The Maintenance (or Not) of Polygenic Variation by Soft Selection in Heterogeneous Environments

Abstract

On the basis of single-locus models, spatial heterogeneity of the environment coupled with strong population regulation within each habitat (soft selection) is considered an important mechanism maintaining genetic variation. We studied the capacity of soft selection to maintain polygenic variation for a trait determined by several additive loci, selected in opposite directions in two habitats connected by dispersal. We found three main types of stable equilibria. Extreme equilibria are characterized by extreme specialization to one habitat and loss of polymorphism. They are analogous to monomorphic equilibria in singe-locus models and are favored by similar factors: high dispersal, weak selection, and low marginal average fitness of intermediate genotypes. At the remaining two types of equilibria the population mean is intermediate but variance is very different. At fully polymorphic equilibria all loci are polymorphic, whereas at low-variance equilibria at most one locus remains polymorphic. For most parameters only one type of equilibrium is stable; the transition between the domains of fully polymorphic and low-variance equilibria is typically sharp. Low-variance equilibria are favored by high marginal average fitness of intermediate genotypes, in contrast to single-locus models, in which marginal overdominance is particularly favorable for maintenance of polymorphism. The capacity of soft selection to maintain polygenic variation is thus more limited than extrapolation from single-locus models would suggest, in particular if dispersal is high and selection weak. This is because in a polygenic model, variance can evolve independently of the mean, whereas in the single-locus two-allele case, selection for an intermediate mean automatically leads to maintenance of polymorphism.

Regional heterogeneity and gene flow maintain variance in a quantitative trait within populations of lodgepole pine

“…Although Slatkin suggested that this effect would only be important under strong selection, Barton (1999) has shown that gene flow through a cline can result in substantial increases in variance under weak selection as well. Other models based on single populations experiencing stabilizing selection and immigration of non-locally adapted alleles (Tufto 2000) or two populations inhabiting different environments connected by gene flow (Spichtig & Kawecki 2004) have made similar qualitative conclusions, showing that gene flow can maintain genetic variation within populations, but that this effect will only occur under limited migration and strong selection.…”

Multilocus Genetics and the Coevolution of Quantitative Traits

“…In the multilocus model, selection determines not only the mean trait value of a species but also its genetic variance (see Bü rger and Gimelfarb 2004;Spichtig and Kawecki 2004;Bü rger 2005). In particular, genetic variance depends on the type of net selection that the species experiences (where net selection refers to the combined effect of direct stabilizing selection and selection due to the between-species interaction).…”

“…The evolution of phenotypic variances depends on the type of net selection experienced by the two species, which can be seen from equations (5) and (6). Mutualists and exploiters (which have positive ␥ values) are always under net stabilizing selection, which tends to remove genetic variation (Wright 1935;Barton 1986;Spichtig and Kawecki 2004). Their mean fitness decreases with the deviation from the corresponding fitness maximum and with genetic variance.…”

“…For the same reason, competitors and victims (which have negative ␥ values) are under net stabilizing selection if ͦ ␥ ͦ Ͻ , but under net disruptive selection in the opposite case. Net disruptive selection tends to increase genetic variation (e.g., Bü rger and Gimelfarb 2004; Spichtig and Kawecki 2004;Bü rger 2005). Finally, each species can be under net directional selection if the respective fitness maximum or minimum is outside of the range of phenotypes currently present in the population.…”

“…First, in species under net stabilizing selection, alternative equilibria with similar mean phenotypes (close to the values) may be stable simultaneously (see Barton 1986;Bü rger and Gimelfarb 1999). Second, in victims experiencing net disruptive selection, the equilibrium allele frequencies generally are no longer identical, and loci with weak effects may become fixed for one of the two alleles (see Bü rger and Gimelfarb 2004;Spichtig and Kawecki 2004;Bü rger 2005). Finally, both simple and complex heteroclinic cycles are less regular than those shown in Figure 2, more than one type of either class of cycles can coexist for the same parameter values, and complex cycles can be truly chaotic.…”