States is public land administered by the USDA FS.3 Management on these forests has evolved over time due to changes in society’s preferences for timber and nontimber ecosystem services provided from public lands. Following a major World War II expansion, USDA FS timber sales in MPB habitat leveled off after 1960 (Smith et al. 2009). Federal legislation such as the Multiple Use Sustained Yield Act of 1960, the Wilderness Act of 1964, and the National Forest Management Act of 1976 re3 In the United States, 74% of lodgepole pine forests— the primary host for the MPB—are administered by the USDA FS (Smith et al. 2009).

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quired forest outputs other than timber be given due consideration in the management of national forests. In 1990, USDA FS timber sales dropped precipitously in much of the western United States. This drop has been attributed to the mild recession in the early 1990s, softwood timber trade disputes between the United States and Canada starting in the mid-1980s, and federal timber sale restrictions in response to a number of high-profile environmental issues (Gorte 1994; Murray and Wear 1998; Wear and Murray 2004).4 While USDA FS timber harvests are sensitive to changes in price in the short run (Adams, Binkley, and Cardellichio 1991), they are largely insensitive to changes in price in the long run (Berck 1979). The implication is that macroeconomic conditions and trade disputes may be capable of explaining the initial decline in harvests but would be unable to explain the sustained reduction in timber sale offerings over the last two decades. Wear and Murray (2004) use an econometric model of the U.S. softwood lumber and timber markets to show that the decrease in public timber sale offerings cannot be explained by decreases in regional or national timber demand. They find that federal timber sale restrictions led to a shrinking market share for timber producers in the western United States. Due to the restrictions and increasing public outcry for other nontimber benefits from public forests, the USDA FS began favoring ecosystem management over timber management, as seen by the continued reduction in federal timber sales (Bengston 1994; Sedjo 1995).

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cycle (Samman and Logan 2000).5 A representative forest model is presented that captures the general forest dynamics present in MPB habitat; specific forest types can be reflected by varying the model’s parameters. Following Heavilin and Powell (2008), the forest is homogeneous but divided into three size classes: seed base (X ), young trees ( Y ), and adult trees (A ). Young trees have a diameter at breast height (dbh) less than 8 inches. Although young trees have fewer defensive mechanisms and could provide enough nutrients for the MPB larvae to develop, they seldom provide enough clearance in the inner bark for larval development. Adult trees are characterized by a dbh 8 inches and larger. While adults have the strongest defenses against MPB attack, they are also large enough to house egg galleries and act as an ample nutrient source. Each size class is measured in trees or seeds per hectare. The laws of motion for the beginning-of-period density in each size class are given by X t + 1 = (1 − δX)X t + bYY t + bAA t,

[1]

Y t + 1 = (1 − δY − λ t)Y t + δXX t,

[2]

A t + 1 = (1 − d − π t − λ t γ t)A t + δYY t − h t, 144444244443

[3]

AH t

The ecological component of the model presents a dynamic predator-prey relationship between MPBs and the forest with time, set in annual increments to match the MPB life

where growth and mortality are assumed to occur prior to timber harvesting, differentiating the harvestable stock A H t from A t. Each year, a proportion (δ X and δ Y) of the seed base and young trees mature to the successive size class. Contributions to the seed base are made by the young and adult size classes at rates b Y and b A. Only adult trees are considered viable for commercial harvest ht and susceptible to natural mortality (at constant rate d ) or MPB-induced mortality (at time-varying rate π t). Wildfire affects both young and adult trees and occurs through a combination of an exogenous rate of ignition λ t = 1/I t and an en-

4 One particularly influential issue was the proposed listing of the northern spotted owl under the Endangered Species Act in 1989. As a result, a federal court prohibited harvesting on a large share of the national forest timber sale program in the region in 1989 (Murray and Wear 1998).

5 The model is similar to one presented in two previous MPB papers: Sims, Aadland, and Finnoff (2010), which focuses on the endogenous nature of MPB risk and Aadland, Sims, and Finnoff (2012), which focuses on a spatiotemporal analysis of MPB epidemics.

III. THEORETICAL MODEL Ecological Model of Managed Forest

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dogenous rate of damage γ t. The probability of a fire igniting depends on the fire return interval (I t), which differs by forest type and region.6 To reduce notational complexity, fire ignition is assumed to immediately result in a ground fire that kills all young trees. The ground fire may also transition to a crown fire killing adult trees. The ability for a ground fire to transition to a crown fire is endogenously determined by the amount of combustible fuel in the forest (Van Wagner 1977), given here by the combined stock of young and adult trees.7 Following Daigneault, Miranda, and Sohngen (2010), the proportion of adult trees that die if a wildfire occurs is increasing in the fuel load at a decreasing rate γt =

z(Y t + A t)

, 1 + z(Y t + A t)

[4]

where 0 < z < 1 determines how much the abundance of young and adult trees contributes to fire severity. Increasing the fire return interval will leave more young and adult trees in the forest, which increases the severity of a fire. This captures the complex variations in fire regime between forest types. For example, Ponderosa pine forests are characterized by frequent fires (I < 30 years) of low severity, while lodgepole pine forests are characterized by less frequent (I > 200 years) but more severe stand-replacing fires. To capture the less frequent but more severe fires resulting from 6 The fire return interval is the average number of years between fire events at one location. Several studies (Amacher, Malik, and Haight 2005, 2006; Englin, Boxall, and Hauer 2000; Reed 1984) model the fire return interval as the λ parameter from a Poisson arrival process. 7 It could be argued that MPB-killed trees should also contribute to the amount of fuel. For simplicity, we abstract from this approach for two reasons. First, while MPB-killed trees have long been assumed to increase fire hazard (for a review see Parker, Clancy, and Mathiasen 2006), recent research suggests that MPB-killed trees may increase or decrease fire hazard depending on the type of fire and the time since MPB outbreak (Jenkins et al. 2008). Second, the number of MPB-killed trees is small, since our analysis is focused on the preoutbreak condition of the forest. Specifically, MPB-killed trees would contribute an average of less than 1% to the fuel load in our analysis. We feel that such an approach is acceptable, since our focus is on indentifying the root of the current outbreak and not forecasting its future impact.

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fire suppression activities (Bradshaw and Lueck 2011; Holmes, Prestemon, and Abt 2008; Yoder and Blatner 2004), we assume the fire return interval is increasing over time (Gibson and Negroń 2009), while holding the effects of harvesting on fuel load constant. There are additional means of fuel management (Amacher, Malik, and Haight 2005, 2006) that reduce fire severity, but they are not considered here. Successful MPB attacks cut off nutrient exchange between the roots and the tree, interupt water translocation, lower wood moisture content, and weaken defense mechanisms, which eventually lead to tree death (Samman and Logan 2000). The probability a pine tree will die from MPBs is determined by the interaction between the number of MPBs attacking the tree and the level of tree resistance (Berryman et al. 1985). The probability of successful attack at the tree level translates into a known rate of MPB-induced mortality at the forest level. Following Heavilin and Powell (2008), we define the rate of MPBinduced mortality as πt =

B2t B2t + a2t

,

[5]

where B t is the number of MPBs per hectare and a t reflects the resistance of susceptible trees to MPB attack in year t. This parameter decreases as trees become drought-stressed or as the emergence of MPBs—driven by temperature cues—becomes more synchronized in time, making the population of attacking beetles more effective in attacking new hosts. Equation [5] is characteristic of the type III functional response in predator-prey interactions (Holling 1959) and captures threshold dynamics characteristic of MPBs (Berryman et al. 1985). To be consistent with available USDA FS data, the severity of MPB damage is measured by the number of trees killed per hectare by MPBs: π t A t. The relationship between MPB populations and the forest stock involves a one-year lag, as adult MPBs typically emerge from the tree a year after initial infestation (Samman and Logan 2000). MPB density at time t is therefore a function of the density of successfully

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attacked trees at time t − 1 and the number of newly emerged beetles per successfully attacked tree,φ : B t = φ(π t − 1A t − 1)ν ,

[6]

where ν < 1 is a curvature parameter, modeling a proportional decrease in successful reproduction when large beetle populations begin to overutilize available host resources. Together, equations [5] and [6] capture the recursive nature of the MPB population. Equations [1]–[3] and [5]–[6] have also been shown to successfully replicate data on MPB attack dynamics at a landscape level (Heavilin and Powell 2008). Incorporating Climate Change: Thermal Response

The sensitivity of the MPB life cycle to variations in temperature has been well documented (Powell and Bentz 2009; Safranyik and Carroll 2006). We model the effect of temperature on MPB dynamics by allowing for a change in the overall reproductive success beetles have in any given year, φ/a t (Heavilin and Powell 2008).8 Since MPB development takes place in the phloem or inner bark of the tree, a thermal response model is used to connect measured phloem temperatures to the number of newly infested trees created by a single MPB-infested tree (Powell and Bentz 2009). The model is driven by hourly phloem temperatures for the year between the old and new attacks and calculates a distribution of MPB emergence per day, P(t). The degree to which this distribution exceeds a critical threshold predicts the ratio of new-to-old infestations, r t. Values of r t grow or shrink depending on beetle life-cycle events, which are controlled by the phloem temperature. If the emergence distribution is narrow and steep (characteristic 8 Warmer summer temperatures aid in synchronizing adult beetle emergence, increasing the success rate of subsequent attacks (Powell and Bentz 2009) and reducing the tree resistance parameter a t in equation [5]. Likewise, warmer winter temperatures increase larval survival (Safranyik and Carroll 2006), reflected as a larger value for φ in equation [6]. Proportional changes in a t and φ have little impact on model results.

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of higher average temperatures), the beetles are relatively effective in killing new hosts; broader emergence curves (lower mean temperatures) result in smaller values of r t. The thermal response model’s r t predictions can be correlated with the tree resistance parameter, a t, in the bioeconomic model. We can then write a t as a function of r t, which links the results of the thermal response model with the ecological component of the bioeconomic model:9 at = φ

( ) 0.5A t

ν

[7]

.

rt

For a given adult tree stock, higher temperatures trigger larger values of r t, thereby lowering host tree resistance. Ecosystem Service Production in MPB Habitat

Society in the model is made up of many identical households, which receive instantaneous utility from a composite good unrelated to the forest, Q t, and ecosystem services derived from public forests. Ecosystem services are comprised of timber products h t and nontimber services such as amenity values, wildlife habitat, and biodiversity. Nontimber ecosystem services depend on the quality of the forest resource (Englin, Boxall, and Hauer 2000), proxied by the stock of living adult 10 trees A H t . For tractability, period t utility of the representative household is given by U(Q t,h t,AH t ;α t) = ln(Q t) + (1 − α t) ln(h t) + α t ln(AH t ),

[8]

where α t is the nontimber preference parameter, which captures the relative weight house9 The thermal response model predicts π A = t t r t π t − 1A t − 1, while the bioeconomic model predicts π t A t = 2 2 ν φ (π t − 1A t − 1) A t. The predictions are reconciled by a2t + φ2 (π t − 1A t − 1)2ν assuming that π t = 0.5, which occurs when a2t = B2t = φ2 (π t − 1A t − 1)2ν . 10 USDA FS lands provide many nontimber forest benefits. The standing forest stock may proxy some of these nontimber benefits better than others. Extending the model to account for specific nontimber forest benefits is a topic for future research.

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holds place on nontimber ecosystem services in relation to timber ecosystem services. We normalize the nontimber preference parameter to the unit interval 0 ≤ α t ≤ 1.11 It is through changes in α t that the model can track changes in social attitudes toward ecosystem services over time. Each year the representative household inA elastically supplies L = L Q t + L t units of labor, which are allocated between the production of the composite commodity (L Q t ) and the production of timber products (L A t ). Production of Qt is directly proportional to labor inputs: Q t = LQ t . Harvesting adult timber requires labor and depends on the harvestable stock according to harvest function: H h t = ρLA t At ,

[9]

where ρ is a scale parameter measuring the efficiency of harvesting activities.12 The inclusion of stocks in the harvest function is a simple way of accounting for complex spatial considerations inherent in timber harvesting. For instance, fewer trees in the forest will result in longer distances to transport logging equipment into the forest and drag felled trees back to roads. Harvests of standing dead trees (salvage harvesting) may also be important in fuel management (Amacher, Malik, and Haight 2005) but are not included in our model given the focus on documenting trends in public forest harvest policy. There are no discernible trends in salvage harvesting. Since adult harvest levels are supplied by USDA FS data, ignoring salvage harvests will not change the decline in harvest levels or harvesting’s contribution to the MPB outbreak. Optimal forest management seeks an appropriate balance between timber and nontimber ecosystem services, given societal preferences. However, there may be political and judicial factors that cause changes in forest management to lag changes in preferences. Specifically, a social planner chooses a har11 Lower values of α indicate that society values public t forestland more for timber services, whereas high values of α t indicate a higher relative preference for nontimber services. 12 Thinning activities by the USDA FS are assumed to produce commercially viable material and are treated identically to harvesting.

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vest program to solve the following problem:13 ∞

max 兺 β t − 1 U(Q t,h t,AH t ;α t − s), {h t }∞t = 1 t = 1

[10]

where 0 ≤ β ≤ 1 is the annual discount factor and s ≥ 0 allows for any lag between changes in preferences and timber harvesting. The problem in [10] is solved subject to the ecological equations of motion [1]–[6], initial conditions for stocks, and the constraints Qt +

ht ρAH t

[10a]

= L,

h t > 0.

[10b]

The solution to [10] is found through a series of substitutions that incorporate all applicable dynamics, changing the choice variable from harvest to stock of adult trees (Azariadis 1993). Normalizing labor supply to one, the first-order condition requires harvesting to proceed until the discounted future marginal benefits and costs are equal.14 The current and discounted future benefit of harvesting an additional tree is 1 − αt − s

冦

ht

∂AH t + 1 ∂γ t + 1 ∂A t + 1 + β Ψt + 1 ∂γ t + 1 ∂A t + 1 ∂h t

冧冦 ∞

+

冦

兺 β k Ψt + k

k=2

冧

∂AH t + k ∂π t + k ∂B t + k ∂A t + 1 ∂π t + k ∂B t + k ∂A t + 1 ∂h t

冧

∞

+

兺 βk Ψt + kΔseed t+k k=3

r fire

,

[11]

13 The USDA FS’s fire suppression budget increased substantially following the 1988 Yellowstone fires (O’Toole 2006). This increase could be interpreted as a shift in forest management similar to the decrease in timber harvesting that began in 1990. However, our reading of the evidence is that the budget increase is a response to a period of larger fires, rather than a fundamental change in the USDA FS’s attitude toward fire suppression (Calkin et al. 2005). As a result, we chose not to treat fire suppression as an additional choice variable. 14 Interested readers should consult the Appendix for a more detailed presentation of the solution procedure and the first-order condition found by equating expressions [11] and [13]. The equivalence of our solution procedure and the traditional method of Lagrange multipliers is also shown in the Appendix.

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where Ψt =

1 − αt − s ht

−

AH t − ht 2 Q t ρ(AH t )

+

αt − s AH t

[12]

is the marginal net benefit of an adult tree at time t . Equation [11] contains both direct and indirect benefits of harvesting. The first term in [11] represents the immediate benefit of timber harvesting. Harvesting in period t also indirectly lowers the severity of fires by reducing the adult stock in t + 1 (second term) and reduces MPB risk by lowering the MPB stock in t + 2. Harvesting also recursively lowers MPB risk in all future periods (third term). The last term is the present value at t + 3 of lower fire damage in all future periods working through the seed effect. The term Δseed r fire captures the effect of harvesting on fire risk through the seed base. The term is defined mathematically in the Appendix. Due to the relatively slow growth of a forest, this effect is negligible. The current and discounted future cost of harvesting an additional tree is 1 Q t ρAH t

+ β {Ψt + 1(1 − d − π t + 1 − λ t + 1γ t + 1) } ∞

+

兺 βk Ψt + kΔseed t+k . k=3

[13]

The first term represents the labor cost of harvesting in terms of reduced production of the composite commodity. Harvesting a tree in period t means it is not available to provide utility for timber and nontimber benefits in period t + 1. The opportunity cost in t + 1 of harvesting in period t (second term) is lower because the tree may be killed by fire or MPBs (at time-varying rates λ t + 1 γ t + 1 and π t + 1) or natural causes (at rate d ) before next period’s harvesting decision. The last term is negligible and represents the present value at t + 3 of the reduction in the future seed base caused by harvesting in period t . The term Δseed captures the effect of harvesting on the seed base and is defined in the Appendix. The optimal harvest condition found by equating [11] and [13] provides a rule to determine optimal harvest management for a

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given set of model parameters and preferences. If observed annual USDA FS harvest data are assumed to optimally respond to changes in preferences, the harvest condition can be used to determine the implied relative preference for nontimber ecosystem services, α t − s. The derived value of α t − s is consistent with stocks that are determined by the equations of motion, given observed harvests. IV. DYNAMIC CALIBRATION

To derive the values for α t − s implied from observed data, the model is simulated as if observed harvests were optimal while controlling for both the effects of fire suppression15 and the echo effects of previous largescale disturbances.16 Figure 1 shows observed values for public forest timber sales, temperature and hectares burned for the years 1960 through 2008, and hectares of MPB infestations and trees killed by MPBs from 1977 through 2008. Each variable displays a relatively constant or declining trend prior to 1990. After 1990, timber harvests plummet while average temperatures, hectares burned, hectares of MPB infestations, and trees killed by MPBs all rise. The sample period contains all the relevant drivers needed to determine the contributions of climate change, fire suppression, and timber harvests in the current MPB epidemic. Model Parameters

Table 1 presents a set of economic and ecological parameters selected to obtain a realistic initial condition in 1960 consistent with 15 1960 is the first year hectares burned and adult (green) timber harvest data are available. While fire suppression began much earlier than 1960, the effect of fire suppression from 1960 onward is clear, as the number of hectares burned initially decreases and then begins to increase in the late 1980s (Figure 1). 16 U.S. forest inventory analysis data are problematic for our purpose, as they include the effects of all previous disturbances to forests, including past MPB outbreaks. To allow a clear focus on changes in preferences toward nontimber values, we simulate a hypothetical forest unaffected by past disturbances. This allows us to determine what portion of the dynamic response in the hypothetical forest can be attributed to fire suppression and the change in preferences in the absence of the echo effects of past disturbances.

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TABLE 1 Model Parameters and Initial Condition Parameter

Definition

Value

Source Koch 1996; Fowells 1965; Lotan and Critchfield 1990 Koch 1996; Fowells 1965; Lotan and Critchfield 1990 Koch 1996; Fowells 1965; Lotan and Critchfield 1990 Koch 1996; Fowells 1965; Lotan and Critchfield 1990 Heavilin and Powell 2008

δX

Rate of germination of seeds in seed base

0.001

δY

Rate of maturation of young trees

0.004

bY

Rate of seed production in young trees

0.0018

bA

Rate of seed production in adult trees

0.1

a1960

MPBs/hectare required for a 50% chance of MPBinduced mortality in adult trees in 1960 Average MPB offspring per infested tree Rate of natural adult tree mortality Rate of decrease in beetle reproduction with increases in beetle-induced mortality in adult trees Harvest efficiency parameter Fire severity parameter Average fire return interval in MPB-habitat in 1960

φ d ν ρ z I1960 β

Annual discount factor

157,653 4,500 0.015 0.5 0.03255 0.00054 100 0.96

Bentz 2006 Runkle 1985 Berryman et al. 1985 Romme et al. 2006 Hann and Bunnell 2001; Romme et al. 2006 Row, Kaiser, and Sessions 1981

Initial Condition Corresponding to 1960 U.S. Department of Agriculture Forest Service Harvest Data π X A

0.3% 57,160 seeds/hectare 499 trees/hectare

B Y Q

8,397 beetles/hectare 4,082 trees/hectare 0.697

Note: MPB, mountain pine beetle.

the observed harvest level. This condition is characterized by 8,397 MPBs, 57,000 seeds, and 499 adult trees per hectare. The sensitivity of model results to selected parameter values is investigated in the Appendix. The first step in the calibration process determines the scale parameter ρ , measuring the efficiency of adult harvesting. On public lands, inefficiencies arise from changes in the skills of the logging labor employed or the presence of administrative requirements that hinder the efficiency of the harvesting effort. This parameter is scaled to 0.03255 to provide an initial condition where society equally values timber and nontimber ecosystem services:α 1960 − s = 0.5.17 The discount rate is set to 4% (implying an annual discount factor of β = 0.96) in accordance with USDA FS practice (Row, Kaiser, and Sessions 1981). Natural mortality (d) is set to 1.5% (Runkle 1985). The parameters dictating seed production (b V,b A), germination (δ X), and maturation (δ Y) in Table 1 pro17 This assumption is made for convenience and does not affect the general result.

duce a comparable and defensible initial condition typical of USDA FS land in the western United States (Koch 1996).18 These forestspecific parameters allow the forest to reestablish within 80 to 140 years following a stand-replacing disturbance (Lotan and Critchfield 1990). Fire-specific parameters I and z are based on fire regimes found in MPB habitat. Fire regimes are generally classified based on fire return interval I (frequency) and the percent replacement of overstory trees γ t (severity) (Hann and Bunnell 2001). The fire regime in MPB habitat has historically ranged from frequent fires of low severity (I < 30 and γ t < 25% ) to less frequent stand-replacing fires (I > 200 and γ t > 75%) (Romme et al. 18 Mature lodgepole pine stands (a primary host for MPBs) contain anywhere from 850 to 1,350 trees per hectare and hold anywhere from 60,000 to 400,000 viable seeds per hectare (Koch 1996). Younger stands may contain up to 20,000 trees per hectare and 35,000 to 1,200,000 viable seeds per hectare (Fowells 1965). Stand densities for other pine species and mixed pine stands are likely to be much lower.

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2006). We assume the fire return interval is initially 100 years and z is selected to provide an initial fire severity of 50%: z = 0.00054. To illustrate the effect of fire suppression on fire regimes, we increase the fire return interval by 6 months for every year from 1960 to 2008. This corresponds to a 50% departure over the nearly 100 years fire suppression has taken place on public lands.19 Due to the inverse relationship between fire frequency and severity, a 50% departure from a 100-year fire return interval also produces fire-induced tree mortality that temporally corresponds to the burned hectare data in Figure 1. MPB-specific parameters a t , φ , and ν depend on site conditions, tree species, climate, and geography, among other things. Proportional changes in a t and φ have little impact on the model. The key value is the ratio of beetle reproductive success to tree resistance: φ/a t. Using aerial survey data, Heavilin and Powell (2008) estimate this ratio to be approximately 0.071 in 1990. Previous studies provide multiple measures of φ by counting the number of beetles emerging from an infested tree (e.g., Bentz 2006). These studies generally place φ between 4,000 and 5,000 beetles per infested tree. This suggests a 1990 is approximately 157,653 beetles per hectare, assuming φ = 4,500 beetles per infested tree. In the absence of data prior to 1990 and as discernable changes in temperature in the western United States have been relatively recent (Figure 1), we assume this level of tree resistance was constant prior to 1990. Finally Berryman et al. (1985) report a decreasing relationship between MPB offspring and the number of MPB attacks per square meter of tree surface area. This indicates decreasing reproductive returns from increases in adult-tree mortality and implies a degree of curvature in [6]. In the absence of any additional quantitative results to guide us, we set ν = 0.5. 19 Fire regime classifications can be used to measure the degree of departure from historic fire return intervals due to fire suppression (Koch 1996). Class 1 represents ecosystems with low departure ( < 33%); Class 2 indicates ecosystems with moderate departure (33–66%); and Class 3 indicates ecosystems with high departure ( > 66%) from historic conditions. MPB habitat in the western United States may exhibit low to high departure from historic fire return intervals.

163

Measuring Implied Preferences for Nontimber Ecosystem Services

The optimal harvest condition given by the equality of [11] and [13] serves as a bridge between preferences and optimal forest management. Given household preferences for forest ecosystem services, the optimal harvest condition could be used to solve for welfaremaximizing harvest levels in each period. Instead, we use USDA FS harvest data as a measure of annual harvests and apply the optimal harvest condition to solve for household preferences that would make observed annual USDA FS harvests optimal. Assuming political and judicial delays are minimal (s = 1), the equations of motion are used to determine the (unobserved) stocks, and the first-order condition is “flipped” to solve for the implied relative preference for nontimber ecosystem services, α t − 1, from 1959 to 2007.20 Necessary data to measure implied preferences include annual harvest of live (green) trees from national forests in the geographic range of the MPB (USDA FS Regions 1 through 6). While annual USDA FS harvest data are publically available from Cut and Sold Reports at a regional level, these reports do not distinguish between harvests of live and dead trees. Periodic Timber Sale Accomplishment Reports21 (PTSAR) do distinguish annual live timber sales on USDA FS land and were used as a proxy for h t.22 These board foot volume measures of total harvests must be converted to trees per hectare. Using his-

20 The s = 1 assumption is made for exposition. Changing s will shift the time period over which implied relative preferences are solved for but will not alter the dynamic path of harvests (which is based on observed data) or tree and MPB stocks. 21 See the USDA FS web pages for more information: www.fs.fed.us/forestmanagement/products/ptsar/index. shtml. 22 Using timber sales as a proxy for timber harvest has limitations. While PTSAR indicates the annual volume of timber for the year of the sale, these contracts may cover up to three years, so the timber may not have been harvested in the year of the sale. While sales data may not exactly match annual variation in harvest levels, it should capture the underlying shift in preferences toward nontimber ecosystem services of public forestlands that occurred around 1990.

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Land Economics

toric data from the USDA FS Land Areas Reports23 from 1997 through 2008, we calculate that Regions 1 through 6 consistently make up 75% of total USDA FS area. This hectare measure is used to calculate average board feet per hectare of live timber sold within the geographic range of the MPB. The board feet measure is then converted to trees per hectare assuming 25 board feet per tree, which is consistent with an 80-year-old stand of lodgepole pine.24 This provides a measure of the number of pine trees harvested per hectare on USDA FS land in MPB habitat. Model projections show that the decrease in adult timber harvesting after 1990 follows an increase in preferences for nontimber ecosystem services (moving averages shown in Figure 2). This corresponds to Wear and Murray’s (2004) findings. However, forest management alone is not capable of replicating the MPB-induced mortality witnessed between 1990 and 2008. The dotted line in Figure 3 shows MPB-induced tree mortality controlling for the effects of fire suppression and changes in timber harvesting. In addition to the changes in forest management, this period has also seen an increase in mean annual temperature throughout the western United States (Figure 1). Temperature increases raise MPB attack success by synchronizing adult beetle emergence and increasing survival. In addition to underestimating MPB-induced mortality, ignoring the influence of climate also fails to capture the full effect of the shift in preferences. Since increasing temperatures cause trees to be more susceptible to MPB attack, society’s desire to leave more trees in the forest also amplifies the effects of climate change on MPB populations. For these reasons, it is essential to accurately measure the effect of climate change in our bioeconomic model.

23 See the USDA FS web page for more information: www.fs.fed.us/land/staff/lar/. 24 Board foot per tree will vary depending on species, forest density, and site conditions. Lotan and Critchfield (1990) find yields range from 11 board feet per tree for a 50-year-old stand to over 80 board feet per tree for a 140year-old stand for lodgepole pine on medium-quality sites in Montana and Idaho.

February 2013

Measuring the Effect of Climate Change

To parameterize the thermal response model, hourly phloem temperatures are needed for the year between the old and new attacks. A continuous south-side phloem temperature record exists from July 19, 1992, through August 18, 2003, for a MPB outbreak in the Stanley Valley of central Idaho. The phloem temperature record is used to project temperatures for the years 1990–2050 assuming a 0.0443⬚C/year increasing trend in annual mean temperatures. Using nonlinear rate curves and fitted variances for all eight developmental phases through which a MPB must pass between host attack and emergence of brood to attack new hosts the following year, a distribution of MPB emergence per day, P , is calculated. The degree to which this distribution exceeds a critical threshold predicts the ratio of new-toold infestations, r t: 245

rt =

冮 max(8.10P(τ) − 0.181,0)dτ,

[14]

152

where 152 and 245 are the Julian day measures for June 1 and August 30 in the year of beetle emergence.25 The values 8.10 and 0.181 are maximum likelihood estimates for reduced-form biological parameters using phloem temperatures measured on the south (warm) side of hosts in the Stanley Valley.26 Using φ = 4,500 MPBs per tree, ν = 0.5, and a reasonable estimate of initial host density27 gives the final relationship between the thermal response model and tree resistance: 63,640 at =

冪r t

.

[15]

25 These dates relate to seasonal cutoffs in emergence that arise due to temperature requirements at various stages of the beetle life cycle (Powell and Bentz 2009). If beetles emerge earlier than June 1, the larvae are susceptible to the summer heat and the pupae will be present at a time (fall) when they will be frozen. If beetles emerge later than August 30, eggs are likely to be frozen. 26 For more information see Powell and Bentz (2009). 27 Before an outbreak saturates, we may assume that the number of susceptibles is approximately the initial host density; in the Stanley Valley a reasonable estimate is A t = 400 trees per acre.

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165

FIGURE 2 Shift in Preferences Implied by USDA FS Harvest Data: Preferences for Nontimber Ecosystems Services αt Are Measured from the First-Order Condition in [11] and [13] with USDA FS Timber Sale Data Substituted for ht

FIGURE 3 Simulation Results from 1990 to 2008 Using Annual USDA FS Timber Sales Data as Proxy for Harvests: Model Results Ignoring the Effects of Climate Change (dotted line) Yield MPB-Induced Mortality below Historic Levels (x); Benchmark Model (solid line) Includes the Effect of Climate Change to Ensure Results Consistent with Observed Levels of MPB-Induced Mortality.

The thermal response model was simulated for each year using the temperature projections and tree resistance trajectories outlined above. To avoid projecting temperature anomalies in the Stanley Valley to the rest of the western

United States, we use the results of the thermal response model to calculate trends in tree resistance. A logarithmic regression was used to estimate constant exponential rates of decrease in a t from these data, generating rates ranging from − 0.29% to − 1.1% per year de-

166

Land Economics

pending on the base year. Combined with historic harvest levels and an increasing fire return interval, we find that a decrease in a t of 0.65% per year is capable of replicating the historic levels of MPB-induced mortality witnessed between 1990 and 2008 (solid lines in Figure 3). These results incorporate historic changes in preferences for ecosystem services, fire suppression, and the effects of climate change. V. ISOLATING THE EFFECT OF FOREST MANAGEMENT

To illustrate the implications of the model, we construct a benchmark that replicates historic MPB-induced mortality by accounting for changes in preferences for ecosystem services, fire behavior, and climate. The shift toward nontimber ecosystem services creates a direct effect on MPB-induced mortality by leaving more susceptible trees in the forest. Fire suppression has decreased the prevalence of fire, also leaving more susceptible trees in the forest. The recent warming trend within MPB habitat also increased the rate of MPBinduced mortality. These individual effects combine to produce an indirect amplification effect. That is, additional trees left in the forest due to changing preferences and fire suppression are now more vulnerable to MPB attack as a result of climate change. To capture the peak of the current outbreak, we simulate past 2008. Preferences are assumed to remain at the 2007 level, while changes in fire behavior and climate continue to impact forest and MPB dynamics through 2020, at which time the outbreak will have largely run its course. This allows optimal harvest levels to be calculated from 2009 to 2020. Combining these simulated harvest levels with the observed harvest levels allows us to calculate MPB and forest dynamics over the entire outbreak, as shown by the solid lines in Figure 4. The period 1990 to 2008 is characterized by a sharp decrease in harvest levels, along with a brief increase in harvest levels at the end of the period. Projecting the model into the future, optimal management calls for a gradual decrease in harvest levels from 2009 to 2020 as the stock of trees is reduced by

February 2013

MPBs. In this benchmark model, the increasing importance of nontimber ecosystem services and the general decline in harvests combine with fire suppression and a changing climate to induce cycles in the MPB stock due to “echo effects” inherent in the ecological model. Such cycles are a natural MPB phenomenon, causing an outbreak that peaks in 2011 at approximately 30.9 trees per hectare killed. To isolate the roles of fire suppression and changing preferences in the current MPB outbreak, we consider counterfactual scenarios where preferences for nontimber ecosystem services remain constant and the effects of fire suppression are omitted. This approach captures the direct and indirect amplification effects of changing preferences and fire suppression. In the case when fire suppression is assumed to have not occurred, the fire return interval remains at the 1960 level. Without fire suppression there are fewer trees available for MPB to attack. The dynamic response is similar to the benchmark model but with a slightly less severe MPB outbreak that peaks in 2012 at approximately 29.2 trees per hectare killed. In the scenario of invariant preferences, the social planner responds to climate-driven increases in MPB-induced mortality by gradually reducing harvest levels, as opposed to the drastic decline in harvests when preferences shift (Figure 4A). This counterfactual scenario sees more trees harvested, fewer trees available for MPBs to attack, and a less severe increase in MPB populations (Figure 4B). The result is a delayed and less severe MPB outbreak that peaks in 2014 at 19.3 trees per hectare killed (Figure 4C). Consistent with previous research (Wear and Murray 2004), results indicate that the decrease in adult timber harvesting after 1990 follows an increase in preferences for nontimber ecosystem services. The bioeconomic model takes this result one step further. Given the effects of fire suppression, the decrease in timber harvesting left more susceptible trees standing in the forest, which directly increased MPB populations even in the absence of climate change. These additional trees have also become more susceptible to MPB attack due to the impact of climate change. The result has been a shift in the ecological regime

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167

FIGURE 4 Effect of Changing Preferences on Severity and Timing of MPB Outbreaks: Solid Lines Reflect the Benchmark Model, Where the Harvest Decision Responds to a Shift in Society’s Preferences toward Nontimber Ecosystem Services; Dashed Lines Reflect the Counterfactual Scenario, Where Society’s Preferences for Ecosystem Services Remain Unchanged.

from a primarily climate-independent disturbance processes (timber harvesting) to a climate-dependent one (MPB outbreaks). VI. CONCLUSIONS

This paper focuses on understanding and quantifying the role of U.S. public forest management—through fire suppression and timber harvesting—on MPB outbreaks. A history of fire suppression on public forestlands has decreased the prevalence of fire, leaving more susceptible trees in the forest. Simulations indicate that fire suppression is responsible for

a negligible portion of the increase in MPBinduced tree mortality in the current outbreak. A larger portion is explained by the sharp decrease in timber harvesting after 1990, which is consistent with a shift in preferences toward valuing the forest for nontimber ecosystem services such as amenity value, wildlife habitat, and biodiversity.28 This shift toward nontimber ecosystem services and the subsequent 28 Our choice of utility function restricts the elasticity of substitution between goods to 1. Timber harvesting will have played more (less) of a role in the current outbreak the larger (smaller) the degree of substitutability between goods.

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Land Economics

reduction in harvesting led to more susceptible trees in the forest and an increase in MPBinduced mortality that temporally corresponds to the ongoing outbreak in the western United States. The increase in susceptible trees also exacerbates the effects of climate change, which amplified MPB outbreaks further. While simulations suggest that climate change is a primary driver of the MPB epidemic, the shift in preferences for ecosystem services indirectly expedited the MPB outbreak and substantially increased tree mortality. This result implies that the current unprecedented MPB outbreak is, to a large extent, an artifact of the fundamental change in public forest management that took place nearly two decades ago. While our results present a general overview, it is important to note that fire suppression and changes in preferences for ecosystem services may have played more or less of a role in the current MPB outbreak in specific forest types. For example, fire suppression is expected to have a minimal impact in lodgepole pine and subalpine forests, whose historic fire return interval is greater than 100 years (Romme et al. 2006). However, in the Ponderosa pine forests of Arizona, New Mexico, and southern Colorado, the fire return interval is historically much shorter, implying a greater role for fire suppression in this forest type (Romme et al. 2006). If the objective is to apply our results to a specific forest type, forest estate models may be a preferable alternative to the more general model of forest dynamics presented herein. Our results also highlight how changes in public forest management have altered the disturbance regime in western forests. Following the increase in timber harvesting after World War II and the initiation of fire suppression activities, timber harvesting became the dominant disturbance regime. The shift toward nontimber ecosystem services eliminated harvesting as a dominant disturbance. In its absence, MPB-induced mortality appears to be claiming that role, implying larger MPB outbreaks even if climatic factors were held constant. However, as a growing body of evidence indicates, the MPB’s role as a natural disturbance agent may be fundamentally altered by climate change, leading to even more severe outbreaks in the future. The shift

February 2013

in social attitudes for ecosystem services, therefore, not only helped create the current outbreak by leaving more trees in the forest but also exacerbated the effects of climate change by shifting from a relatively climateindependent disturbance regime (timber harvesting) to a climate-dependent one (MPB outbreaks). It may be decades before the full impact of the change in preferences and the subsequent change in disturbance regimes is revealed, given that forests exhibit such a long ecological memory (Peterson 2002). In the meantime, society needs to weigh the risk of more severe future MPB outbreaks with the desire for less actively managed public forests. If the benefits from increases in nontimber ecosystem services outweigh the corresponding losses from amplified MPB outbreaks, elevated forest mortality may represent part of a painful but necessary transition to a new, less intensively managed forest. If not, there may be a role for more active forest management on public forests. Answering this question is beyond the scope of this paper and we leave it to future work. APPENDIX Derivation of the Euler Equation: Substitution Method A social planner chooses harvesting levels to maximize ∞

兺 βt − 1 {ln(Qt) + (1 − αt − s)ln(ht) t=1 + α t − s ln(AH t ) },

[A1]

subject to equations [1]–[6] and [10a]. The need to link harvests with the preference parameter α t − s requires a single optimality condition. As all constraints are given by equalities, a method of substitution is followed (Azariadis 1993). All the biological and economic constraints are substituted into [A1], changing the choice variable from h t to A t + 1. Later in the Appendix we show that this method is equivalent to the method of Lagrangian multipliers. First, labor endowments are normalized to one such A H that LQ t = 1 − L t . Noting that A t = A t + 1 + h t and substituting [10a], we can rewrite [A1] as

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∞

(

兺 βt − 1 冦ln 1 − ρ(A t=1

)

ht

Substituting [6] and [2] into [A3] then yields

t + 1 + h t)

冧

+ (1 − α t − s)ln(h t) + α t − s ln(A t + 1 + h t) .

[A2]

(

ht = 1 − d − − λt

To account for the ecological components, we start by substituting [4] and [5] into [3] to get

(

ht = 1 − d −

B t2 B t2 + a2

− λt

z(Y t + A t)

)

1 + z(Y t + A t)

At

冢

1−d− − λt

(φ(π t − 1A t − 1)ν )2 (φ(π t − 1A t − 1)ν )2 + a2

z((1 − δ Y − λ t − 1)Y t − 1 + δXX t − 1 + A t)

)

1 + z((1 − δ Y − λ t − 1)Y t − 1 + δXX t − 1 + A t)

+ δY(1 − δY − λ t − 1)Y t − 1 + δYδXX t − 1 − A t +1.

(φ(π t − 1A t − 1)ν )2 (φ(π t − 1A t − 1)ν )2 + a2

z((1 − δY − λ t − 1)Y t − 1 + δX(1 − δX)X t − 2 + δXbYY t − 2 + δXbAA t − 2 + A t)

冣

At

1 + z((1 − δY − λ t − 1)Y t − 1 + δX(1 − δX)X t − 2 + δXbYY t − 2 + δXbAA t − 2 + A t)

Due to the recursive nature of the MPB dynamics and the forest stocks, one must continually substitute π, B, X, and Y into [A5] to fully account for the shadow value of B, X, and Y. The resulting expression can then be substituted into [A2] to fully account for equations [1]–[6] and [10a]. This substitution procedure also changes the choice variables from harvests to the stock of adult trees. A similar solution procedure is described by Azariadis (1993) and was used in previous research to study the effect of cattle cull rates on the age structure of a cattle stock (Aadland 2004). Following the series of substitutions outlined above and taking derivatives with respect to A t + 1 yields our first-order condition for welfare-maximizing levels of harvest:

ht ∞

+

−

1 Q t ρAH t

冦

+ β Ψt + 1

∂AH t+1

∂γ t + 1 ∂A t + 1

∂γ t + 1 ∂A t + 1 ∂h t

∂AH t + k ∂π t + k ∂B t + k ∂A t + 1

兺 βk 冦Ψt + k∂π k=2

t+k

∂B t + k ∂A t + 1 ∂h t

冧

兺 βk {Ψt + kΔseed t+k

r fire

冧

}

= β {Ψt + 1(1 − d − π t + 1 − λ t + 1γ t + 1) } ∞

兺 βk {Ψt + kΔseed t + k }, k=3 [A6]

where

=

∂AH t + k ∂γ t + k ∂Y t + k ∂X t + k − 1 ∂A t + 1 ∂γ t + k ∂Y t + k ∂X t + k − 1 ∂A t + 1

Δseed t+k =

∂h t

[A7] ,

∂AH t + k ∂Y t + k ∂X t + k − 1 ∂A t + 1 ∂Y t + k ∂X t + k − 1 ∂A t + 1

[A5]

∂h t

[A8]

Equations [A7] and [A8] indicate the complexity of the “seed effect” terms, succinctly presented as r fire and Δseed Δseed t+k t + k in the text. Alternative Dynamic Optimization: Method of Lagrangian Multipliers An alternative solution method is to use the method of Lagrangian multipliers. The present value Lagrangian expression for the problem is ∞

(

ht

)

兺 βt 冦ln 1 − ρAH + (1 − αt)ln(ht) t=0

t AH [ (1 − d − π − λ γ )A + α t ln(AH ) + λ t t t t t t A H + δYY t − AH ] + βλ [ A − h − A t t+1 t t t + 1] X + βλ t + 1 [(1 − δX)X t + bYY t + bAA t − X t + 1 ] + βλY t + 1 [ (1 − δY − λ t)Y t + δXX t − Y t + 1 ]

k=3

+

r fire Δseed t+k

L=

∞

+

[A4]

[A3]

+ δY(1 − δY − λ t − 1)Y t − 1 + δYδX(1 − δX)X t − 2 + δYδXbYY t − 2 + δYδXbAA t − 2 − A t + 1.

1 − αt − s

At

Finally, substituting [1] into [A4] yields

+ δYY t − A t + 1.

ht =

169

冧

ν + βλB t + 1 [ φ(π t A t) − B t + 1 ] ,

[A9]

where λ t is the rate of fire ignition (not a shadow price). The key variables introduced by the optimi-

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Land Economics

zation procedure are the co–state variables given by λ it + 1. They can be interpreted as the (shadow) value of an additional unit of each state variable (i = {AH , A, X, Y, and B }) in period t + 1. They provide a signal to the decision maker in period t of the opportunity costs or gains of harvests. First-order conditions with respect to the control and state variables (h t, AH t , A t, X t, Y t, and B t) are ∂L ∂h t

=

1 − αt ht

∂L ∂AH t

αt

=

AH t

1

−

(

ρAH t 1−

)

ht ρAH t

− βλA t + 1 = 0,

ht

+

(

2 ρ(AH t ) 1−

)

ht ρAH t

∂A t

[

= 1 − d − πt − λtγt − + bAβλX t+1 +

λtγtAt Yt + At

∂X t ∂L

]

βλB t+1

∂Y t

[A12]

Y X = (1 − δ X)βλX t + 1 + δ X βλ t + 1 − λ t = 0,

[

= δY −

λtγtAt Yt + At

∂B t

=−

[

2A t B t B2t + a2t

[A13]

]

X (1 − γ t) λAH t + bYβλ t + 1

Y + (1 − δY − λ t)βλY t + 1 − λ t = 0,

∂L

[A11]

(1 − γ t) λAH t

− λA t = 0, ∂L

[A14]

]

(1 − π t) λAH t

+ [ νφ(π t A t)ν − 1

2A t B t B2t + a2t

]

(1 − π t) βλB t+1

− λB t = 0.

[A15] First-order conditions with respect to the co-state variables (λ it + 1) are ∂L ∂λAH t

= (1 − d − π t − λ t γ t)A t + δYY t − AH t = 0,

[A16]

= AH t − h t − A t + 1 = 0,

[A17]

∂L ∂λA t+1

= (1 − δX)X t + bYY t + bAA t − X t + 1 = 0,

[A18]

= (1 − δY − λ t)Y t + δXX t − Y t + 1 = 0,

[A19]

= φ(π t A t)ν − B t + 1 = 0.

[A20]

∂L ∂λY t+1 ∂L ∂λB t+1

1 − αt

νB2t φ(π t A t)ν − 1 B2t + a2t

∂λX t +1

Optimality condition [A10] requires harvesting to be expanded until the net marginal benefits of harvesting in the current period just equals the marginal cost of harvesting (in terms of forgone use of labor to produce Q):

AH + βλA t + 1 − λ t = 0.

∂L

[A10]

∂L

February 2013

ht

1

− βλA t+1 =

[A10a]

.

(

ρAH t

)

h 1 − tH ρA t

Net marginal benefits subtract the opportunity cost of harvests (βλA t + 1), which is the discounted value of an additional adult tree in period t + 1. For the harvestable stock of adult trees, equation [A11] can be rewritten as λAH t =

αt AH t

ht

+ 2 ρ(AH t )

(

)

h 1 − tH ρA t

+ βλA t + 1.

[A11a]

When adult trees are optimally harvested, the value of an additional unit of harvestable adult trees in period t, λAH has three components. The first term is t the marginal nonmarket value of an additional standing adult tree. The second term is the forgone value of harvests from leaving the tree standing. The third term is the t + 1 marginal value of an adult tree left standing in period t. The value of adult trees throughout the ecosystem is differentiated from that of the harvestable stock following [A12]:

[

λA t = 1 − d − πt − λtγt − + bAβλX t+1 +

λtγtAt Yt + At

νB2t φ(π t A t)ν − 1 B2t + a2t

]

(1 − γ t) λAH t βλB t + 1.

[A12a]

The value of an additional adult comes from three additive sources. The first follows from its availability for harvests where this magnitude is diminished by natural mortality (d ), the probability of a successful beetle attack (π t ) and the fire risk—not only in total

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(λ t γ t) but the marginal increase in fire risk from an additional adult ([(λ t γ t A t)/(Y t + A t)](1 − γ t)). The second is through the contributions of adults in period t to the seed base in period t + 1. The third is a reduction in the value of an additional adult tree that follows from an increase in beetles. Equation [A13] provides the value of an additional unit of the seed base under optimal harvests: X Y λX t = (1 − δX)βλ t + 1 + δXβλ t + 1.

[A13a]

The seed base in t has value through its (net) own growth plus its contribution to the young tree class. The value of an additional young tree from [A14] is

[

λY t = δY −

λtγtAt Yt + At

]

X (1 − γ t) λAH t + bYβλ t + 1

+ (1 − δY − λ t)βλY t + 1.

[A14a]

The first term captures the value of a young tree that transitions to being a harvestable adult and the contribution to the marginal fire risk. A young tree also has value as it contributes to the seed base (second term) and contributes to its own growth (third term) net of its contributions to adults and fire mortality. The final value the optimal program uncovers is that of the beetle stock from [A15]: λB t = −

[ [

2A t B t B2t + a2t

]

(1 − π t) λAH t

+ νφ(π t A t)ν − 1

2A t B t B2t + a2t

]

(1 − π t) βλB t + 1.

[15a]

171

Reconciling the Substitution and Lagrangian Multiplier Methods In contrast to the more traditional Lagrangian multiplier method, we chose to present the results from the substitution procedure as described in the first section of this Appendix. The substitution approach has two benefits for our application. First, the effect of all 11 first-order conditions [A10]–[A20] can be conveyed in a single equation found by equating [11] and [13]. Second, while shadow values capture the net benefits of the state variables, they are not the best tool to highlight the dual role that adult trees serve. Adult trees provide timber (and nontimber) benefits while also serving as the hosts that support future MPB populations. Shadow values collapse all these future values into a single measure. We found it more straightforward to convey this tension between leaving adult trees and harvesting adult trees using the substitution method, which decomposes the shadow values into their benefit and cost components. Next, we reconcile the substitution and Lagrange procedures by showing that they produce the same solution. Start by setting [A10] equal to [A11] and solving for λAH t : 1 − αt ht

AH t − ht

−

(

2

ρAH t

)

+

h 1 − tH ρA t

lim β t λW t W t = 0, t r∞

for W = (AH ,A,X,Y,B). While little insight can be garnered analytically about optimal choices over time, some analytical insight can be found from an inspection of the optimized steady state, an analysis of which is available from the authors by request.

AH t

= λAH t = Ψt.

[A21]

Equation [A21] shows that Ψt from the main text is the shadow value of harvestable adult trees. Plugging this expression into [A12] evaluated in period t + 1, we find

[

1 − d − π t + 1 − λ t + 1γ t + 1 −

An additional beetle in period t causes a loss of harvestable adult trees (first term) and a loss in value due to the increase in the t + 1 stock of beetles (second term). Equations [A16]–[A20] require the ecosystem dynamics to follow the given laws of motion. The equations of optimality must be simultaneously solved over all time periods given the initial conditions on the state variables and the transversality conditions (Azariadis 1993, 211):

αt

+ bAβλX t+2 +

λ t + 1γ t + 1A t + 1 Yt + 1 + At + 1

νB2t + 1φ(π t + 1A t + 1)ν − 1 B2t + 1 + a2t + 1

]

(1 − γ t + 1) Ψt + 1

A βλB t + 2 = λ t + 1.

Multiplying through by β, simplifying the third term, and substituting for βλA t + 1 from [A10]:

[

β 1 − d − π t + 1 − λ t + 1γ t + 1 − + b Aβ2 λX t +2 +

νB t + 2 At + 1

β2 λB t +2 =

λ t + 1γ t + 1A t + 1 (1 − γ t + 1) Ψt + 1 Yt + 1 + At + 1

]

1 − αt ht

1

−

. ht 1− H ρA t

(

ρAH t

)

Substituting for λB t + 2 from [A15a] and Q t = ht L− : ρAH t

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[

β 1 − d − π t + 1 − λ t + 1γ t + 1 − 2 + b Aβ2 λX t +2 − β

−β

2ν2 B

λ t + 1γ t + 1A t + 1 (1 − γ t + 1) Ψt + 1 Yt + 1 + At + 1

]

2νπ t + 2(1 − π t + 2)A t + 2

[

At + 1

t + 3(1 − π t + 2) B λt + 3 At + 1

]

=

1 − αt ht

−

1 ρAH t Qt

+ β [1 − d − π t + 1 − λ t + 1γ t + 1 ]Ψt + 1 + β3 (1 − δX)bAλ tX+ 3

λAH t +2

+ β3 δXbAλ tY+ 3 =

1 ρAH t Qt

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.

+β

Substituting for λAH t + 2 = Ψt + 2 and rearranging: 1 ρAH t Qt

+ β [1 − d − π t + 1 − λ t + 1γ t + 1 ]Ψt + 1 + b Aβ2 λX t+2 = +β

+ β2 −β

1 ρAH t Qt

(1 − γ t + 1)Ψt + 1

2νπ t + 2(1 − π t + 2)A t + 2

[

At + 1

2ν2 B t + 3(1 − π t + 2) At + 1

ρAH t Qt

∂π t + k ∂B t + k ∂A t + 1 ∂h t

冧.

λB t+3

− β3 δXb A

Ψt + 2

]

.

+ β [1 − d − π t + 1 − λ t + 1γ t + 1 ]Ψt + 1 3 AH + β3 (1 − δX)bAλX t + 3 + β δ Xb AδYλ t + 3

λ t + 3γ t + 3A t + 3 Yt + 3 + At + 3

(1 − γ t)λAH t+3

+ β3 δXbAbYβλX t+4

[A22]

Each subsequent substitution for λB introduces a new shadow value for the harvestable adult stock and MPB stock in the next period. In the text, we represent this intertemporal relationship between MPB shadow values using a time summation from t + 2 to infinity. In words, a change in the MPB population in one period has impacts on future populations due to the recursive nature of the beetle dynamics. The relationship between λB and λAH reflects the fact that beetles kill adult trees, which in turn eliminates timber and nontimber values. This effect can be expressed as a sum of chained partial derivatives and incorporated into [A22] to give 1

∂AH t + k ∂π t + k ∂B t + k ∂A t + 1

Substituting for λY t + 3 from [A14a]:

ht

Yt + 1 + At + 1

冦

兺 β k Ψt + k

k=2

1 − αt

λ t + 1γ t + 1A t + 1

ht

λ t + 1γ t + 1A t + 1 (1 − γ t + 1)Ψt + 1 Yt + 1 + At + 1

∞

+

1 − αt

+ β3 δXbA(1 − δY − λ t)βλY t+4 =

1 − αt ht

λ t + 1γ t + 1A t + 1 +β (1 − γ t + 1)Ψt + 1 Yt + 1 + At + 1 ∂AH t + k ∂π t + k ∂B t + k ∂A t + 1

∞

+


t+k

∂B t + k ∂A t + 1 ∂h t

冧.

X Substituting for λAH t + 3 = Ψt + 3 and λ t + 3 from [A13a] and combining like terms:

1 ρAH t Qt

+ β [1 − d − π t + 1 − λ t + 1γ t + 1 ]Ψt + 1 + β3 {δXbAδYΨt + 3 + β [ δXbAbY + (1 − δX) 2 bA] λX t+4}

+ β [1 − d − π t + 1 − λ t + 1γ t + 1 ]Ψt + 1 + b Aβ2 λX t+2 = +β +

1 − αt

Yt + 1 + At + 1


Substituting for from [A13a]:

=

(1 − γ t + 1)Ψt + 1

∂AH t+k t+k

λ t + 3γ t + 3A t + 3 (1 − γ t)Ψt + 3 Yt + 3 + At + 3

冧

+ β [ δXbA(1 − δY − λ t) + (1 − δX)bAδX] λY t+4

ht

λ t + 1γ t + 1A t + 1

∞

冦

− β3 δ Xb A

∂π t + k ∂B t + k ∂A t + 1 ∂B t + k ∂A t + 1 ∂h t

1 − αt ht

冧.

X Y λX t + 2 = (1 − δX)βλ t + 3 + δXβλ t + 3

∞

+

λ t + 1γ t + 1A t + 1 +β (1 − γ t + 1)Ψt + 1 Yt + 1 + At + 1 ∂AH t + k ∂π t + k ∂B t + k ∂A t + 1


t+k

∂B t + k ∂A t + 1 ∂h t

冧.

Each subsequent substitution for λX and λY introduces a new shadow value for the seed and young tree

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stock in the next period. However, each subsequent substitution for λY also introduces a new shadow value for the harvestable adult stock. This introduction of a new λAH in each period gives rise to a new Ψ in each period as well. Repeated substitutions after t + 2 produce two λAH (and thus Ψ) in each period. One λAH captures the fact that adult trees provide the seeds needed for forest regeneration (a benefit). The other λAH captures how new seeds produce young trees that exacerbate fire severity and kill adult trees in the future (an opportunity cost). In the text, we represent both of these impacts using a summation (from t + 3 to infinity) of chained partials similar to the notation employed with the MPB term. Employing this “summed partial derivative” notation and rearranging we can rewrite the above expression as 1 ρAH t Qt

+ β [1 − d − π t + 1 − λ t + 1γ t + 1 ]Ψt + 1 ∞

+

兺 βk Ψt + kΔseed t+k = k=3

+β

λ t + 1γ t + 1A t + 1 Yt + 1 + At + 1

∞

+

冦

兺 β k Ψt + k

k=2

1 − αt ht

(1 − γ t + 1)Ψt + 1

∂AH t + k ∂π t + k ∂B t + k ∂A t + 1 ∂π t + k ∂B t + k ∂A t + 1 ∂h t

冧

∞

+

兺 βk Ψt + kΔseed t+k k=3

r fire

.

173

This expression is identical to the first-order condition presented in the main paper. The left side of the expression is equation [13] while the right side is equation [11]. Sensitivity Analysis Our model incorporates climate change, changing preferences for public forests, and fire suppression to produce a MPB outbreak that peaks at 30.903 trees per hectare killed by MPBs. When the impact of climate change is held constant, the peak of the MPB outbreak is lowered by 19.007 trees per hectare. This implies that MPB outbreak severity would decrease by 61.5% in the absence of climate change. When preferences for nontimber ecosystem services are held constant, the peak of the MPB outbreak is lowered by 11.663 trees per hectare. This implies that MPB outbreak severity would decrease by 37.7% if preferences for nontimber ecosystem services remain unchanged. Removing the influence of fire suppression reduces the peak of the MPB outbreak by 1.730 trees per hectare. This implies that the absence of fire suppression would lower MPB outbreak severity by 5.6%. This section investigates the sensitivity of these results to the choice of parameter values presented in Table 1. Due to the complexity of the model, an analytical comparative analysis is not possible. Instead we report how the percentage increase in MPB-induced tree mortality changes for a 5% change in each parameter value (Table A1).

TABLE A1 Sensitivity of Model Results to a 5% Change in Parameter Values % Decrease in Maximum MPB-Induced Tree Mortality Due to the Absence of:

Results with Benchmark Parameter Values

δX δY bY bA a1960 φ d ν ρ z I1960 β

Benchmark Parameter Values

Parameter Range

0.001 0.004 0.0018 0.1 157,653 4,500 0.015 0.5 0.03255 0.00054 100 0.96

(0.00095, 0.00105) (0.0038, 0.0042) (0.00171, 0.00189) (0.095, 0.105) (149771, 165536) (4275, 4725) (0.01425, 0.01575) (0.475, 0.525) (0.0309, 0.0342) (0.00051, 0.00057) (95, 105) (0.9597, 0.9634)

Climate Change

Preference Change

Fire Suppression

61.5

37.7

5.6

Results across the Parameter Range (61.5, 61.5) (63.1, 60.0) (61.9, 61.1) (63.7, 59.3) (60.6, 62.3) (62.3, 60.7) (60.4, 62.8) (65.2, 54.3) (61.4, 61.6) (61.3, 61.7) (63.3, 59.8) (61.5, 61.5)

(37.7, 37.7) (38.3, 37.3) (38.0, 37.6) (38.3, 36.9) (37.3, 38.2) (38.2, 37.3) (37.8, 37.9) (35.9, 37.0) (36.0, 39.5) (37.6, 37.8) (38.1, 37.2) (37.8, 37.7)

(5.6, 5.6) (6.0, 5.2) (5.7, 5.5) (6.5, 5.3) (5.6, 5.6) (5.6, 5.6) (5.3, 6.1) (8.0, 2.3) (5.6, 5.6) (5.5, 5.7) (7.1, 4.9) (5.6, 5.6)

Note: The percentage decreases sum to slightly more than 100% due to the interaction effects of climate change, preferences, and fire suppression. MPB, mountain pine beetle.

174

Land Economics

Acknowledgments This research was supported by the Utah Agricultural Experiment Station, Utah State University, and approved as journal paper number 8483.

References Aadland, David. 2004. “Cattle Cycles, Heterogeneous Expectations and the Age Distribution of Capital.” Journal of Economic Dynamics and Control 28 (10): 1977–2002. Aadland, David, Charles Sims, and David Finnoff. 2012. “Spatial Dynamics of Optimal Management in Bioeconomic Systems.” Unpublished manuscript, Utah State University. Abbott, Brant, Brad Stennes, and G. Cornelis van Kooten. 2008. “An Economic Analysis of Mountain Pine Beetle Impacts in a Global Context.” Unpublished manuscript, Department of Economics, University of Victoria. Adams, Darius M., Clark S. Binkley, and Peter A. Cardellichio. 1991. “Is the Level of National Forest Timber Harvest Sensitive to Price?” Land Economics 67 (1): 74–84. Alig, Ralph J., Darius M. Adams, Bruce McCarl, J. M. Callaway, and Steven Winnett. 1997. “Assessing Effects of Mitigation Strategies for Global Climate Change with an Intertemporal Model of the U.S. Forest and Agriculture Sectors.” Environmental and Resource Economics 9 (3): 259–74. Allen, Craig D., Melissa Savage, Donald A. Falk, Kieran F. Suckling, Thomas W. Swetnam, Todd Schulke, Peter B. Stacey, Penelope Morgan, Martos Hoffman, and Jon T. Klingel. 2002. “Ecological Restoration of Southwestern Ponderosa Pine Ecosystems: A Broad Perspective.” Ecological Applications 12 (5): 1418–33. Amacher, Gregory S., Arun S. Malik, and Robert G. Haight. 2005. “Not Getting Burned: The Importance of Fire Prevention in Forest Management.” Land Economics 81 (2): 284–302. ———. 2006. “Reducing Social Losses from Forest Fires.” Land Economics 82 (3): 367–83. Aukema, Brian H., Allan L. Carroll, Yanbing Zheng, Jun Zhu, Kenneth F. Raffa, R. Dan Moore, Kerstin Stahl, and Stephen W. Taylor. 2008. “Movement of Outbreak Populations of Mountain Pine Beetle: Influences of Spatiotemporal Patterns and Climate.” Ecography 31 (3): 348–58. Azariadis, Costas. 1993. Intertemporal Macroeconomics. Cambridge, MA: Blackwell Publishers. Bengston, David N. 1994. “Changing Forest Values and Ecosystem Management.” Society and Natural Resources 7 (6): 515–33. Bentz, Barbara J. 2006. “Mountain Pine Beetle Population Sampling: Inferences from Lindgren Pher-

February 2013

omone Traps and Emergence Cages.” Canadian Journal of Forest Research 36 (2): 351–60. Berck, Peter. 1979. “The Economics of Timber: A Renewable Resource in the Long Run.” Bell Journal of Economics 10 (2): 447–62. Berryman, Alan A., Brian Dennis, Kenneth F. Raffa, and Nils C. Stenseth. 1985. “Evolution of Optimal Group Attack, with Particular Reference to Bark Beetles (Coleoptera: Scolytidae).” Ecology 66 (3): 898–903. Bradshaw, Karen M., and Dean Lueck, eds. 2011. Wildfire Policy: Law and Economics Perspectives. Washington, DC: Resources for the Future Press. Calkin, David E., Krista M. Gebert, J. Greg Jones, and Ronald P. Neilson. 2005. “Forest Service Large Fire Area Burned and Suppression Expenditure Trends, 1970–2002.” Journal of Forestry 103 (4): 179–83. Carroll, A., S. Taylor, J. Re´gnie`re, and L. Safranyik. 2004. “Effects of Climate Change on Range Expansion by the Mountain Pine Beetle in British Columbia.” In Mountain Pine Beetle Symposium: Challenges and Solutions, Report BC-X-399, ed. T. Shore, J. E. Brooks, and J. E. Stone, 223–32. Kelowna, BC: Natural Resources Canada. Daigneault, Adam J., Mario J. Miranda, and Brent Sohngen. 2010. “Optimal Forest Management with Carbon Sequestration Credits and Endogenous Fire Risk.” Land Economics 86 (1): 155–72. Durlauf, Steven N., and H. Peyton Young, eds. 2001. Social Dynamics. Economic Learning and Social Evolution. Cambridge, MA: MIT Press. Englin, Jeffrey, Peter Boxall, and Grant Hauer. 2000. “An Empirical Examination of Optimal Rotations in a Multiple-Use Forest in the Presence of Fire Risk.” Journal of Agricultural and Resource Economics 25 (1): 14–27. Englin, Jeffrey, and John M. Callaway. 1993. “Global Climate Change and Optimal Forest Management.” Natural Resource Modeling 7 (3): 191– 202. Fowells, H. A. 1965. Silvics of Forest Trees of the United States. Agriculture Handbook No. 271. Washington, DC: U.S. Department of Agriculture. Gibson, Ken, and Jose´ F. Negroń. 2009. “Fire and Bark Beetle Interactions.” In The Western Bark Beetle Reserach Group: A Unique Collaboration with Forest Health Protection, Proceedings of a Symposium at the 2007 Society of American Foresters Conference, ed. Jane L. Hayes, and John E. Lundquist, 51–70. Washington, DC: U.S. Department of Agriculture, Forest Service. Gorte, Ross W. 1994. “Lumber Prices, 1993.” In CRS Report for Congress. Washington, DC: Congressional Research Service. Hann, Wendel J., and David L. Bunnell. 2001. “Fire and Land Management Planning and Implemen-

89(1)


tation across Multiple Scales.” International Journal of Wildland Fire 10 (4): 389–403. Harrington, Richard, Richard A. Fleming, and Ian P. Woiwod. 2001. “Climate Change Impacts on Insect Management and Conservation in Temperate Regions: Can They Be Predicted?” Agricultural and Forest Entomology 3 (4): 233–40. Heavilin, Justin, and James Powell. 2008. “A Novel Method of Fitting Spatio-temporal Models to Data, with Applications to the Dynamics of Mountain Pine Beetles.” Natural Resource Modeling 21 (4): 489–524. Holling, C. S. 1959. “The Components of Predation as Revealed by a Study of Small Predation of the European Pine Sawfly.” Canadian Entomologist 91: 293–320. Holmes, Thomas P., Jeffrey P. Prestemon, and Karen L. Abt, eds. 2008. The Economics of Forest Disturbances: Wildfires, Storms and Invasive Species. Dordrecht: Springer. Jenkins, Michael J., Elizabeth Hebertson, Wesley Page, and C. Arik Jorgensen. 2008. “Bark Beetles, Fuels, Fires and Implications for Forest Management in the Intermountain West.” Forest Ecology and Management 254 (1): 16–34. Koch, Peter. 1996. Lodgepole Pine in North America. Madison, WI: Forest Products Society. Konoshima, Masashi, Claire A. Montgomery, Heidi J. Albers, and Jeffrey L. Arthur. 2008. “SpatialEndogenous Fire Risk and Efficient Fuel Management and Timber Harvest.” Land Economics 84 (3): 449–68. Kurz, W. A., C. C. Dymond, G. Stinson, G. J. Rampley, E. T. Neilson, A. Carroll, T. Ebata, and L. Safranyik. 2008. “Mountain Pine Beetle and Forest Carbon Feedback to Climate Change.” Nature 452 (24): 987–90. Logan, Jesse A., and James A. Powell. 2001. “Ghost Forests, Global Warming and the Mountain Pine Beetle.” American Entomologist 47 (3): 160–73. ———. 2009. “Ecological Consequences of Climate Change Altered Forest Insect Disturbance Regimes.” In Climate Warming in Western North America: Evidence and Environmental Effects, ed. Frederic H. Wagner, 167. Salt Lake City: University of Utah Press. Logan, Jesse A., Jacques Re´gnie`re, and James A. Powell. 2003. “Assessing the Impacts of Global Warming on Forest Pest Dynamics.” Frontiers in Ecology and the Environment 1 (3): 130–37. Lotan, J. E., and W. B. Critchfield. 1990. “Pinus contorta Dougl. Ex Loud: Lodgepole Pine.” In Silvics of North America, Vol. 1, Conifers, ed. R. M. Burns and B. H. Honkala, 302–15. Agricultural Handbook 654. Washington, DC: U.S. Department of Agriculture. Lubowski, Ruben N., Andrew J. Plantinga, and Robert N. Stavins. 2006. “Land-Use Change and Car-

175

bon Sinks: Econometric Estimation of the Carbon Sequestration Supply Function.” Journal of Environmental Economics and Management 51 (2): 135–52. Mas-Colell, Andreu, Michael D. Whinston, and Jerry R. Green. 1995. Microeconomic Theory. New York: Oxford University Press. Murray, Brian C., and David N. Wear. 1998. “Federal Timber Restriction and Interregional Arbitrage in U.S. Lumber.” Land Economics 74 (1): 76–91. Newell, Richard G., and Robert N. Stavins. 2000. “Climate Change and Forest Sinks: Factors Affecting the Costs of Carbon Sequestration.” Journal of Environmental Economics and Management 40 (3): 211–35. O’Toole, Randal. 2006. “Money to Burn: Wildfire and the Budget.” In The Wildfire Reader, A Century of Failed Forest Policy, ed. George Wuerthner, 250– 61. Sausalito, CA: Foundation for Deep Ecology, with Island Press. Parker, Thomas J., Karen M. Clancy, and Robert L. Mathiasen. 2006. “Interactions among Fire, Insects and Pathogens in Coniferous Forests of the Interior Western United States and Canada.” Agricultural and Forest Entomology 8 (3): 167–89. Patriquin, Mike N., Adam M. Wellstead, and William A. White. 2007. “Beetles, Trees, and People: Regional Economic Impact Sensitivity and Policy Considerations Related to the Mountain Pine Beetle Infestation in British Columbia, Canada.” Forest Policy and Economics 9 (8): 938–46. Peterson, Gary D. 2002. “Contagious Disturbance, Ecological Memory, and the Emergence of Landscape Pattern.” Ecosystems 5 (4): 329–38. Phillips, Blake R., James A. Breck, and Trevor J. Nickel. 2007. “Managing the Economic Impacts of Mountain Pine Beetle Outbreaks in Alberta.” In Information Bulletin. Edmonton, AB: Western Centre for Economic Research. Powell, James A., and Barbara J. Bentz. 2009. “Connecting Phenological Predictions with Population Growth Rates for Mountain Pine Beetle, an Outbreak Insect.” Landscape Ecology 24 (5): 657–72. Reed, William J. 1984. “The Effects of the Risk of Fire on the Optimal Rotation of a Forest.” Journal of Environmental Economics and Management 11 (2): 180–90. Romme, W. H., J. Clement, J. Hicke, D. Kulakowski, L. MacDonald, T. Schoennagel, and T. Veblen. 2006. “Recent Forest Insect Outbreaks and Fire Risk in Colorado Forests: A Brief Synthesis of Relevant Research.” Fort Collins, CO: Colorado Forest Restoration Institute. Row, Clark, H. Fred Kaiser, and John Sessions. 1981. “Discount Rate for Long-Term Forest Service Investments.” Journal of Forestry 79 (6): 367–69. Runkle, James R., ed. 1985. Disturbance Regimes in Temperate Forests. New York: Academic Press.

176

Land Economics

Safranyik, Les, and Allan L. Carroll. 2006. “The Biology and Epidemiology of the Mountain Pine Beetle in Lodgepole Pine Forests.” In The Mountain Pine Beetle: A Synthesis of Its Biology, Management and Impacts on Lodgepole Pine, ed. Les Safranyik and Bill Wilson, 3–66. Victoria, BC: Canadian Forest Service, Pacific Forestry Centre, Natural Resources Canada. Samman, S., and J. Logan. 2000. Assessment and Response to Bark Beetle Outbreaks in the Rocky Mountain Area. Gen. Tech. Rept. RMRS-GTR-62. Washington, DC: U.S.Department of Agriculture, Forest Service. Schoennagel, Tania, Thomas T. Veblen, and William H. Romme. 2004. “The Interaction of Fire, Fuels, and Climate across Rocky Mountain Forests.” Bioscience 54 (7): 661–76. Sedjo, Roger A. 1995. “Ecosystem Management: An Uncharted Path for Public Forests.” Resources 121 (Fall): 10,15–20. Sims, Charles, David Aadland, and David Finnoff. 2010. “A Dynamic Bioeconomic Analysis of Mountain Pine Beetle Epidemics.” Journal of Economic Dynamics and Control 34 (12): 2407–19. Smith, W. Brad, Patrick D. Miles, Charles H. Perry, and Scott A. Pugh. 2009. Forest Resources of the

February 2013

United States, 2007. Gen. Tech. Rept. WO-78. Washington, DC: U.S.Department of Agriculture, Forest Service. Sohngen, Brent, and Robert Mendelsohn. 2003. “An Optimal Control Model of Forest Carbon Sequestration.” American Journal of Agricultural Economics 85 (2): 448–57. Taylor, S. W., and A. L. Carroll. 2004. “Disturbance, Forest Age, and Mountain Pine Beetle Outbreak Dynamics in BC: A Historical Perspective.” In Mountain Pine Beetle Symposium: Challenges and Solutions, ed. T. L. Shore, J. E. Brooks and J. E. Stone, 41–51. Report BC-X-399. Kelowna, BC: Natural Resources Canada. Van Wagner, C. E. 1977. “Conditions for the Start and Spread of Crown Fire.” Canadian Journal of Forest Research 7 (1): 23–34. Wear, David N., and Brian C. Murray. 2004. “Federal Timber Restrictions, Interregional Spillovers, and the Impact on U.S. Softwood Markets.” Journal of Environmental Economics and Management 47 (2): 307–30. Yoder, Jonathan, and Keith Blatner. 2004. “Incentives and Timing of Prescribed Fire for Wildfire Risk Management.” Journal of Forestry 102 (6): 38–41.