The dynamics of finite haploid populations with overlapping generations. I. Moments, fixation probabilities and stationary distributions

Abstract

Much of the work on finite populations with overlapping generations has been limited to deriving effective population numbers with the tacit assumption that the dynamics of the population will be similar to a population with nonoverlapping generations and the appropriate population number. In this paper, some exact and approximate results will be presented on the behavior of the first two moments of the gene frequencies. The probability of fixation of a neutral gene is found equal to the initial average reproductive value of the gene, and the means and covariances of the stable distribution with mutation in both directions are found by a simple extension of the values found by assuming nonoverlapping generations.