Patterns of interacting populations in heterogeneous environments

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The goal of my research program is to mechanistically understand the effects of temporal and spatial variation on the dynamics of interacting populations and to study the patterns emerging from this interplay. The approach is to derive a variety of mathematical models and to study their behavior using analytical and numerical methods. The models are dynamical systems, given by ordinary or partial differential equations, difference or integrodifference equations, or some combination thereof. The techniques include linear and non-linear analysis, homogenization, stability theory, traveling waves, and numerical analysis. The program consists of several interconnected research directions, strategic and tactical, that inform and benefit from one another. Strategic projects capture the essence of a certain mechanism or interaction and study the resulting patterns in general. These include the interplay of Hopf- and Turing-bifurcations in the diffusive Leslie-Gower-May model with spatial heterogeneity; simple food-web models in advective media; and traveling pulse solutions in integrodifference equations. Tactical models are specific to a particular situation and aim to understand a particular situation by connecting models and data. These include the dispersal behavior of the Emerald Ash borer and its impact on host trees; effects of dams and other migration barriers on fish in Southern Ontario streams; and effect of treatment on evolution of resistance in cancer. The research program offers a wide variety of excellent training opportunities for undergraduate and graduate students as well as for a postdoctoral fellow. Students learn mathematical analysis, numerical software packages, interdisciplinary collaboration, as well as communication and presentation skills.