Effects of demographic stochasticity and life-history strategies on times and probabilities to fixation: an individual-based model

Abstract

Previous works has suggested that the harmonic mean population size can summarize the consequences of demographic fluctuations on the genetic frequencies of populations. We test this hypothesis by studying a model in which the demography and genetic composition of the population are both determined by the behavior of the individuals within the population. We propose an effective population size that allows us to compare our model with the classical Wright-Fisher diffusion both for neutral alleles and those under selection. We find that using our approximation for the effective population size, the Wright-Fisher diffusion provides good results for the times to absorption and probabilities of fixation of a given neutral allele and in cases where selection is not too strong. However, the times and laws to fixation are not always well predicted due to large fluctuations in population size caused by small growth rates or strong competition between individuals, that cannot be captured by the constant population size approximation. The discrepancy between our model and the Wright-Fisher diffusion is accentuated in the presence of demo-genetic feed-back. Our results imply that the Wright-Fisher diffusion is not appropriate when studying probabilities and times to fixation in long-lived species with low reproductive rates.