Peak and Persistent Excess of Genetic Diversity Following an Abrupt Migration Increase

Abstract

Genetic diversity is essential for population survival and adaptation to changing environments. Demographic processes (e.g., bottleneck and expansion) and spatial structure (e.g., migration, number, and size of populations) are known to shape the patterns of the genetic diversity of populations. However, the impact of temporal changes in migration on genetic diversity has seldom been considered, although such events might be the norm. Indeed, during the millions of years of a species' lifetime, repeated isolation and reconnection of populations occur. Geological and climatic events alternately isolate and reconnect habitats. We analytically document the dynamics of genetic diversity after an abrupt change in migration given the mutation rate and the number and sizes of the populations. We demonstrate that during transient dynamics, genetic diversity can reach unexpectedly high values that can be maintained over thousands of generations. We discuss the consequences of such processes for the evolution of species based on standing genetic variation and how they can affect the reconstruction of a population's demographic and evolutionary history from genetic data. Our results also provide guidelines for the use of genetic data for the conservation of natural populations. GENETIC diversity in a population of constant size results from the balance between the occurrence of new mutations and the loss of alleles by genetic drift (Fisher 1922;Wright 1931;Kimura and Crow 1964). The expected population genetic diversity can thus be estimated from the effective population size and the mutation rate in the population. In subdivided populations this estimate should further account for the strength of migration (Maruyama 1970;Smith 1970;Nei 1973): limited migration allows for strong differentiation between populations, while strong migration tends to homogenize genetic diversity between populations. Genetic diversity is also known to be affected by population demographic changes; following bottlenecks and founder events, a loss of genetic diversity is expected to occur (Nei et al. 1975). Recently, spatial population expansions were shown to lead to increased differentiation between populations and to generate a low level of genetic diversity at the front of the expansion (Excoffier et al. 2009).Although theoretical studies on the dynamics of genetic diversity in subdivided populations started appearing in the 1970s (Nei and Feldman 1972;Latter 1973;Nei 1973;Nagylaki 1974Nagylaki , 1977, the transient dynamics and nonequilibrium states of genetic diversity still do not have a good theoretical basis. Early authors characterized the ultimate rate of change of genetic diversity after a perturbation (either a change in population size or gene flow; Nei and Feldman 1972;Latter 1973;Nei 1973;Nagylaki 1974Nagylaki , 1977. They found that changes in genetic diversity are related to the total effective population size, which results in a slow dynamics of genetic diversity change. They thus first highlighted that nonequilibrium ...

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