Date of Award:

5-2007

Document Type:

Dissertation

Degree Name:

Doctor of Philosophy (PhD)

Department:

Mathematics and Statistics

Advisor/Chair:

James Powell

Abstract

Under normative conditions the mountain pine beetle (Dendroctonus ponderosae Hopkins) has played a regulating role in healthy lodgepole pine (Pinus contorta) forests. However, recently eruptive outbreaks that result from large pine beetle populations have destroyed vast tracts of valuable forest. The outbreaks in North America have received a great deal of attention from both the timber industry and government agencies as well as biologists and ecologists.

In this dissertation we develop a landscape-scaled integrodifference equation model describing the mountain pine beetle and its effect on a lodgepole pine forest. The model is built upon a stage-structured model of a healthy lodgepole pine forest with the addition of beetle pressure in the form of an infected tree class. These infected trees are produced by successful beetle attack, modelled by response functions. Different response functions reflect different probabilities for various densities. This feature of the model allows us to test hypotheses regarding density-dependent beetle attacks.

To capture the spatial aspect of beetle dispersal from infected trees we employ dispersal kernels. These provide a probabilistic model for finding given beetle densities at some distance from infected trees. Just as varied response functions model different attack dynamics, the choice of kernel can model different dispersal behavior. The modular nature of the Red Top Model yields multiple model candidates. These models allow discrimination between broad possibilities at the land scape scale: whether or not beetles are subject to a threshold effect at the lands cape scale and whether or not host selection is random or directed. We fit the model using estimating functions to two distinct types of data: aerial damage survey data and remote sensing imagery. Having constructed multiple models, we introduce a novel model selection methodology for spatial models based on facial recognition technology.

Because the regions and years of aerial damage survey and remote sensing data in the Sawtooth National Recreation Area overlap, we can compare the results from data sets to address the question of whether remote sensing data actually provides insight to the system that coarser scale but less expensive and more readily available aerial damage survey data does not.

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Included in

Mathematics Commons

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