Spatial Dynamics of Mountain Pine Beetle Epidemics with Optimal Forest Management Charles Sims 1, David Aadland 2 & David Finnoff 2 1 Utah State University 2 University of Wyoming

Mountain Pine Beetle are endemic to the Rocky Mountains Current epidemic covers more than 2 million acres in Colorado & Wyoming; another 40 million acres in British Columbia Contributing factors are global warming, fire suppression and reduced timber harvesting Sims et al JEDC Sims et al. 2011

Snowy Range Mountains, WY

Literature Sampling: Spatial Dynamics in Resource Economics Sanchirico & Wilen (2005, JEEM) Costello & Polasky (2008, JEEM) Brock & Xepapadeas (2008, JEDC) Smith, Sanchirico & Wilen (2009, JEEM) Epanchin-Neil & Wilen (2011, RFF wp) Space/Time tradeoff: human behavior; choice variables; number of species, patches, and time periods; migration; interdependencies

Model & Solution Procedure Abstract model 3 classifications for trees (X,Y,A) Mountain pine beetle stock (B) 6 × 6 landscape grid Spatial heterogeneity Density-dependent MPB dispersal Forward-looking, rational forest managers Solution procedure Approx. linear harvest rule (Blanchard & Kahn 1980) Linear harvest rule with nonlinear biological system Linear quadratic approx. (Brock & Xepapadeas 2008)

Forest Dynamics on cell (i,j) Seed base: Young trees: Adult trees: MPB risk :

MPB Reproduction and migration Reproduction: Migration Stage 1 Stage 2

Local Optimal Management Benefit of harvesting Opportunity cost of harvesting MPB migration effect MPB reproduction effect First-order condition for h t (i,j) where Ψ i (i,j) is the marginal net benefit of an adult tree at time t on cell (i,j)

Reduced-form local harvest rules First-order Taylor series approx. Linearized system exhibits saddle path stability and implies linear harvest rules Each rule is a function of 4X36=144 contemporaneous state variables

Landscape Spatial MPB Externality Local managers look to neighboring cells to estimate migration onto own forest BUT local managers unconcerned about neighboring welfare Spatial nature of externality may cause local managers to over or under harvest

Central Optimal Management First-order condition same as for local planner with addition of spatial MPB externality captured by appending two additional terms on the right side MPB migration externality MPB reproduction externality

Steady State (Endemic Population) Analysis Type 1: Centralized h 8% higher Externality impact = 2% Type 2: Centralized h 5% higher Externality impact = 0.1% Type 3: Centralized h 0.4% lower Externality impact = -1% Type 4: Centralized h 4% higher Externality impact = 0.1% Type 5: Centralized h 5% higher Externality impact = 0.2% Type 6: Centralized h 2% higher Externality impact = -0.3%

Preliminary Findings Local managers anticipate MPB spread; anticipatory harvesting Harvesting can accelerate spread & dampen MPB outbreaks/cycles Spatial externality comprised of two parts that work in opposite directions Central managers may harvest more or less than local managers Internalizing spatial externality requires combination of taxes and subsidies

Future work Is the location of the outbreak important? How do results change with different spatial size? Consider landscape with different management objectives Eventually overlay on actual forested areas

The End. Comments?