Limit Theorems for Some Stochastic Evolution Models

Limit theorems are proved for two stochastic models of molecular evolution in finite populations of fixed size. An additive fitness model is shown to be asymptotically neutral in the sense that the relative fitnesses converge in probability to one and the gene frequency distribution converges to the same limiting distribution as when all mutations are selectively neutral. A multiplicative fitness model is studied and weak convergence theorems are proved for the vector whose components are the fitnesses of individuals in the population.