The Fixation of Locally Beneficial Alleles in a Metapopulation

Abstract

Extinction, recolonization, and local adaption are common in natural spatially structured populations. Understanding their effect upon genetic variation is important for systems such as genetically modified organism management or avoidance of drug resistance. Theoretical studies on the effect of extinction and recolonization upon genetic variance started appearing in the 1970s, but the role of local adaption still has no good theoretical basis. Here we develop a model of a haploid species in a metapopulation in which a locally adapted beneficial allele is introduced. We study the effect of different spatial patterns of local adaption, and different metapopulation dynamics, upon the fixation probability of the beneficial allele. Controlling for the average selection pressure, we find that a small area of positive selection can significantly increase the global probability of fixation. However, local adaption becomes less important as extinction rate increases. Deme extinction and recolonization have a spatial smoothing effect that effectively reduces spatial variation in fitness.T HE fixation of novel alleles is a longstanding research topic, with work on panmictic populations dating back to the beginning of population genetics (Fisher 1922;Wright 1931). Fixation quantifies the dynamics of a rare allele by describing the probability and the expected time for it to increase to a significant frequency within a population (through selective forces or genetic drift). Fixation is therefore an important factor in determining genetic diversity and the rate of evolution. A low fixation probability and a short fixation time will produce a low genetic diversity where single alleles successively sweep through a population. A high fixation probability, or a long fixation time, will tend to increase the number of alleles segregating in a population, thus increasing genetic diversity. These issues can be of direct practical concern. For example, conservation genetics often aims to maximize the genetic diversity of endangered populations (Robert et al. 2003;Gao and Zhang 2005;Jamieson et al. 2006;Bohme et al. 2007), and health or agricultural programs aim to minimize the fixation probability of alleles for insecticide, drug, or vaccine resistance (McLean 1995;Heinemann 1999;Scott et al. 2000).Few populations can truly be described as panmictic. Populations are often spatially fragmented and form a metapopulation system (Hanski and Gaggiotti 2004), with individual fragments going extinct and later being recolonized by migrants from surrounding populations.In a metapopulation many factors can vary from deme to deme, such as the selective advantage of an allele, s, the frequency of an allele, or the force of genetic drift. Under certain circumstances the spatial structure of a metapopulation has no effect, and fixation probability will be the same as that for a panmictic population (Maruyama 1970;Nagylaki 1982). In an ideal, panmictic population where individual reproductive success follows a Poisson distribution with mea...

Species range expansion by beneficial mutations

“…Our results are consistent with previous results for discrete demes. When discrete demes (or metapopulations) experience heterogeneous selection, low migration rates favour establishment of a new mutation (Nagylaki 1980; Tachida & Iizuka, 1991; Gavrilets & Gibson, 2002; Whitlock & Gomulkiewicz, 2005; Vuilleumier et al. , 2008).…”

A metapopulation model for the introgression from genetically modified plants into their wild relatives

“…The main work on this (Whitlock 2003) only describes the probability of fixation of a new mutation, and does not give any approximations for the fixation probability of alleles with a higher frequency. However, it is well known that extinction and recolonization can lead to drastic reductions in the effective population size (Slatkin 1977; Whitlock and Barton 1997; Whitlock 2003; Vuilleumier et al. 2008).…”

“…2008). Using a simulation approach, Vuilleumier et al. (2008) showed that this reduction in effective population size indeed leads to a reduction in the probability of fixation of a beneficial allele.…”

“…2003), whereas genes that do not give a direct advantage in the wild relative may actually be mildly deleterious because of the wasted resources that are used for expressing those genes (Heil and Baldwin 2002). Population dynamics were simulated with extinction rates ranging from 0 to 0.4, following the model of Vuilleumier et al. (2008).…”

A framework for estimating the fixation time of an advantageous allele in stepping‐stone models

“…Much work has focused on how different aspects of population subdivision affect the fixation probability of an advantageous allele (Patwa & Wahl, 2008), such as extinction and recolonization of demes (Barton, 1993; Whitlock, 2003; Cherry, 2003b, 2004), the impact of selfing and dominance of mutations (Whitlock, 2003; Roze & Rousset, 2003), frequency‐dependent selection (Cherry, 2003a; Pannell et al. , 2005), and environmental heterogeneity (Lenormand, 2002; Whitlock & Gomulkiewicz, 2005; Vuilleumier et al. , 2008).…”