Construction and analysis of mechanistic, predictive, and empirically testable models in ecology and ecotoxicology via rigorous chemical and physical laws

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My main research objective is to understand the role of nutrients in the growth and competition of herbivores and biodegradation of bacteria, and to apply these new fundamental understandings to control deleterious populations and toxic organic matter, including species invasions and ecotoxicology. Control of invasive species has been an extremely important topic globally because the economic effects of invasive species are enormous (estimated global damages at $1.4 trillion annually according to the United Nations Environment Programme). Industry-induced pollution has been a severe environmental problem around the world as the US Environmental Protection Agency and the Canadian Council of Ministers of the Environment have indicated. To guide experiments and management for solving these world-wide issues, mathematical modeling plays a pivotal and necessary role by connecting the known dynamical components, which usually fit together in complex nonlinear ways. My work in mathematical biology has evolved from cyclic population dynamics to fundamental stoichiometric modeling and analysis, and then to applications of stoichiometric theory and the spread of infectious diseases. In nutrient deficient environments, the consideration of nutrient cycling, or stoichiometry, can be essential for population models. I plan to advance the stoichiometric modeling into a more mechanistic level, which may lead to some fundamental laws in theoretical biology. Its application to species invasions can guide the government towards improved management policies. To study the impacts of abiotic factors, such as nutrient and turbidity, on key biological responses is essential for determining the competition result of native and invasive species. The other application of the stoichiometric concept is ecotoxicology. I will construct a stoichiometric biodegradation model to estimate methane production from tailings ponds and end pit lakes, generated by the oil sands industry, in Alberta. An associated project is the risk assessment of oil sands pollution on the persistence and biodiversity of an ecosystem in Alberta, which is a joint project with the Alberta government. Another separate project is focused on the spread of infectious diseases including their transmission modes and rates. I propose an integrated program of mathematical, computational, and experimental studies that will provide a new generation of mechanistic models with chemical and physical constraints. Most mathematical models are non-smooth dynamical systems which may generate novel dynamics and bifurcations. Analytical techniques include local and global stability analysis, bifurcation analysis, theory of monotone dynamical systems, persistence theory, perturbation theory, sensitivity analysis, wavelet analysis, etc. Furthermore, these mechanistic models will be challenged and calibrated by experimental data.