Study of the effect of plant toxicity on a plant -herbivore model and its applications
Abstract
Over the past two decades, numerous empirical studies have been focused on the chemical defenses of plants against herbivores, and documented substantial effects of plant toxins on diet choice and feeding behavior of herbivores. But analytical models have failed thus far to incorporate toxin-mediated effects of browsing on plant population dynamics. This thesis is concerned with ecosystem consequences of chemically mediated mammalian herbivory. The impact of plant toxicity on the dynamics of a plant-herbivore interaction is investigated by studying mathematical models that include a toxin-determined functional response. In the toxin-determined functional response, the traditional Holling Type II response is modified to include the negative effect of toxin on herbivore growth, which can overwhelm the positive effect of biomass ingestion at sufficiently high plant toxicant concentrations. These models will theoretically explore how chemically mediated interactions can be expected to affect vegetation dynamics. A Lotka-Volterra type of competition between plants is also included in the models. These models are studied both analytically and numerically. Tools in dynamical systems theory are employed to obtain analytical results, including the existence of a three-dimensional limit cycle (in the biologically feasible region) by constructing a Poincaré map and using bifurcation theory. Numerical simulations of the models exhibit a rich variety of complex dynamics including Hopf and period doubling bifurcations. The model results are applied to a a tall fescue-prairie vole system. The model outcomes are consistent with observed patterns including species coexistence and sustained oscillations. Results of the model suggest that differences in dynamical behavior stem from interspecific differences in plant biology and strategies for growth and defense as well as variation in responses of herbivores to toxins. Analysis also suggests that herbivores may capable of promoting coexistence of plant species by ameliorating competitive effects and hence enhancing biodiversity.
Degree
Ph.D.
Advisors
Feng, Purdue University.
Subject Area
Mathematics
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