Dying on the way: The influence of migrational mortality on neutral models of spatial variation

Abstract

Migrational mortality is introduced into the classical Malécot model for migration, mutation, and random genetic drift. To assess the influence of mortality, its effect on the backward migration rates and on the probabilities of identity in allelic state are studied. Perhaps surprisingly, some of the former may increase, but as is intuitive, their sum always decreases. As expected, in the island model, mortality does not change the migration pattern, but it decreases the migration rate. Furthermore, it decreases the expected heterozygosity, but increases the genetic diversity and differentiation. The circular habitat and the unbounded, linear stepping-stone model also illustrate the general results. Arbitrary migration is also analyzed. If migration is sufficiently weak, then mortality diminishes every migration rate; it decreases the expected heterozygosity and the genetic similarity between demes. In the strong-migration limit, mortality may raise or lower the probability of identity in state. Perhaps unexpectedly, under mild and reasonable biological assumptions, mortality does not alter the diffusion limit of the probabilities of identity.