A MUTATION-SELECTION-RECOMBINATION MODEL IN POPULATION GENETICS

We construct a new continuous time selection-mutation-recombination model for population dynamics, which describes the development of the distribution of the different gametes in the population. We show that cyclic mutation rates can result in stable and unstable limit cycles due to Hopf bifurcation. In addition, we give a qualitative characterization of the whole dynamics in the simplex, which is the phase space of the system. If only selection acts, then Fisher’s Fundamental Law is valid: the mean fitness is a Lyapunov function and every orbit converges to some rest point.