Frequency-Dependent Selection and the Evolution of Assortative Mating

Abstract

A long-standing goal in evolutionary biology is to identify the conditions that promote the evolution of reproductive isolation and speciation. The factors promoting sympatric speciation have been of particular interest, both because it is notoriously difficult to prove empirically and because theoretical models have generated conflicting results, depending on the assumptions made. Here, we analyze the conditions under which selection favors the evolution of assortative mating, thereby reducing gene flow between sympatric groups, using a general model of selection, which allows fitness to be frequency dependent. Our analytical results are based on a two-locus diploid model, with one locus altering the trait under selection and the other locus controlling the strength of assortment (a ''one-allele'' model). Examining both equilibrium and nonequilibrium scenarios, we demonstrate that whenever heterozygotes are less fit, on average, than homozygotes at the trait locus, indirect selection for assortative mating is generated. While costs of assortative mating hinder the evolution of reproductive isolation, they do not prevent it unless they are sufficiently great. Assortative mating that arises because individuals mate within groups (formed in time or space) is most conducive to the evolution of complete assortative mating from random mating. Assortative mating based on female preferences is more restrictive, because the resulting sexual selection can lead to loss of the trait polymorphism and cause the relative fitness of heterozygotes to rise above homozygotes, eliminating the force favoring assortment. When assortative mating is already prevalent, however, sexual selection can itself cause low heterozygous fitness, promoting the evolution of complete reproductive isolation (akin to ''reinforcement'') regardless of the form of natural selection.

Effects of genetic architecture on the evolution of assortative mating under frequency-dependent disruptive selection

“…In other words, the evolution of choosiness in this model may have two stable equilibria: an intermediate equilibrium with partial isolation and a high equilibrium with complete isolation. These results were later confirmed by Pennings et al (2008), Otto et al (2008), and Ripa (2009), who showed that the bistability is a consequence of positively frequency-dependent sexual selection. For small mutational step sizes, the intermediate equilibrium forms a barrier against speciation.…”

“…Our main results are that speciation is easiest if choosiness can evolve through a single large mutational step and that additional ecological loci enlarge the number of evolutionary outcomes. Compared to models with one ecological locus and infinitesimal mutations for the mating trait (Pennings et al, 2008;Kopp and Hermisson, 2008;Otto et al, 2008;de Cara et al, 2008;Ripa, 2009), both effects increase the range of parameters where speciation is possible.…”

“…To resolve this problem, several studies have recently developed simplified models, which are analytically tractable and have helped explain some of the controversial results from previous numerical studies (Matessi et al, 2001;de Cara et al, 2008;Pennings et al, 2008;Kopp and Hermisson, 2008;Otto et al, 2008;Ripa, 2009). To achieve analytical tractability, however, the new models needed to rely on simplifying genetic assumptions:…”

“…In many cases, this assumption will be innocuous. In particular, if assortative mating is cost-free, the conditions for invasion of large and small choosiness modifiers are identical, as long as they point into the same direction (Pennings et al, 2008;Otto et al, 2008;Durinx and Van Dooren, 2009). …”

“…The models by Pennings et al (2008), de Cara et al (2008, Otto et al (2008), and Ripa (2009) are based on the simplifying assumption that the ecological trait is determined by a single locus with two alleles and additive effects. Such simplifications, which are made to achieve mathematical tractability, can be problematic if they introduce a bias or if they rule out important outcomes.…”