Title: Spatial evolutionary games with small selection coefficients
Speaker: Rick Durrett
Speaker Info: Duke University
Brief Description:
Special Note:
Abstract:
The use of evolutionary game theory biology dates to work of Maynard-Smith who used it to explain why most fights between animals were of the limited war type. In the mid 1990s Nowak and May demonstrated that a spatial distribution of players can explain the existence of altruism, which would die out in a homogeneously mixing population. Recently, evolutionary games have been used to model cancer, e.g., the fact that stromal cells may cooperate with prostate tumor cells to help cancer spread. We use results of Cox, Durrett, and Perkins for voter model perturbations to study spatial evolutionary games when the fitness differences between strategies are small. There are two main results: on the d-dimensional lattice the effect of space is equivalent to (i) changing the entries of the game matrix and (ii) replacing the replicator ODE by a related PDE. On the torus there are two different weak regimes that lead to a PDE and an ODE respectively. In the second case, our results allow us to prove results of Tarnita and Nowak. The first result comes from a 2014 paper in Electronic Journal of Probability. The second has not yet been published but can be seen online at Stochastic Processes and Their Applications. Both papers are on my web page.Date: Saturday, May 07, 2016