Using diffusion models to simulate the effects of land use on grizzly bear dispersal in the Rocky Mountains

Timber harvests proposed for Trail Creek Watershed, in southwestern Montana, U.S.A., have been opposed because grizzly bear (Ursus arctos horribilis) dispersal from northern Montana wildernesses into the Greater Yellowstone Ecosystem may be less likely. We used an individual-based model to simulate grizzly bear responses to: 1) region-level management practices represented by ownership patterns, and 2) watershed-level changes in habitat availability due to proposed harvests and road building. We assigned permeabilities (i.e., values that represent how easily a bear can move through a patch) to ownership blocks (region-level) and habitat patches (watershed-level) based upon a literature review, and used a correlated random-walk diffusion model to simulate movements. Simulated bears were placed into rasterized landscapes in a stratified random manner. At the regional level, bears moved less than or equal to 1500 times (i.e., approximately 1530 km), and their destinations were tallied. At the watershed level, the number of moves required for bears to leave the watershed were tallied. Sensitivity analyses were used to determine the variability of the results with respect to changes in some parameters of interest (i.e., permeabilities of private lands, harvest permeabilities, and disturbance indices). At the watershed-level, removal of forest habitat under proposed Harvest I (1.77% of the watershed cut) led to simulated grizzlies using slightly more moves (i.e., less than or equal to 5.6%, P = 0.042) to exit the watershed than under existing conditions. Harvests of 3.5% of the watershed (planned Harvest II) did not alter the number of moves required to exit the watershed (P = 0.068). When disturbances associated with roads and harvests were also examined, large increases in number of movements required to exit the watershed occurred ( less than or equal to 151%, P = 0.002). These analyses suggest that grizzly bears would be disturbed while timber harvests were ongoing, but that long-term changes in movement would not occur if roads were closed following harvests. The analyses demonstrate the utility of applying individual-based diffusion models to landscape-level movements of animals, and identifies the need for telemetry studies to determine movement rates through specific habitats.