Renato Vicente (University of Sao Paulo)
Abstract. We have introduced in arXiv:1106.4783v1 a framework for the mathematical modeling of evolution in group structured populations. The population is divided into a fixed large number of groups of fixed size. From generation to generation, new groups are formed that descend from previous groups, through a two-level Fisher-Wright process, with selection between groups and within groups and with migration between groups at rate m. We have focused on the situation in which the population is entirely composed by a wild type N and analyze the stability of this initial state against invasion by a mutant type A. The main questions are conditions for the viability of the mutant type A to spread, and the fashion in which it spreads when it does. We analyze the early stages of the evolution, during which the number of type A alleles is small compared to the size of the population.This work is a collaboration with Roberto Schonmann (Dept. of Mathematics/UCLA and University of Sao Paulo) and Nestor Caticha (Dept. of Physics/ University of Sao Paulo).