Complementarity in the provision of ecosystem services reduces the cost of mitigating amplified natural disturbance events Charles Simsa,b,1, David Aadlandc, James Powelld,e, David C. Finnoffc, and Ben Crabbf a Howard H. Baker Jr. Center for Public Policy and bDepartment of Economics, University of Tennessee, Knoxville, TN 37920; cDepartment of Economics and Finance, University of Wyoming, Laramie, WY 82071; and Departments of dMathematics and Statistics and eBiology and fRemote Sensing/Geographic Information Systems Laboratory, Department of Wildland Resources, Utah State University, Logan, UT 84322
Edited by Stephen W. Pacala, Princeton University, Princeton, NJ, and approved October 14, 2014 (received for review April 22, 2014)
Climate change has been implicated as a root cause of the recent surge in natural disturbance events such as storms, wildfires, and insect outbreaks. This climate-based surge has led to a greater focus on disturbance-mitigating benefits of ecosystem management. Quantifying these benefits requires knowledge of the relationship between natural and anthropogenic disturbances, which is lacking at the temporal and spatial scales needed to inform ecosystem-based management. This study investigates a specific relationship between timber harvesting and climate-amplified outbreaks of mountain pine beetle. If harvesting is located to mitigate long-distance insect dispersal, there is potential for a win–win outcome in which both timber production and forest conservation can be increased. This spatially targeted harvesting strategy lowers the cost of providing disturbance-mitigating ecosystem services, because valuable timber products are also produced. Mitigating long-distance dispersal also produces net gains in forest conservation across various stakeholder groups. These results speak to ongoing federal efforts to encourage forest vegetation removal on public forestlands to improve forest health. These efforts will lower the cost of responding to climateamplified natural disturbance events but only if vegetation removal efforts are spatially located to reduce disturbance risk. Otherwise, efforts to improve forest health may be converting forest conservation services to timber services.
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efficiency frontier natural capital forest conservation stratified dispersal insect outbreaks
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timber harvesting and natural forest disturbances are poorly understood (18). Large temporal and spatial variations, nonlinear or threshold changes, and inabilities to predict the effect of climate on natural disturbance processes cloud causal relationships (9, 19). The model developed here shows this interaction for the current mountain pine beetle (MPB) outbreak in the western United States and Canada. The current MPB (Dendroctonus ponderosae Hopkins) outbreak began in the late 1990s and is more severe (70–90% mortality of mature lodgepole pines) and expansive (88 million acres impacted) than any previous outbreak. MPB-induced forest mortality is resulting in billions of dollars in economic impact (20), converting vast tracts of forest to a carbon source (21) and occurring in new habitats with unknown ecological consequences (5). Climate change, fire suppression, and changes in timber harvesting have been implicated as causes of the outbreak (22). Here, we show how forest management could be altered to alleviate impacts to ecosystem services. The spatiotemporal model combines timber harvesting, stratified MPB dispersal, and threshold effects important for explaining MPB outbreaks (23, 24). Local dispersal is governed by nonFickian diffusion, whereas long-distance dispersal (LDD) is modeled using a logistic regression model that identifies probable locations for outlier outbreaks (Materials and Methods). The model is fit to a study area in northern Colorado to explain the spread and intensity of the current outbreak given harvest activities in the area. Alterations to the temporal and spatial profile of
E
cosystem service provisioning is a joint production problem using natural capital (1). Jointly produced services may be complementary or competitive. When they are complementary, the provision of one service accompanies the expansion of another service. When they are competitive, the provision of one can be increased by reducing the provision of another service. These relationships between ecosystem services are being altered by climate-amplified natural disturbance events (CANDEs), such as storms, wildfires, and insect outbreaks (2–5). CANDEs depreciate natural capital in unprecedented ways and elevate the importance of disturbance-mitigating ecosystem services (6). Because CANDEs differ from historical baselines, ecosystem service provisioning should be reevaluated (7, 8) with increased attention on the impact of climate on natural disturbance processes (9–11). Unfortunately, ecosystem service provisioning is often considered in the absence of natural disturbances (8, 12–15). We couple a forest assessment model with a stratified insect dispersal model to investigate management of a natural capital stock (forests) in response to a CANDE (insect outbreak). We show that seemingly competitive ecosystem services (forest conservation and timber production) become complementary over the course of the outbreak. This complementarity has the potential to decrease the future cost of mitigating CANDEs. Forest management represents one of the few economically viable strategies available to mitigate CANDEs (16) and has been adopted on a large scale (17). Unfortunately, interactions between 16718–16723 | PNAS | November 25, 2014 | vol. 111 | no. 47
Significance Climate change has been implicated as a root cause of the recent surge in natural disturbance events, leading to a greater focus on disturbance-mitigating benefits of ecosystem management. Quantifying these benefits requires knowledge of the relationship between natural and anthropogenic disturbances, which is lacking at the temporal and spatial scales needed to inform ecosystem-based management. This study investigates a specific relationship between timber harvesting and climateamplified insect outbreaks. If harvesting is located to mitigate long-distance insect dispersal, there is potential for a win–win outcome, in which both timber production and forest conservation can be increased. This spatially targeted harvesting strategy lowers the cost of providing disturbance-mitigating ecosystem services and produces net gains in forest conservation across various stakeholder groups. Author contributions: C.S., D.A., J.P., D.C.F., and B.C. designed research; C.S., D.A., J.P., and D.C.F. performed research; C.S., D.A., J.P., D.C.F., and B.C. analyzed data; and C.S., D.A., J.P., and D.C.F. wrote the paper. The authors declare no conflict of interest. This article is a PNAS Direct Submission. 1
To who correspondence should be addressed. Email: [email protected].
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 1073/pnas.1407381111/-/DCSupplemental.
www.pnas.org/cgi/doi/10.1073/pnas.1407381111
timber harvesting are used to predict the intensity and extent of future MPB outbreaks. Although spatial dynamic models of forest disturbance have received increased attention, most of the previous work abstracts from forest management (25, 26) or includes forest management in a stylized landscape (27, 28). The modeling approach that we developed could be applicable to any forest disturbance that is (i) spatially concentrated, with clear hotspots and dispersal of damage, and (ii) amenable to management by harvesting. Northern Colorado is an appropriate study area because of the severity of the recent MPB outbreak in this area, the proximity to population centers, such as Denver and Fort Collins, and the variety of forest management objectives within the region. The 11,862-km2 study area encompasses Rocky Mountain National Park, three national forests, four wilderness areas, the Arapaho National Recreation Area, Eldora ski area, resort communities, and smaller towns (Fig. 1A and SI Appendix, Data). The study area is placed on a Cartesian spatial grid with 120-m resolution, giving 823,760 total cells. Regions in the area range from no pine trees to dense forests with up to 1,400 trees per hectare (Fig. 1B and SI Appendix, Data). The US Department of Agriculture (USDA) Forest Service (FS) Aerial Detection Survey (ADS) is used to create a spatial database depicting the location and amount of MPB-induced tree mortality (redtops) from 1995 to 2010 (Fig. 1C and SI Appendix, Data). The uptick in MPB activity in 2000 is taken to be the start of the outbreak. To explore potential strategies to enhance disturbance-mitigating services, we contrast several alternative harvest scenarios to a benchmark that matches northern Colorado harvest activity from 2000 to 2013. It is constructed by proportionally allocating
annual USDA FS measures of volume harvested to cells that (i) are forested, (ii) have an average slope < 20%, (iii) are in the appropriate national forest unit, and (iv) fall within management areas that allow timber harvesting (categories 3–5 in Fig. 1A). Model fit across the grid is summarized by comparing benchmark predictions and ADS data for the total number of redtops (R2 = 0:93) and the total number of infested cells (R2 = 0:78) (SI Appendix, Figs. S1 and S2). Alternative harvest scenarios vary with respect to the timing, intensity, and location of harvest activities (SI Appendix, Table S1). The first scenario considers a harvest moratorium during the outbreak. The second and third scenarios increase the amount of harvesting on all cells in the benchmark scenario by 100%, 500%, and 1,000% after 2000 (reactive management) and from 1995 to 1999 (proactive management). The 500% increase roughly corresponds to harvest activity in timber-intensive areas of the western United States before 1990. In addition to increases in harvest timing and intensity, managers may alter the location of harvests to limit MPB dispersal. A fourth hotspot scenario focuses benchmark harvesting on areas where the predicted probability of becoming an outlier outbreak is larger than 8%, similar to current efforts to thin dense forests to prevent insect outbreaks and wildfires (17). A fifth rapid response scenario uses ADS data to strategically harvest in cells with redtops to prevent local spread, consistent with efforts to control the spread of invasive tree insects and diseases (18). Although political viability and costeffectiveness vary across scenarios, comparisons identify adjustments in current forest management along the extensive (number of cells harvested), intensive (number of trees harvested), and temporal (harvesting before or during an outbreak) margins. Results
Fig. 1. Characteristics of the northern Colorado study area. The black line delineates the boundaries of the study area. Where possible, boundaries were selected in areas with few pine trees to minimize MPB dispersal from outside of the study area. (A) USDA FS management areas reflect the diversity of management objectives. (B) The study area ranges from regions with no pine trees to dense forests with up to 1,400 trees per hectare. (C) ADS data of MPB-induced tree mortality in the northern Colorado study area. Nat., natural; Pub and Pvt, public and private.
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represent ecosystem service frontiers during the outbreak—the maximum level of live trees (Fig. 2A) and undisturbed forest area (Fig. 2B) attainable for a specified level of timber production. Points inside the frontiers are technically inefficient in the sense that it is possible to increase forest conservation and timber production by moving to a strategy on the frontier. Technical efficiency can be improved without reducing the provisioning of either ecosystem service by altering current spatial and temporal patterns of timber harvesting to mimic hotspot and proactive (500% and 1,000%) strategies. Identifying the highest valued combination of forest conservation and timber (allocative efficiency) depends on social preferences for the ecosystem services and the shape of the frontiers. Movement along the frontiers captures the physical tradeoff between timber production and forest conservation. At high levels of timber production, the frontier is downward sloping and convex, suggesting that small increases in one service come at the expense of large decreases in the other. However, below current levels of timber production ( 8 in) are susceptible to MPBinduced mortality and harvesting. The law of motion for the beginning-ofperiod density in the adult category is given by ði,jÞ
ði,jÞ
At+1 = At ði,jÞ ht
ði,jÞ
ði,jÞ
+ JM,t − Rt
ði,jÞ
− ht ,
[3] ði,jÞ Rt
is the commercial harvest of adult trees, and is the number where of trees that is successfully attacked by MPB in year t and will die in the following year. For simplicity, the model does not consider germination of seeds that may contribute to the juvenile age class. If the model is simulated for T > M periods, this simplification implies an eventual lack of new growth into the adult age class, because all juveniles have already moved into the adult class. In these instances, the initial juvenile age class will need to be reseeded. MPB-Induced Mortality. For MPB populations to reach epidemic levels, two requirements must be satisfied. First, there must be a sustained period of favorable weather over several years (32). Weather conditions during the dispersal period and larval development can influence MPB populations directly through survival and/or indirectly through impacts to host tree resistance and timing of new beetle emergence (33). Second, there must be an abundance of susceptible host trees (32, 34). An abundance of susceptible host trees combined with homogenous forest structure aid in moving from endemic to epidemic MPB populations (35). Thus, as areas that are climatically favorable for MPB increase because of climate change, forest structure will be the primary factor influencing the probability and severity of MPB outbreak (36).
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Fig. 4. Winners and losers produced by moving to a hotspot harvest strategy during an MPB outbreak. Green cells represent areas that experience a net gain in (A) timber harvesting and (B) number of live trees when moving to a hotspot harvest strategy. Red cells represent areas that experience a net loss in (A) timber harvesting and (B) number of live trees when moving to a hotspot harvest strategy. All stakeholder groups and management categories experience forest conservation gains at the intensive (change in live trees) and extensive (change in forest area) margins.
Assuming that it takes 1 y for a successfully attacked tree to turn red, the number of new successfully attacked trees in cell ði,jÞ in year t is ði,jÞ
Rt ði,jÞ
ði,jÞ ði,jÞ = min zEt−1 ,At ,
[4]
ði,jÞ
where Et−1 = maxðQt−1 − D,0Þ is the number of effective MPBs that exceeds a critical attack threshold, D, in cell ði,jÞ, and z is the number of new redtops per effective MPB. The total number of beetles at t − 1 arriving in cell ði,jÞ from all other cells is " ði,jÞ
Qt−1 = ðΔxÞ2
X
# ði,jÞ←ðl,kÞ
Pt−1
ði,jÞ←long
+ Pt−1
,
[5]
ðl,kÞ ði,jÞ←ðl,kÞ
captures local dispersal from cell ðl,kÞ to cell ði,jÞ, and where Pt−1 ði,jÞ←long captures the density of beetles that spread to cell ði,jÞ Pt−1 through LDD. Local Flight Dispersal. During local flight dispersal (LFD), beetles fly above the forest understory but below the tree crowns. Most locally dispersed beetles locate suitable host trees within 2 d of emergence by flying downwind until an attractive odor plume is encountered (37). The time that it takes to locate a suitable host tree determines the distance traveled during local dispersal, but typically, beetles will travel no more than 100 m through LFD (38, 39). The density of beetles (number per kilometer2), which connects LFD from cell ðl,kÞ with the central location x ðl,kÞ to cell ði,jÞ with the central location ði,jÞ ← ðl,kÞ x ði,jÞ , is Pt−1 . The in-season (that is, during the few summer weeks during which MPBs fly) dispersal of MPB is assumed to follow the ecological diffusion model (40): h i ∂Bðx,sÞ ðl,kÞ = ∇2 μt−1 Bðx,sÞ , ∂s
[6]
ðl,kÞ
where μt−1 represents MPB motility in cell ðl,kÞ at time t − 1, and Bðx,sÞ is the density of (locally) dispersing beetles at x on day s of dispersal (23). Motility in this model is inversely proportional to residence time (41) in a patch. For MPB, large motility would be expected in regions with few trees (where beetles have no reason to linger), whereas motility should decline sharply in patches that are densely stocked with pines (because beetles spend more time interacting with potential hosts). Unlike a normal diffusion model, which eventually spreads all dispersers infinitesimally thin, the ecological diffusion model distributes dispersers into habitats in proportion to the residence time. Following the information in ref. 23, we assume that motility (kilometers2 per day) in cell ðl,kÞ at time t ‒ 1 is an exponentially declining function of adult host density in cell ðl,kÞ: " ðl,kÞ
μt−1 = μ0 exp −ðμ1 + logðμ0 ÞÞ
# ðl,kÞ At−1 , 1;000
[7]
where μ0 is the maximum beetle dispersal per year in an area with no pine trees, and μ1 is a constant describing the rapid decline of motility in the presence of hosts. To predict the number of beetles dispersing from one cell to another cell, we solve Eq. 6 with the initial condition ðl,kÞ B x ðl,kÞ ,s = 0 = FθRt−1 ,
[8]
where F is the number of emerging MPBs per host, and θ is the proportion of emerging MPBs that engage in LFD. Then, the density of beetles arriving at cell ði,jÞ from cell ðl,kÞ can be written as ði,jÞ←ðl,kÞ Pt−1
= B x
ði,jÞ
,s = 1 :
[9]
Here, individual beetles are assumed to die if they have not found a host within 1 d of leaving their brood tree ðs ∈ ½0;1Þ, and s = 1 is the end time for dispersal (1 d). Simulating the model described above requires numerically solving the ecological diffusion equation every simulation year distributed over all cells in space. To implement the dispersal simulations efficiently, we used homogenization to transform Eq. 6 into a related partial differential equation on much larger scales, effectively reducing the number of cells without sacrificing accuracy (40), and then, we solved the equation numerically using the alternating direction implicit (ADI) method (42). The ADI approach is a standard 2D solution procedure for diffusion equations that replaces the usual implicit discretization (which requires inversion of a large, sparse matrix system) with layered tridiagonal systems in alternating directions. Because the ADI and homogenization
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procedures may not exactly conserve the number of beetles each year, we calculated the total number of emerging beetles initially, normalized solutions, and multiplied by the starting number of beetles to conserve beetles during the solution procedure. LDD. There is evidence of LDD at the scale of tens (43, 44) and hundreds (35) of kilometers because of convective winds that transport beetles above the forest canopy. This LDD can create outlying spots of infestation beyond the main zone of the outbreak. These outlier spots represent new initial conditions for each time step of the LFD model and ultimately, may coalesce with the main outbreak or other outlier outbreaks. LDD through pathways, such as wind and human intervention, is an inherently random event, but after MPBs arrive at a distant location, there may be features of the landscape that increase the likelihood that a particular cell is successfully attacked. Previous studies indicate that successful bark beetle attack can be predicted using elevation, direct solar radiation, forest density, beetle pressure, and amount of forest edge (25, 45–48). Our methodology uses these natural features of the landscape to predict where outlier outbreaks of MPB are likely to establish. Not all new redtop trees in a given year arise from LDD, and therefore, we begin by defining the area that qualifies for LDD. To identify LDD areas, we create a weighted measure of the cumulative number of redtops within a 5-km radius of each cell in our study area (CRT ). The weights decline linearly away from the center of the circle, with a weight of one at the center and a weight of zero at 5 km. Any cell ði,jÞ with CRT ði,jÞ < 5 that was aerially surveyed is considered a candidate for LDD. LDD candidate cells are updated each year as the outbreak spreads. We use a logistic regression model and 3 separate y (2000, 2005, and 2010) of USDA FS ADS data to estimate the probability that an LDD candidate cell will become an outlier. The sample size or total potential number of cells per year of observation for LDD is N = 430;280. Each LDD candidate cell either contained redtops [y ði,jÞ = 1] or had no redtops [y ði,jÞ = 0]. According to ADS data, only 26,833 cells contained redtops and are actual outliers. The probability that cell ði,jÞ will harbor an outlier population is Pr y ði,jÞ = 1uði,jÞ’ β = π ði,jÞ =
ði,jÞ’
eu β , 1 + euði,jÞ’ β
[10]
where uði,jÞ is a vector of cell-specific factors that influences the probability of MPB outlier outbreaks (SI Appendix, Table S3), and β is a vector of logistic coefficients. The signs of all coefficients match our expectations (SI Appendix, Predicting Outlier Outbreaks). Using the estimated coefficients (SI Appendix, Table S3) and the values of the explanatory variables on each cell, Eq. 10 gives predicted probability π^ði,jÞ for LDD on each candidate cell. The predicted probabilities are compared with a threshold probability, π, to determine whether cell ði,jÞ experiences LDD. Predicted values π^ði,jÞ > π result in LDD and successful MPB attack [Ωði,jÞ = 1]; predicted values π^ði,jÞ < π result in no LDD [Ωði,jÞ = 0]. We also incorporate specific local and global processes that cause LDD to evolve as redtops occupy more cells (SI Appendix, Predicting Outlier Outbreaks). The logit LDD model performs significantly better than a completely random LDD process. The logit model correctly predicts about 28% of actual outlier cells, whereas the random process correctly predicts only 6% of actual outlier cells. After a cell is identified as supporting successful LDD, it is seeded with a portion of the emerging beetles. Specifically, the proportion of all emerging beetles from across the grid that engage in LDD is evenly distributed to all cells identified as LDD recipients: ði,jÞ←long
Pt
= Ωij Fð1 − θÞ
X ðl,kÞ
, ðl,kÞ
Rt
X
Ωðl,kÞ ,
[11]
ðl,kÞ
P ðl,kÞ where is the aggregate number of redtops in year t, and ðl,kÞ Rt P ðl,kÞ is the total number of new outlier spots. ðl,kÞ Ω Parameterizing Dispersal and Model Validation. Parameters governing LFD, attack success, and reproductive success (SI Appendix, Table S2) were determined by fitting model predictions to ADS observations in the Sawtooth National Recreation Area of central Idaho for 1995–2005 using maximum likelihood to optimize correspondence between predicted and observed presence on 25-ha blocks. LFD was predicted under the assumption that individual beetles were only capable of 1 d of travel. Simulations using selected parameters for μ0 , μ1 , F, and z reproduced observed spatial patterns in the Sawtooth National Recreation Area with 85% accuracy, and population growth rate dynamics were resolved with 92% accuracy (23). These parameters were also used to test model validity in the
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Lake Chelan region of the eastern Cascades. Without any additional parameterization, model correspondence with observations in the Chelan study area was over 85% in space, and growth rate dynamics were 93% accurate. Thus, the model captures fundamental mechanisms of MPB attack and dispersal and not simply details specific to the area in which it was parameterized. To balance LDD and short-distance dispersal, we set θ = 0:975 based on evidence that up to 2.5% of a population may engage in LDD (38). Rate of natural tree mortality (d) was set at 2% based on the work by Runkle (49).
The juvenile age class scale parameter (b) was selected to ensure that no more than 90 juvenile trees were in any point on the grid.
1. Turner RK, Daily GC (2008) The ecosystem services framework and natural capital conservation. Environmental and Resource Economics 39(1):25–35. 2. Dale VH, et al. (2001) Climate change and forest disturbances. BioScience 51(9): 723–734. 3. Woollings T, Gregory JM, Pinto JG, Reyers M, Brayshaw DJ (2012) Response of the North Atlantic storm track to climate change shaped by ocean-atmosphere coupling. Nat Geosci 5:313–317. 4. Westerling AL, Turner MG, Smithwick EA, Romme WH, Ryan MG (2011) Continued warming could transform Greater Yellowstone fire regimes by mid-21st century. Proc Natl Acad Sci USA 108(32):13165–13170. 5. Logan JA, Regniere J, Powell JA (2003) Assessing the impacts of global warming on forest pest dynamics. Front Ecol Environ 1(3):130–137. 6. Barbier EB, et al. (2008) Coastal ecosystem-based management with nonlinear ecological functions and values. Science 319(5861):321–323. 7. Gedan KB, Kirwan ML, Wolanski E, Barbier EB, Silliman BR (2011) The present and future role of coastal wetland vegetation in protecting shorelines: Answering recent challenges to the paradigm. Clim Change 106(1):7–29. 8. Polasky S, Nelson E, Lonsdorf E, Fackler P, Starfield A (2005) Conserving species in a working landscape: Land use with biological and economic objectives. Ecol Appl 15(4):1387–1401. 9. Millar CI, Stephenson NL, Stephens SL (2007) Climate change and forests of the future: Managing in the face of uncertainty. Ecol Appl 17(8):2145–2151. 10. Bowman DM, et al. (2013) Forest fire management, climate change, and the risk of catastrophic carbon losses. Front Ecol Environ 11(2):66–67. 11. Malhi Y, et al. (2009) Exploring the likelihood and mechanism of a climate-changeinduced dieback of the Amazon rainforest. Proc Natl Acad Sci USA 106(49): 20610–20615. 12. Naidoo R, Ricketts TH (2006) Mapping the economic costs and benefits of conservation. PLoS Biol 4(11):e360. 13. Nelson E, et al. (2008) Efficiency of incentives to jointly increase carbon sequestration and species conservation on a landscape. Proc Natl Acad Sci USA 105(28):9471–9476. 14. Ando A, Camm J, Polasky S, Solow A (1998) Species distributions, land values, and efficient conservation. Science 279(5359):2126–2128. 15. Spies TA, et al. (2007) Potential effects of forest policies on terrestrial biodiversity in a multi-ownership province. Ecol Appl 17(1):48–65. 16. Long JN (2009) Emulating natural disturbance regimes as a basis for forest management: A North American view. For Ecol Manage 257(9):1868–1873. 17. Dellasala DA, Williams JE, Williams CD, Franklin JF (2004) Beyond smoke and mirrors: A synthesis of fire policy and science. Conserv Biol 18(4):976–986. 18. Boyd IL, Freer-Smith PH, Gilligan CA, Godfray HC (2013) The consequence of tree pests and diseases for ecosystem services. Science 342(6160):1235773. 19. Lindenmayer DB, Laurance WF (2012) A history of hubris–cautionary lessons in ecologically sustainable forest management. Biol Conserv 151(1):11–16. 20. Abbott B, Stennes B, Cornelis van Kooten G (2009) Mountain pine beetle, global markets, and the British Columbia forest economy. Can J For Res 39(7):1313–1321. 21. Kurz WA, et al. (2008) Mountain pine beetle and forest carbon feedback to climate change. Nature 452(7190):987–990. 22. Sims C, Aadland D, Finnoff D, Powell JA (2013) How ecosystem service provision can increase forest mortality from insect outbreaks. Land Econ 89(1):154–176. 23. Powell JA, Bentz BJ (2014) Phenology and density-dependent dispersal predict patterns of mountain pine beetle (Dendroctonus ponderosae) impact. Ecol Modell 273(10):173–185. 24. Heavilin J, Powell J (2008) A novel method of fitting spatio-temporal models to data, with applications to the dynamics of mountain pine beetles. Nat Resour Model 21(4): 489–524. 25. Walter JA, Platt RV (2013) Multi-temporal analysis reveals that predictors of mountain pine beetle infestation change during outbreak cycles. For Ecol Manage 302(15): 308–318. 26. Chapman TB, Veblen TT, Schoennagel T (2012) Spatiotemporal patterns of mountain pine beetle activity in the southern Rocky Mountains. Ecology 93(10):2175–2185. 27. Busby GM, Albers HJ, Montgomery CA (2012) Wildfire risk management in a landscape with fragmented ownership and spatial interactions. Land Econ 88(3):496–517. 28. Sims C, Aadland D, Finnoff D (2010) A dynamic bioeconomic analysis of mountain pine beetle epidemics. J Econ Dyn Control 34(12):2407–2419.
29. Whitehead RJ, Safranyik L, Russo G, Shore TL, Carroll AL (2004) Silviculture to reduce landscape and stand susceptibility to the mountain pine beetle. Mountain Pine Beetle Symposium: Challenges and Solutions, Natural Resources Canada Report BC-X-399, eds Shore TL, Brooks JE, Stone JE (Natural Resources Canada, Canadian Forest Service, Kelowna, British Columbia, Canada), pp 233–244. 30. Amman GD, McGregor MD, Schmitz RF, Oakes RD (1988) Susceptibility of lodgepole pine to infestation by mountain pine beetles following partial cutting of stands. Can J For Res 18(6):688–695. 31. Preisler HK, Mitchell RG (1993) Colonization patterns of the mountain pine beetle in thinned and unthinned Lodgepole Pine Stands. Forest Science 39(3):528–545. 32. Safranyik L (1978) Effects of climate and weather on mountain pine beetle populations. Proceedings of Symposium on Theory and Practice of Mountain Pine Beetle Management in Lodgepole Pine Forests, eds Berryman AA, Amman GD, Stark RW (Univ of Idaho, Moscow, ID), pp 77–84. 33. Carroll A, Taylor S, Regniere J, Safranyik L (2004) Effects of climate change on range expansion by the mountain pine beetle in British Columbia. Mountain Pine Beetle Symposium: Challenges and Solutions, Natural Resources Canada Report BC-X-399, eds Shore TL, Brooks JE, Stone JE (Natural Resources Canada, Canadian Forest Service, Kelowna, British Columbia, Canada), pp 223–232. 34. Raffa KF (2008) Cross-scale drivers of natural disturbances prone to anthropogenic amplification: The dynamics of bark beetle eruptions. BioScience 58(6):501–517. 35. Safranyik L, Carroll A (2006) The biology and epidemiology of the mountain pine beetle in lodgepole pine forests. The Mountain Pine Beetle: A Synthesis of Its Biology, Management and Impacts on Lodgepole Pine, eds Safranyik L, Wilson B (Canadian Forest Service, Pacific Forestry Centre, Natural Resources Canada, Victoria, British Columbia, Canada), pp 3–66. 36. Taylor S, Carroll A (2004) Disturbance, forest age, and mountain pine beetle outbreak dynamics in BC: A historical perspective. Mountain Pine Beetle Symposium: Challenges and Solutions, Natural Resources Canada Report BC-X-399, eds Shore TL, Brooks JE, Stone JE (Natural Resources Canada, Canadian Forest Service, Kelowna, British Columbia, Canada), pp 41–51. 37. Byers JA (1999) Effects of attraction radius and flight paths on catch of scolytid beetles dispersing outward through rings of pheromone traps. J Chem Ecol 25(5): 985–1005. 38. Safranyik L, Linton DA, Silversides R, McMullen LH (1992) Dispersal of released mountain pine beetles under the canopy of a mature lodgepole pine stand. J Appl Entomol 113(1-5):441–450. 39. Robertson C, Nelson TA, Boots B (2007) Mountain pine beetle dispersal: The spatialtemporal interaction of infestations. For Sci 53(3):395–405. 40. Garlick MJ, Powell JA, Hooten MB, McFarlane LR (2011) Homogenization of largescale movement models in ecology. Bull Math Biol 73(9):2088–2108. 41. Turchin P (1998) Quantitative Analysis of Movement: Measuring and Modeling Population Redistribution in Animals and Plants (Sinauer, Sunderland, MA). 42. Pfeiffer D, et al. (2008) Spatial Analysis in Epidemiology (Oxford Univ Press, New York). 43. Furniss MM, Furniss RL (1972) Scolytids (Coleoptera) on snowfields above timberline in Oregon and Washington. Can Entomol 104(9):1471–1478. 44. Robertson C, Nelson TA, Jelinski DE, Wulder MA, Boots B (2009) Spatial–temporal analysis of species range expansion: The case of the mountain pine beetle, Dendroctonus ponderosae. J Biogeogr 36(8):1446–1458. 45. Coops NC, Wulder MA, White JC (2006) Integrating remotely sensed and ancillary data sources to characterize a mountain pine beetle infestation. Remote Sens Environ 105(2):83–97. 46. Wulder MA, White JC, Bentz B, Alvarez MF, Coops NC (2006) Estimating the probability of mountain pine beetle red-attack damage. Remote Sens Environ 101(2): 150–166. 47. Bone C, White JC, Wulder MA, Robertson C, Nelson TA (2013) Impact of forest fragmentation on patterns of mountain pine beetle-caused tree mortality. Forests 4(2): 279–295. 48. Kautz M, Schopf R, Ohser J (2013) The “sun-effect”: Microclimatic alterations predispose forest edges to bark beetle infestations. Eur J For Res 132(3):453–465. 49. Runkle JR (1985) Disturbance regimes in temperate forests. The Ecology of Natural Disturbance and Patch Dynamics, eds Pickett STA, While PS (Academic, San Diego), pp 17–33.
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ACKNOWLEDGMENTS. We thank T. Reader with the Colorado State Forest Service and M. Etzenhouser with the US Department of Agriculture Forest Service for providing insights and data on timber markets in the study area. We would also like to acknowledge helpful comments and suggestions from seminar participants at Colorado State University, Virginia Tech, Oak Ridge National Laboratory’s Environmental Sciences Division, and the National Institute for Mathematical and Biological Synthesis.
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PNAS | November 25, 2014 | vol. 111 | no. 47 | 16723
Edited by Stephen W. Pacala, Princeton University, Princeton, NJ, and approved October 14, 2014 (received for review April 22, 2014)
Climate change has been implicated as a root cause of the recent surge in natural disturbance events such as storms, wildfires, and insect outbreaks. This climate-based surge has led to a greater focus on disturbance-mitigating benefits of ecosystem management. Quantifying these benefits requires knowledge of the relationship between natural and anthropogenic disturbances, which is lacking at the temporal and spatial scales needed to inform ecosystem-based management. This study investigates a specific relationship between timber harvesting and climate-amplified outbreaks of mountain pine beetle. If harvesting is located to mitigate long-distance insect dispersal, there is potential for a win–win outcome in which both timber production and forest conservation can be increased. This spatially targeted harvesting strategy lowers the cost of providing disturbance-mitigating ecosystem services, because valuable timber products are also produced. Mitigating long-distance dispersal also produces net gains in forest conservation across various stakeholder groups. These results speak to ongoing federal efforts to encourage forest vegetation removal on public forestlands to improve forest health. These efforts will lower the cost of responding to climateamplified natural disturbance events but only if vegetation removal efforts are spatially located to reduce disturbance risk. Otherwise, efforts to improve forest health may be converting forest conservation services to timber services.
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efficiency frontier natural capital forest conservation stratified dispersal insect outbreaks
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timber harvesting and natural forest disturbances are poorly understood (18). Large temporal and spatial variations, nonlinear or threshold changes, and inabilities to predict the effect of climate on natural disturbance processes cloud causal relationships (9, 19). The model developed here shows this interaction for the current mountain pine beetle (MPB) outbreak in the western United States and Canada. The current MPB (Dendroctonus ponderosae Hopkins) outbreak began in the late 1990s and is more severe (70–90% mortality of mature lodgepole pines) and expansive (88 million acres impacted) than any previous outbreak. MPB-induced forest mortality is resulting in billions of dollars in economic impact (20), converting vast tracts of forest to a carbon source (21) and occurring in new habitats with unknown ecological consequences (5). Climate change, fire suppression, and changes in timber harvesting have been implicated as causes of the outbreak (22). Here, we show how forest management could be altered to alleviate impacts to ecosystem services. The spatiotemporal model combines timber harvesting, stratified MPB dispersal, and threshold effects important for explaining MPB outbreaks (23, 24). Local dispersal is governed by nonFickian diffusion, whereas long-distance dispersal (LDD) is modeled using a logistic regression model that identifies probable locations for outlier outbreaks (Materials and Methods). The model is fit to a study area in northern Colorado to explain the spread and intensity of the current outbreak given harvest activities in the area. Alterations to the temporal and spatial profile of
E
cosystem service provisioning is a joint production problem using natural capital (1). Jointly produced services may be complementary or competitive. When they are complementary, the provision of one service accompanies the expansion of another service. When they are competitive, the provision of one can be increased by reducing the provision of another service. These relationships between ecosystem services are being altered by climate-amplified natural disturbance events (CANDEs), such as storms, wildfires, and insect outbreaks (2–5). CANDEs depreciate natural capital in unprecedented ways and elevate the importance of disturbance-mitigating ecosystem services (6). Because CANDEs differ from historical baselines, ecosystem service provisioning should be reevaluated (7, 8) with increased attention on the impact of climate on natural disturbance processes (9–11). Unfortunately, ecosystem service provisioning is often considered in the absence of natural disturbances (8, 12–15). We couple a forest assessment model with a stratified insect dispersal model to investigate management of a natural capital stock (forests) in response to a CANDE (insect outbreak). We show that seemingly competitive ecosystem services (forest conservation and timber production) become complementary over the course of the outbreak. This complementarity has the potential to decrease the future cost of mitigating CANDEs. Forest management represents one of the few economically viable strategies available to mitigate CANDEs (16) and has been adopted on a large scale (17). Unfortunately, interactions between 16718–16723 | PNAS | November 25, 2014 | vol. 111 | no. 47
Significance Climate change has been implicated as a root cause of the recent surge in natural disturbance events, leading to a greater focus on disturbance-mitigating benefits of ecosystem management. Quantifying these benefits requires knowledge of the relationship between natural and anthropogenic disturbances, which is lacking at the temporal and spatial scales needed to inform ecosystem-based management. This study investigates a specific relationship between timber harvesting and climateamplified insect outbreaks. If harvesting is located to mitigate long-distance insect dispersal, there is potential for a win–win outcome, in which both timber production and forest conservation can be increased. This spatially targeted harvesting strategy lowers the cost of providing disturbance-mitigating ecosystem services and produces net gains in forest conservation across various stakeholder groups. Author contributions: C.S., D.A., J.P., D.C.F., and B.C. designed research; C.S., D.A., J.P., and D.C.F. performed research; C.S., D.A., J.P., D.C.F., and B.C. analyzed data; and C.S., D.A., J.P., and D.C.F. wrote the paper. The authors declare no conflict of interest. This article is a PNAS Direct Submission. 1
To who correspondence should be addressed. Email: [email protected].
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 1073/pnas.1407381111/-/DCSupplemental.
www.pnas.org/cgi/doi/10.1073/pnas.1407381111
timber harvesting are used to predict the intensity and extent of future MPB outbreaks. Although spatial dynamic models of forest disturbance have received increased attention, most of the previous work abstracts from forest management (25, 26) or includes forest management in a stylized landscape (27, 28). The modeling approach that we developed could be applicable to any forest disturbance that is (i) spatially concentrated, with clear hotspots and dispersal of damage, and (ii) amenable to management by harvesting. Northern Colorado is an appropriate study area because of the severity of the recent MPB outbreak in this area, the proximity to population centers, such as Denver and Fort Collins, and the variety of forest management objectives within the region. The 11,862-km2 study area encompasses Rocky Mountain National Park, three national forests, four wilderness areas, the Arapaho National Recreation Area, Eldora ski area, resort communities, and smaller towns (Fig. 1A and SI Appendix, Data). The study area is placed on a Cartesian spatial grid with 120-m resolution, giving 823,760 total cells. Regions in the area range from no pine trees to dense forests with up to 1,400 trees per hectare (Fig. 1B and SI Appendix, Data). The US Department of Agriculture (USDA) Forest Service (FS) Aerial Detection Survey (ADS) is used to create a spatial database depicting the location and amount of MPB-induced tree mortality (redtops) from 1995 to 2010 (Fig. 1C and SI Appendix, Data). The uptick in MPB activity in 2000 is taken to be the start of the outbreak. To explore potential strategies to enhance disturbance-mitigating services, we contrast several alternative harvest scenarios to a benchmark that matches northern Colorado harvest activity from 2000 to 2013. It is constructed by proportionally allocating
annual USDA FS measures of volume harvested to cells that (i) are forested, (ii) have an average slope < 20%, (iii) are in the appropriate national forest unit, and (iv) fall within management areas that allow timber harvesting (categories 3–5 in Fig. 1A). Model fit across the grid is summarized by comparing benchmark predictions and ADS data for the total number of redtops (R2 = 0:93) and the total number of infested cells (R2 = 0:78) (SI Appendix, Figs. S1 and S2). Alternative harvest scenarios vary with respect to the timing, intensity, and location of harvest activities (SI Appendix, Table S1). The first scenario considers a harvest moratorium during the outbreak. The second and third scenarios increase the amount of harvesting on all cells in the benchmark scenario by 100%, 500%, and 1,000% after 2000 (reactive management) and from 1995 to 1999 (proactive management). The 500% increase roughly corresponds to harvest activity in timber-intensive areas of the western United States before 1990. In addition to increases in harvest timing and intensity, managers may alter the location of harvests to limit MPB dispersal. A fourth hotspot scenario focuses benchmark harvesting on areas where the predicted probability of becoming an outlier outbreak is larger than 8%, similar to current efforts to thin dense forests to prevent insect outbreaks and wildfires (17). A fifth rapid response scenario uses ADS data to strategically harvest in cells with redtops to prevent local spread, consistent with efforts to control the spread of invasive tree insects and diseases (18). Although political viability and costeffectiveness vary across scenarios, comparisons identify adjustments in current forest management along the extensive (number of cells harvested), intensive (number of trees harvested), and temporal (harvesting before or during an outbreak) margins. Results
Fig. 1. Characteristics of the northern Colorado study area. The black line delineates the boundaries of the study area. Where possible, boundaries were selected in areas with few pine trees to minimize MPB dispersal from outside of the study area. (A) USDA FS management areas reflect the diversity of management objectives. (B) The study area ranges from regions with no pine trees to dense forests with up to 1,400 trees per hectare. (C) ADS data of MPB-induced tree mortality in the northern Colorado study area. Nat., natural; Pub and Pvt, public and private.
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represent ecosystem service frontiers during the outbreak—the maximum level of live trees (Fig. 2A) and undisturbed forest area (Fig. 2B) attainable for a specified level of timber production. Points inside the frontiers are technically inefficient in the sense that it is possible to increase forest conservation and timber production by moving to a strategy on the frontier. Technical efficiency can be improved without reducing the provisioning of either ecosystem service by altering current spatial and temporal patterns of timber harvesting to mimic hotspot and proactive (500% and 1,000%) strategies. Identifying the highest valued combination of forest conservation and timber (allocative efficiency) depends on social preferences for the ecosystem services and the shape of the frontiers. Movement along the frontiers captures the physical tradeoff between timber production and forest conservation. At high levels of timber production, the frontier is downward sloping and convex, suggesting that small increases in one service come at the expense of large decreases in the other. However, below current levels of timber production ( 8 in) are susceptible to MPBinduced mortality and harvesting. The law of motion for the beginning-ofperiod density in the adult category is given by ði,jÞ
ði,jÞ
At+1 = At ði,jÞ ht
ði,jÞ
ði,jÞ
+ JM,t − Rt
ði,jÞ
− ht ,
[3] ði,jÞ Rt
is the commercial harvest of adult trees, and is the number where of trees that is successfully attacked by MPB in year t and will die in the following year. For simplicity, the model does not consider germination of seeds that may contribute to the juvenile age class. If the model is simulated for T > M periods, this simplification implies an eventual lack of new growth into the adult age class, because all juveniles have already moved into the adult class. In these instances, the initial juvenile age class will need to be reseeded. MPB-Induced Mortality. For MPB populations to reach epidemic levels, two requirements must be satisfied. First, there must be a sustained period of favorable weather over several years (32). Weather conditions during the dispersal period and larval development can influence MPB populations directly through survival and/or indirectly through impacts to host tree resistance and timing of new beetle emergence (33). Second, there must be an abundance of susceptible host trees (32, 34). An abundance of susceptible host trees combined with homogenous forest structure aid in moving from endemic to epidemic MPB populations (35). Thus, as areas that are climatically favorable for MPB increase because of climate change, forest structure will be the primary factor influencing the probability and severity of MPB outbreak (36).
PNAS | November 25, 2014 | vol. 111 | no. 47 | 16721
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Fig. 4. Winners and losers produced by moving to a hotspot harvest strategy during an MPB outbreak. Green cells represent areas that experience a net gain in (A) timber harvesting and (B) number of live trees when moving to a hotspot harvest strategy. Red cells represent areas that experience a net loss in (A) timber harvesting and (B) number of live trees when moving to a hotspot harvest strategy. All stakeholder groups and management categories experience forest conservation gains at the intensive (change in live trees) and extensive (change in forest area) margins.
Assuming that it takes 1 y for a successfully attacked tree to turn red, the number of new successfully attacked trees in cell ði,jÞ in year t is ði,jÞ
Rt ði,jÞ
ði,jÞ ði,jÞ = min zEt−1 ,At ,
[4]
ði,jÞ
where Et−1 = maxðQt−1 − D,0Þ is the number of effective MPBs that exceeds a critical attack threshold, D, in cell ði,jÞ, and z is the number of new redtops per effective MPB. The total number of beetles at t − 1 arriving in cell ði,jÞ from all other cells is " ði,jÞ
Qt−1 = ðΔxÞ2
X
# ði,jÞ←ðl,kÞ
Pt−1
ði,jÞ←long
+ Pt−1
,
[5]
ðl,kÞ ði,jÞ←ðl,kÞ
captures local dispersal from cell ðl,kÞ to cell ði,jÞ, and where Pt−1 ði,jÞ←long captures the density of beetles that spread to cell ði,jÞ Pt−1 through LDD. Local Flight Dispersal. During local flight dispersal (LFD), beetles fly above the forest understory but below the tree crowns. Most locally dispersed beetles locate suitable host trees within 2 d of emergence by flying downwind until an attractive odor plume is encountered (37). The time that it takes to locate a suitable host tree determines the distance traveled during local dispersal, but typically, beetles will travel no more than 100 m through LFD (38, 39). The density of beetles (number per kilometer2), which connects LFD from cell ðl,kÞ with the central location x ðl,kÞ to cell ði,jÞ with the central location ði,jÞ ← ðl,kÞ x ði,jÞ , is Pt−1 . The in-season (that is, during the few summer weeks during which MPBs fly) dispersal of MPB is assumed to follow the ecological diffusion model (40): h i ∂Bðx,sÞ ðl,kÞ = ∇2 μt−1 Bðx,sÞ , ∂s
[6]
ðl,kÞ
where μt−1 represents MPB motility in cell ðl,kÞ at time t − 1, and Bðx,sÞ is the density of (locally) dispersing beetles at x on day s of dispersal (23). Motility in this model is inversely proportional to residence time (41) in a patch. For MPB, large motility would be expected in regions with few trees (where beetles have no reason to linger), whereas motility should decline sharply in patches that are densely stocked with pines (because beetles spend more time interacting with potential hosts). Unlike a normal diffusion model, which eventually spreads all dispersers infinitesimally thin, the ecological diffusion model distributes dispersers into habitats in proportion to the residence time. Following the information in ref. 23, we assume that motility (kilometers2 per day) in cell ðl,kÞ at time t ‒ 1 is an exponentially declining function of adult host density in cell ðl,kÞ: " ðl,kÞ
μt−1 = μ0 exp −ðμ1 + logðμ0 ÞÞ
# ðl,kÞ At−1 , 1;000
[7]
where μ0 is the maximum beetle dispersal per year in an area with no pine trees, and μ1 is a constant describing the rapid decline of motility in the presence of hosts. To predict the number of beetles dispersing from one cell to another cell, we solve Eq. 6 with the initial condition ðl,kÞ B x ðl,kÞ ,s = 0 = FθRt−1 ,
[8]
where F is the number of emerging MPBs per host, and θ is the proportion of emerging MPBs that engage in LFD. Then, the density of beetles arriving at cell ði,jÞ from cell ðl,kÞ can be written as ði,jÞ←ðl,kÞ Pt−1
= B x
ði,jÞ
,s = 1 :
[9]
Here, individual beetles are assumed to die if they have not found a host within 1 d of leaving their brood tree ðs ∈ ½0;1Þ, and s = 1 is the end time for dispersal (1 d). Simulating the model described above requires numerically solving the ecological diffusion equation every simulation year distributed over all cells in space. To implement the dispersal simulations efficiently, we used homogenization to transform Eq. 6 into a related partial differential equation on much larger scales, effectively reducing the number of cells without sacrificing accuracy (40), and then, we solved the equation numerically using the alternating direction implicit (ADI) method (42). The ADI approach is a standard 2D solution procedure for diffusion equations that replaces the usual implicit discretization (which requires inversion of a large, sparse matrix system) with layered tridiagonal systems in alternating directions. Because the ADI and homogenization
16722 | www.pnas.org/cgi/doi/10.1073/pnas.1407381111
procedures may not exactly conserve the number of beetles each year, we calculated the total number of emerging beetles initially, normalized solutions, and multiplied by the starting number of beetles to conserve beetles during the solution procedure. LDD. There is evidence of LDD at the scale of tens (43, 44) and hundreds (35) of kilometers because of convective winds that transport beetles above the forest canopy. This LDD can create outlying spots of infestation beyond the main zone of the outbreak. These outlier spots represent new initial conditions for each time step of the LFD model and ultimately, may coalesce with the main outbreak or other outlier outbreaks. LDD through pathways, such as wind and human intervention, is an inherently random event, but after MPBs arrive at a distant location, there may be features of the landscape that increase the likelihood that a particular cell is successfully attacked. Previous studies indicate that successful bark beetle attack can be predicted using elevation, direct solar radiation, forest density, beetle pressure, and amount of forest edge (25, 45–48). Our methodology uses these natural features of the landscape to predict where outlier outbreaks of MPB are likely to establish. Not all new redtop trees in a given year arise from LDD, and therefore, we begin by defining the area that qualifies for LDD. To identify LDD areas, we create a weighted measure of the cumulative number of redtops within a 5-km radius of each cell in our study area (CRT ). The weights decline linearly away from the center of the circle, with a weight of one at the center and a weight of zero at 5 km. Any cell ði,jÞ with CRT ði,jÞ < 5 that was aerially surveyed is considered a candidate for LDD. LDD candidate cells are updated each year as the outbreak spreads. We use a logistic regression model and 3 separate y (2000, 2005, and 2010) of USDA FS ADS data to estimate the probability that an LDD candidate cell will become an outlier. The sample size or total potential number of cells per year of observation for LDD is N = 430;280. Each LDD candidate cell either contained redtops [y ði,jÞ = 1] or had no redtops [y ði,jÞ = 0]. According to ADS data, only 26,833 cells contained redtops and are actual outliers. The probability that cell ði,jÞ will harbor an outlier population is Pr y ði,jÞ = 1uði,jÞ’ β = π ði,jÞ =
ði,jÞ’
eu β , 1 + euði,jÞ’ β
[10]
where uði,jÞ is a vector of cell-specific factors that influences the probability of MPB outlier outbreaks (SI Appendix, Table S3), and β is a vector of logistic coefficients. The signs of all coefficients match our expectations (SI Appendix, Predicting Outlier Outbreaks). Using the estimated coefficients (SI Appendix, Table S3) and the values of the explanatory variables on each cell, Eq. 10 gives predicted probability π^ði,jÞ for LDD on each candidate cell. The predicted probabilities are compared with a threshold probability, π, to determine whether cell ði,jÞ experiences LDD. Predicted values π^ði,jÞ > π result in LDD and successful MPB attack [Ωði,jÞ = 1]; predicted values π^ði,jÞ < π result in no LDD [Ωði,jÞ = 0]. We also incorporate specific local and global processes that cause LDD to evolve as redtops occupy more cells (SI Appendix, Predicting Outlier Outbreaks). The logit LDD model performs significantly better than a completely random LDD process. The logit model correctly predicts about 28% of actual outlier cells, whereas the random process correctly predicts only 6% of actual outlier cells. After a cell is identified as supporting successful LDD, it is seeded with a portion of the emerging beetles. Specifically, the proportion of all emerging beetles from across the grid that engage in LDD is evenly distributed to all cells identified as LDD recipients: ði,jÞ←long
Pt
= Ωij Fð1 − θÞ
X ðl,kÞ
, ðl,kÞ
Rt
X
Ωðl,kÞ ,
[11]
ðl,kÞ
P ðl,kÞ where is the aggregate number of redtops in year t, and ðl,kÞ Rt P ðl,kÞ is the total number of new outlier spots. ðl,kÞ Ω Parameterizing Dispersal and Model Validation. Parameters governing LFD, attack success, and reproductive success (SI Appendix, Table S2) were determined by fitting model predictions to ADS observations in the Sawtooth National Recreation Area of central Idaho for 1995–2005 using maximum likelihood to optimize correspondence between predicted and observed presence on 25-ha blocks. LFD was predicted under the assumption that individual beetles were only capable of 1 d of travel. Simulations using selected parameters for μ0 , μ1 , F, and z reproduced observed spatial patterns in the Sawtooth National Recreation Area with 85% accuracy, and population growth rate dynamics were resolved with 92% accuracy (23). These parameters were also used to test model validity in the
Sims et al.
Lake Chelan region of the eastern Cascades. Without any additional parameterization, model correspondence with observations in the Chelan study area was over 85% in space, and growth rate dynamics were 93% accurate. Thus, the model captures fundamental mechanisms of MPB attack and dispersal and not simply details specific to the area in which it was parameterized. To balance LDD and short-distance dispersal, we set θ = 0:975 based on evidence that up to 2.5% of a population may engage in LDD (38). Rate of natural tree mortality (d) was set at 2% based on the work by Runkle (49).
The juvenile age class scale parameter (b) was selected to ensure that no more than 90 juvenile trees were in any point on the grid.
1. Turner RK, Daily GC (2008) The ecosystem services framework and natural capital conservation. Environmental and Resource Economics 39(1):25–35. 2. Dale VH, et al. (2001) Climate change and forest disturbances. BioScience 51(9): 723–734. 3. Woollings T, Gregory JM, Pinto JG, Reyers M, Brayshaw DJ (2012) Response of the North Atlantic storm track to climate change shaped by ocean-atmosphere coupling. Nat Geosci 5:313–317. 4. Westerling AL, Turner MG, Smithwick EA, Romme WH, Ryan MG (2011) Continued warming could transform Greater Yellowstone fire regimes by mid-21st century. Proc Natl Acad Sci USA 108(32):13165–13170. 5. Logan JA, Regniere J, Powell JA (2003) Assessing the impacts of global warming on forest pest dynamics. Front Ecol Environ 1(3):130–137. 6. Barbier EB, et al. (2008) Coastal ecosystem-based management with nonlinear ecological functions and values. Science 319(5861):321–323. 7. Gedan KB, Kirwan ML, Wolanski E, Barbier EB, Silliman BR (2011) The present and future role of coastal wetland vegetation in protecting shorelines: Answering recent challenges to the paradigm. Clim Change 106(1):7–29. 8. Polasky S, Nelson E, Lonsdorf E, Fackler P, Starfield A (2005) Conserving species in a working landscape: Land use with biological and economic objectives. Ecol Appl 15(4):1387–1401. 9. Millar CI, Stephenson NL, Stephens SL (2007) Climate change and forests of the future: Managing in the face of uncertainty. Ecol Appl 17(8):2145–2151. 10. Bowman DM, et al. (2013) Forest fire management, climate change, and the risk of catastrophic carbon losses. Front Ecol Environ 11(2):66–67. 11. Malhi Y, et al. (2009) Exploring the likelihood and mechanism of a climate-changeinduced dieback of the Amazon rainforest. Proc Natl Acad Sci USA 106(49): 20610–20615. 12. Naidoo R, Ricketts TH (2006) Mapping the economic costs and benefits of conservation. PLoS Biol 4(11):e360. 13. Nelson E, et al. (2008) Efficiency of incentives to jointly increase carbon sequestration and species conservation on a landscape. Proc Natl Acad Sci USA 105(28):9471–9476. 14. Ando A, Camm J, Polasky S, Solow A (1998) Species distributions, land values, and efficient conservation. Science 279(5359):2126–2128. 15. Spies TA, et al. (2007) Potential effects of forest policies on terrestrial biodiversity in a multi-ownership province. Ecol Appl 17(1):48–65. 16. Long JN (2009) Emulating natural disturbance regimes as a basis for forest management: A North American view. For Ecol Manage 257(9):1868–1873. 17. Dellasala DA, Williams JE, Williams CD, Franklin JF (2004) Beyond smoke and mirrors: A synthesis of fire policy and science. Conserv Biol 18(4):976–986. 18. Boyd IL, Freer-Smith PH, Gilligan CA, Godfray HC (2013) The consequence of tree pests and diseases for ecosystem services. Science 342(6160):1235773. 19. Lindenmayer DB, Laurance WF (2012) A history of hubris–cautionary lessons in ecologically sustainable forest management. Biol Conserv 151(1):11–16. 20. Abbott B, Stennes B, Cornelis van Kooten G (2009) Mountain pine beetle, global markets, and the British Columbia forest economy. Can J For Res 39(7):1313–1321. 21. Kurz WA, et al. (2008) Mountain pine beetle and forest carbon feedback to climate change. Nature 452(7190):987–990. 22. Sims C, Aadland D, Finnoff D, Powell JA (2013) How ecosystem service provision can increase forest mortality from insect outbreaks. Land Econ 89(1):154–176. 23. Powell JA, Bentz BJ (2014) Phenology and density-dependent dispersal predict patterns of mountain pine beetle (Dendroctonus ponderosae) impact. Ecol Modell 273(10):173–185. 24. Heavilin J, Powell J (2008) A novel method of fitting spatio-temporal models to data, with applications to the dynamics of mountain pine beetles. Nat Resour Model 21(4): 489–524. 25. Walter JA, Platt RV (2013) Multi-temporal analysis reveals that predictors of mountain pine beetle infestation change during outbreak cycles. For Ecol Manage 302(15): 308–318. 26. Chapman TB, Veblen TT, Schoennagel T (2012) Spatiotemporal patterns of mountain pine beetle activity in the southern Rocky Mountains. Ecology 93(10):2175–2185. 27. Busby GM, Albers HJ, Montgomery CA (2012) Wildfire risk management in a landscape with fragmented ownership and spatial interactions. Land Econ 88(3):496–517. 28. Sims C, Aadland D, Finnoff D (2010) A dynamic bioeconomic analysis of mountain pine beetle epidemics. J Econ Dyn Control 34(12):2407–2419.
29. Whitehead RJ, Safranyik L, Russo G, Shore TL, Carroll AL (2004) Silviculture to reduce landscape and stand susceptibility to the mountain pine beetle. Mountain Pine Beetle Symposium: Challenges and Solutions, Natural Resources Canada Report BC-X-399, eds Shore TL, Brooks JE, Stone JE (Natural Resources Canada, Canadian Forest Service, Kelowna, British Columbia, Canada), pp 233–244. 30. Amman GD, McGregor MD, Schmitz RF, Oakes RD (1988) Susceptibility of lodgepole pine to infestation by mountain pine beetles following partial cutting of stands. Can J For Res 18(6):688–695. 31. Preisler HK, Mitchell RG (1993) Colonization patterns of the mountain pine beetle in thinned and unthinned Lodgepole Pine Stands. Forest Science 39(3):528–545. 32. Safranyik L (1978) Effects of climate and weather on mountain pine beetle populations. Proceedings of Symposium on Theory and Practice of Mountain Pine Beetle Management in Lodgepole Pine Forests, eds Berryman AA, Amman GD, Stark RW (Univ of Idaho, Moscow, ID), pp 77–84. 33. Carroll A, Taylor S, Regniere J, Safranyik L (2004) Effects of climate change on range expansion by the mountain pine beetle in British Columbia. Mountain Pine Beetle Symposium: Challenges and Solutions, Natural Resources Canada Report BC-X-399, eds Shore TL, Brooks JE, Stone JE (Natural Resources Canada, Canadian Forest Service, Kelowna, British Columbia, Canada), pp 223–232. 34. Raffa KF (2008) Cross-scale drivers of natural disturbances prone to anthropogenic amplification: The dynamics of bark beetle eruptions. BioScience 58(6):501–517. 35. Safranyik L, Carroll A (2006) The biology and epidemiology of the mountain pine beetle in lodgepole pine forests. The Mountain Pine Beetle: A Synthesis of Its Biology, Management and Impacts on Lodgepole Pine, eds Safranyik L, Wilson B (Canadian Forest Service, Pacific Forestry Centre, Natural Resources Canada, Victoria, British Columbia, Canada), pp 3–66. 36. Taylor S, Carroll A (2004) Disturbance, forest age, and mountain pine beetle outbreak dynamics in BC: A historical perspective. Mountain Pine Beetle Symposium: Challenges and Solutions, Natural Resources Canada Report BC-X-399, eds Shore TL, Brooks JE, Stone JE (Natural Resources Canada, Canadian Forest Service, Kelowna, British Columbia, Canada), pp 41–51. 37. Byers JA (1999) Effects of attraction radius and flight paths on catch of scolytid beetles dispersing outward through rings of pheromone traps. J Chem Ecol 25(5): 985–1005. 38. Safranyik L, Linton DA, Silversides R, McMullen LH (1992) Dispersal of released mountain pine beetles under the canopy of a mature lodgepole pine stand. J Appl Entomol 113(1-5):441–450. 39. Robertson C, Nelson TA, Boots B (2007) Mountain pine beetle dispersal: The spatialtemporal interaction of infestations. For Sci 53(3):395–405. 40. Garlick MJ, Powell JA, Hooten MB, McFarlane LR (2011) Homogenization of largescale movement models in ecology. Bull Math Biol 73(9):2088–2108. 41. Turchin P (1998) Quantitative Analysis of Movement: Measuring and Modeling Population Redistribution in Animals and Plants (Sinauer, Sunderland, MA). 42. Pfeiffer D, et al. (2008) Spatial Analysis in Epidemiology (Oxford Univ Press, New York). 43. Furniss MM, Furniss RL (1972) Scolytids (Coleoptera) on snowfields above timberline in Oregon and Washington. Can Entomol 104(9):1471–1478. 44. Robertson C, Nelson TA, Jelinski DE, Wulder MA, Boots B (2009) Spatial–temporal analysis of species range expansion: The case of the mountain pine beetle, Dendroctonus ponderosae. J Biogeogr 36(8):1446–1458. 45. Coops NC, Wulder MA, White JC (2006) Integrating remotely sensed and ancillary data sources to characterize a mountain pine beetle infestation. Remote Sens Environ 105(2):83–97. 46. Wulder MA, White JC, Bentz B, Alvarez MF, Coops NC (2006) Estimating the probability of mountain pine beetle red-attack damage. Remote Sens Environ 101(2): 150–166. 47. Bone C, White JC, Wulder MA, Robertson C, Nelson TA (2013) Impact of forest fragmentation on patterns of mountain pine beetle-caused tree mortality. Forests 4(2): 279–295. 48. Kautz M, Schopf R, Ohser J (2013) The “sun-effect”: Microclimatic alterations predispose forest edges to bark beetle infestations. Eur J For Res 132(3):453–465. 49. Runkle JR (1985) Disturbance regimes in temperate forests. The Ecology of Natural Disturbance and Patch Dynamics, eds Pickett STA, While PS (Academic, San Diego), pp 17–33.
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ACKNOWLEDGMENTS. We thank T. Reader with the Colorado State Forest Service and M. Etzenhouser with the US Department of Agriculture Forest Service for providing insights and data on timber markets in the study area. We would also like to acknowledge helpful comments and suggestions from seminar participants at Colorado State University, Virginia Tech, Oak Ridge National Laboratory’s Environmental Sciences Division, and the National Institute for Mathematical and Biological Synthesis.
Sims et al.
PNAS | November 25, 2014 | vol. 111 | no. 47 | 16723
