Role of finite populations in determining evolutionary dynamics

Abstract

The connection between the finite size of an evolving population and its dynamical behavior is examined through analytical and computational studies of a simple model of evolution. The infinite population limit of the model is shown to be governed by a special case of the quasispecies equations. A flat fitness landscape yields identical results for the dynamics of infinite and finite populations. On the other hand, a monotonically increasing fitness landscape shows "epochs" in the dynamics of finite populations that become more pronounced as the rate of mutation decreases. The details of the dynamics are profoundly different for any two simulation runs in that events arising from the stochastic noise in the pseudorandom number sequence are amplified. As the population size is increased or, equivalently, the mutation rate is increased, these epochs become smaller but do not entirely disappear.