Date of Award:

Spring 2014

Document Type:

Dissertation

Degree Name:

Doctor of Philosophy (PhD)

Department:

Mathematics and Statistics

Advisor/Chair:

James Powell

Abstract

As data collection and modeling improve, ecologists increasingly discover that interspecies dynamics greatly affect the success of individual species. Models accounting for the dynamics of multiple species are becoming more important. In this work, we explore the relationship between mountain pine beetle (MPB, Dendroctonus ponderosae Hopkins) and two mutualistic fungi, Grosmannia clavigera and Ophiostoma montium. These species are involved in a multipartite symbiosis, critical to the survival of MPB, in which each species benefits. Extensive phenological modeling has been done to determine how temperature affects the timing of life events and cold-weather mortality of MPB. The fungi have also been closely studied to determine how they interact with MPB and how they differ in terms of virulence, response to temperature, and nutritional benefits to developing beetles. Overall, researchers consider G. clavigera to be the superior mutualist. Beetles developing near G. clavigera are larger, produce more brood, and have higher survival rates. Regarding temperature preferences, G. clavigera is considered “cool-loving,” growing at cooler temperatures than O. montium. These findings lead researchers to wonder 1) why has G. clavigera not displaced iv O. montium from the mutualism (if it is the superior mutualist) and 2) what will happen to the MPB-fungus mutualism in the face of a warming climate. In this work we present two models connecting fungal growth in a tree to predictions of MPB emergence: a stochastic, individual-based model and a deterministic, tree-based model. We begin by exploring whether variability in temperature can act as a stabilizing mechanism and find that temperature variability due to MPB periodically transitioning between different thermal environments is the most likely explanation for the continued presence of both fungi in the mutualism. Using the second model, we parameterize and validate the model using attack and emergence observations of MPB and the fungi they are carrying. In the process, we test several submodels to learn more about specific MPB-fungi interactions. Finally, utilizing information from previous fungal growth experiments, we test and parameterize several growth rate curves using Bayesian techniques to determine whether the inclusion of prior knowledge can lead to more realistic fits.

Included in

Mathematics Commons

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