Phase III of Wright’s Shifting Balance Process and the variance among demes in migration rate

Wright’s Shifting Balance Theory (SBT; Wright, 1931, 1969, 1977; Wade and Goodnight, 1991; Wade 1992, 1996) has three phases. Phase I is an ‘exploratory phase’ (Johnson 2008) where different gene combinations arise in different local populations primarily as a result of random drift. Wright believed that the number of genetic fitness optima on the adaptive landscape was so large that the chance sampling of Phase I was necessary for discovering new adaptive gene combinations. In Phase II, gene combinations fix locally by natural selection within populations. During this phase, different local populations are attracted to different fitness peaks and become more genetically different from one another. Wright (1932, p. 358–359) considered adaptive evolution to this point incomplete: “The problem of evolution as I see it is that of a mechanism by which the species may continually find its way from lower to higher peaks.…. To evolve, the species must not be under strict control of natural selection.” Phases I and II permit a species to hold on to selected gains while exploring neighboring genotypic space for even better gene combinations, but together they did not guarantee a transition from lower to higher peaks. In the metaphor of a complex problem with many solutions, each deme is one of “Nature’s many small experiments” in adaptive evolution (Wade and Goodnight 1998). The transition to higher peaks according Wright’s theory required an additional mechanism: Phase III interdemic selection. Wright’s Phase III was a mechanism for spreading the gene combinations underlying the highest adaptive peaks throughout a species. Phase III occurred by the differential migration of individuals out from demes of high mean fitness and into demes of lower mean fitness (e.g., Wade and Goodnight 1991; Ingvarrson 2000). It is controversial for several reasons. First, Wright’s SBT appears most efficacious when there is low migration in Phase I but high migration in Phase III (Moore and Tonsor 1994; Coyne et al. 1997; Lenormand 2002, p. 188): “Gene flow plays a crucial role in shifting balance models; it has to be both low enough for a peak shift to occur (so that drift enables alleles to cross the ‘valley’) and high enough for a high-fitness peak to spread.” Thus, Phases I and III appear to require a restrictive condition, an intermediate migration rate (Gavrilets 1996, p. 1034): “…third phase can proceed only under much more restricted conditions than the previous studies suggested. Migration should be neither too strong not [sic] too weak relative to selection.” Second, Phase III is a type of interdemic or group selection, and levels of selection above that between individuals is viewed by many as ‘unnecessary’ (e.g., Williams 1966; Wild et al. 2009). Third, some models indicate that random migration alone is sufficient to spread adaptive gene combinations from one population to another (Barton 1992; Barton and Rouhani 1991; but see Crow et al. 1990), obviating Wright’s problem along with its solution (i.e., Phase III). Wade and Goodnight (1991) investigated the efficacy of Phase III of Wright’s Shifting Balance Theory (SBT) using laboratory metapopulations of the flour beetle, Tribolium castaneum. We imposed three different strengths of Phase III migration and, in all three cases, found a highly significant response of mean fitness to interdemic selection relative to control metapopulations with identical amounts of island model migration. In this paper, I show that interdemic selection by Phase III of the SBT necessarily increases the variance in migration rate relative to island model migration. As a consequence, the genetic divergence among demes in a metapopulations with Phase III migration is increased relative to one with the same mean rate of island model migration (Sved and Latter 1977; Whitlock 1992). In addition, I show that the increase in genetic variance among populations, measured by Wright’s FST, is proportional to the strength of the interdemic selection. The effect of the nonrandom distribution of migrants on FST can be described using the ecological measure of spatial aggregation introduced by Lloyd (1967), mean crowding. I derive a relationship between the mean crowding of Phase III migrants, M*, and the interdemic selection differential, S, to show that the effect on FST is a function of the strength of interdemic selection. This reveals a diversifying effect of interdemic selection by Phase III migration on the genetic structure of a metapopulation. I illustrate this effect with the variance in migrant numbers between the experimental and control metapopulations of Wade and Goodnight (1991), which had the same mean number of migrants per deme per generation. I also compare the FST values of a segregating single-locus visible marker between these control and experimental metapopulations.