|TITLE:||Linear predictability and biological invasions|
|SPEAKER:||Mark Lewis (University of Alberta)|
|DATE:||Vendredi, 6 Mars 2009|
Classical models for the growth and spread of introduced species track the front of an expanding wave of population density. Underlying equations are typically parabolic partial differential equations and related integral formulations. One method to infer the speed of the expanding wave is to equate the speed of spread of the nonlinear system with the speed of spread of a related linear system. When these two speeds coincide we say that the spread rate is linearly predictable.
In this talk I will discuss linear predictability (or the lack of it) in models for biological invasions, ranging from integrodifference equations to multispecies reaction-diffusion models. I will also connect the theory of spread rates analysis to classical ideas in travelling wave theory. Lastly I will apply some of the results to ecological problems, including movement of vegetation in response to climate change, species competition and the spread of disease.
Much of this work is joint with Hans Weinberger (Minnesota) and Bingtuan Li (Louisville).
About the speaker Mark Lewis is one of the leading researchers in biomathematics in Canada, and indeed, in the world. He received his DPhil. from Oxford under the supervision of J. Murray (one of the founding fathers of biomathematics). After postdoctoral work with Peter Kareiva, he joined the University of Utah as an assistant professor. In 2001, he moved to the University of Alberta, where he is currently a Tier I CRC with a joint appointment between the departments of mathematics and biology. He built and heads the Centre for Mathematical Biology there. His contributions are in dynamical systems, mathematical modeling, and stochastic processes, applied to questions in mathematical biology, in particular population biology and the question of biological invasions, and, more recently, the connection between economics and ecology. One of the most recent topics of his research that captured country-wide attention and media coverage is the effect of fish farms on wild salmon (published in PNAS and Science).
Mark Lewis received the following awards (selection):