Mostly Biomathematics Lunchtime Seminar

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Spatial population dynamics with adaptation to a heterogeneous environment

Speaker: Judith Miller, Georgetown University, Department of Mathematics and Statistics

Location: Warren Weaver Hall 1314

Date: Tuesday, October 16, 2018, 12:30 p.m.

Synopsis:

We model the joint evolution of a population density and the mean, and sometimes variance, of a quantitative trait (that is, a continuous random variable such as flowering time in plants) subject to selection toward an optimum value that varies in space. To do so, we study a family of deterministic models originating from the Kirkpatrick-Barton (1997) reaction-diffusion system. We use analysis and numerics to identify conditions under which the models predict range pinning due to an inux of locally maladapted individuals from the center of a species' range to its borders (“genetic swamping”) versus invasions represented as travelling waves. We highlight differences between the predictions of the Kirkpatrick-Barton model and those of related models incorporating features, such as non-Gaussian dispersal kernels and patchy habitat, that are often represented in nongenetic invasion models.