Critical mutation rates in structured populations

Abstract

The Moran model describes the evolution of a single biallelic gene in a finite population, expressing the balance between drift and mutations. If the mutation rate is small drift dominates and most individuals will display the same allele. If mutations are frequent, an equilibrium between the two alleles is observed. For well mixed populations the critical mutation rate that separates these two regimes is given by ¼c=1/2N, where N is the population size. In this critical state the probability that m individuals share the same allele is constant, independent of m. In spatially structured populations, however, the mutation-drift balance in more subtle and the critical mutation rate has to be determined using the maximum entropy criterion. Numerical simulations have shown that ¼c<1/2N in these cases, indicating that the effect of mutationsis enhanced in structured populations. In this work we will explore the connection between the Moran and the Voter model used in the social sciences to understand how the critical mutation rate depends on the population structure. The supervisor in the US, Prof. Dan Braha, is an expert in complex systems with focus on stochastic models on networks. His recent works on the Voter Model with external perturbations and his interests in structured networks will fit very well in the present project. (AU)