Date of Award:

5-2016

Document Type:

Dissertation

Degree Name:

Doctor of Philosophy (PhD)

Department:

Mathematics and Statistics

Committee Chair(s)

James Powell

Committee

James Powell

Committee

Brynja Kohler

Committee

Luis Gordillo

Committee

Barbara Bentz

Committee

Nghiem Nguyen

Abstract

The mountain pine beetle (MPB, Dendroctonus ponderosae), a tree-killing bark beetle, has historically been part of the normal disturbance regime in lodgepole pine (Pinus contorta) forests. In recent years, warm winters and summers have allowed MPB populations to achieve synchronous emergence and successful attacks, resulting in widespread population outbreaks and resultant tree mortality across western North America. We develop an age-structured forest demographic model that incorporates temperature-dependent MPB infestations: the Susceptible-Infested-Juvenile (SIJ) model. Stability of equilibria is analyzed as a function of population growth rates, and indicates the existence of periodic outbreaks that intensify as growth rates increase. We devise methods to predict outbreak severity and duration as well as outbreak return time.

To assess the vulnerability of natural resources to climate change, we develop a thermally-driven mechanistic model to predict MPB population growth rates using a distributional model of beetle phenology in conjunction with criteria for successful tree colonization. The model uses projected daily minimum and maximum temperatures for the years 2025 to 2085 generated by three separate global climate models. Growth rates are calculated each year for an area defined by latitude range 42° N to 49° N and longitude range 108° W to 117° W on a rectangular grid with approximately 4km resolution. Using these growth rates, we analyze how the optimal thermal window for beetle development is changing with respect to elevation as a result of climate change induced warming. We also use our combined model to evaluate if thermal regimes exist that would promote two generations per year and discuss how yearly growth rates would change as a result.

Outbreaks of MPB are largely driven by host tree stand demographics and spatial effects of beetle dispersal. We augment the SIJ model to account for the spatial effects of MPB dispersal throughout a forest landscape by coupling it with a probability distribution for beetle location after dispersal. The new model generates a train of solitary waves of infestation that move through a forest with constant speed. We move from a discrete to a continuous modelling framework and search for travelling wave solutions which results in predictions of the shape of an outbreak wave profile and of peak infestation as functions of wave speed, which can be calculated analytically. These results culminate in the derivation of an explicit formula for predicting the severity of an outbreak based on the net reproductive rate of MPB and host searching efficiency.

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