Limit Theorems for Density Dependent Population Genetics
Todd Parsons (University of Pennsylvania)
Thursday 25th March, 2010 14:00-15:00 326, Maths Department
Near the beginning of the century, Sewall Wright and Ronald A. Fisher devised an elegant, mathematically tractable model of gene reproduction and replacement that laid the foundation for contemporary population genetics. The Wright-Fisher model and its extensions have given biologists powerful tools of statistical inference that enabled the quantification of genetic drift and selection. Given the utility of these tools, we often forget that their model - for mathematical, and not biological reasons - makes assumptions that are violated in most real-world populations. In this talk, I consider an alternative framework that merges Patrick Moran's continuous time Markov model with the density dependent models of ecological competition proposed by Gause, Lotka and Volterra, that allows for a stochastically varying -- but bounded -- population size. I will show the existence of several weak limits that naturally generalise the weak and strong selection regimes of classical population genetics, while suggesting the possibility of novel biological phenomena. Time allowing, I will also discuss the application of these techniques in other realms of evolutionary ecology, such as the evolution of virulence.