Abstract
The extent to which populations experiencing shared selective pressures adapt through a shared genetic response is relevant to many questions in evolutionary biology. In a number of well studied traits and species, it appears that convergent evolution within species is common. In this paper, we explore how standing, deleterious genetic variation contributes to convergent genetic responses in a geographically spread population, extending our previous work on the topic. Geographically limited dispersal slows the spread of each selected allele, hence allowing other alleles – newly arisen mutants or present as standing variation – to spread before any one comes to dominate the population. When such alleles meet, their progress is substantially slowed – if the alleles are selectively equivalent, they mix slowly, dividing the species range into a random tessellation, which can be well understood by analogy to a Poisson process model of crystallization. In this framework, we derive the geographic scale over which a typical allele is expected to dominate, the time it takes the species to adapt as a whole, and the proportion of adaptive alleles that arise from standing variation. Finally, we explore how negative pleiotropic effects of alleles before an environment change can bias the subset of alleles that get to contribute to a species adaptive response. We apply the results to the many geographically localized G6PD deficiency alleles thought to confer resistance to malaria, whose large mutational target size and deleterious effects make them likely candidates to have been present as deleterious standing variation. We find the numbers and geographic spread of these alleles matches our predictions reasonably well, which suggest that these arose both from standing variation and new mutations since the advent of malaria. Our results suggest that much of adaptation may be geographically local even when selection pressures are wide-spread. We close by discussing the implications of these results for arguments of species coherence and the nature of divergence between species.
