| Summary: | In this thesis, we use a reaction-diffusion equation with chemotaxis to model the interaction between Mountain Pine Beetle (MPB, Dendroctonius ponderosae), Mountain Pine Beetle pheromones, and susceptible trees. The goal is to understand how the movement and attack of MPB is affected by management activities.
We investigate the spatial pattern formation of attack clusters in a system for Mountain Pine Beetle. Mathematical analysis is utilized to discover the spacing between beetle attacks on the susceptible landscape. The model predictions are verified by analyzing aerial detection survey data of Mountain Pine Beetle attack from the Sawtooth National Recreation Area. We find that the distance between Mountain Pine Beetle attack clusters predicted by our model and observed in the Sawtooth National Recreation Area are the same. These results clarify the spatial mechanisms controlling the transition from incipient to epidemic populations and may eventually lead to control measures which protect forests from MPB outbreaks.
Our next avenue of investigation is using an experimental study and theoretical work to help understand the effects of habitat fragmentation on the movement of the MPB. The experimental study consists of trap catch data for MPB in different domains of fragmented habitat. We simulate the experimental system using our mathematical model, testing different hypothesis on initial position of MPB emergence and diffusion speed. Our study provides support for the hypothesis that MPB may move faster in harvested landscapes, and that MPB emerge uniformly over the landscape.
Finally, we use a multi-year spatially explicit model to test the effectiveness of the management strategies of baiting and tree-removal and prescribed burning. We find that baiting and tree-removal is successful at reducing MPB density and forest impact, as long as MPB emergence densities are not too small. We predict that tree removal without baiting can be more successful than combined baiting and tree removal if the searched area has a large density of MPB. Finally, analysis of our model indicates that prescribed burning can be more effective than clearcutting given certain assumptions about the reproductive output and attractiveness of burned trees.
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