Equilibria and dynamics of selection at a diallelic autosomal locus in the Nagylaki-Crow continuous model of a monoecious population

Abstract

Let birth rates and death rates be constant, birth rates positive, fertilities additive, and each birth rate not larger than twice any other birth rate. Global convergence to equilibria is proved for the model in the title. There is at most one polymorphic equilibrium or there are a continuum of equilibria. The phase portraits are given. If there is a polymorphic equilibrium, then the largest negatively invariant set in the state space is a continuous curve connecting the two fixation equilibria. This curve coincides with the Hardy-Weinberg manifold exactly when the death rate is additive. Disregarding extinction, the polymorphic equilibria are the same for the continuous model as for the corresponding discrete model exactly when the death rate is additive.