PDEs in Evolution of Dispersal

Adrian Lam (May 7, 2020)

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Beginning with the work of Alan Hastings in 1983, PDE models have played a major role in the mathematical study of evolution of dispersal. In this talk, I will discuss two classes of PDE models that comes from evolution of dispersal. In the first part, I will discuss existence/non-existence of evolutionarily stable strategies (ESS) in two-species competition models, which is motivated by the adaptive dynamics approach. In the second part, I will introduce a new class of models that describes a population structured by a quantitative trait, which describes the competition of an infinite number of species in a certain sense. We show the convergence to ESS in these models of a quantitative trait, and explain how that is connected to the aforementioned adaptive dynamics framework. This talk contains projects in collaboration with R.S. Cantrell, C. Cosner, M. Golubitsky, W. Hao, B. Perthame, Y. Lou, and F. Lutscher.