Evolution by Fisherian Sexual Selection in Diploids

Abstract

Most models of Fisherian sexual selection assume haploidy. However, analytical models that focus on dynamics near fixation boundaries and simulations show that the resulting behavior depends on ploidy. Here we model sexual selection in a diploid to characterize behaviour away from fixation boundaries. The model assumes two di-allelic loci, a male-limited trait locus subject to viability selection, and a preference locus that determines a female's tendency to mate with males based on their genotype at the trait locus. Using a quasi-linkage equilibrium (QLE) approach, we find a general equation for the curves of quasi-neutral equilibria, and the conditions under which they are attracting or repelling. Unlike in the haploid model, the system can move away from the internal curve of equilibria in the diploid model. We show that this is the case when the combined forces of natural and sexual selection induce underdominance at the trait locus. Sexual selection is considered to be responsible for many striking and bizarre ornaments and mating behaviors found across the animal kingdom. Although there is a large body of theoretical treatment of sexual selection, most studies make simplifying genetic assumptions, such as haploidy or infinitesimally small polygenic inheritance, to make the math more tractable. However, most animal species that exhibit the ornaments attributed to evolution by sexual selection are diploid. This would not concern us if haploid and diploid models behaved identically. However, the small number of studies that have considered sexual selection in diploids have shown that different and unexpected behavior can occur.Using computer simulations, Heisler and Curtsinger (1990) studied a model of diploid Fisherian sexual selection. Among the cases that they considered is a two-locus diploid model analogous to the haploid model considered by Kirkpatrick (1982) in his seminal paper on sexual selection. Unlike Kirkpatrick (1982) who showed the existence of neutrally stable curves, Heisler and Curtsinger (1990) showed that neutrally stable curves do not exist for any of the parameter sets considered, except under a special case of complete dominance at the trait locus. In some cases, trait and preference frequencies tended toward a curve but then moved slowly along it, whereas in other cases the system appeared to move away from a curve. The latter behavior was associated with heterozygote disadvantage of the trait in the numerical examples considered, but the exact conditions under which these two types of behaviors arise remained unclear, and the authors concluded that there was "a definite need for further analysis of diploid sexual selection models."Two studies have made analytical progress by describing the behavior of the diploid two-locus model when either the trait or preference locus is nearly fixed. Gomulkiewicz and Hastings (1990) studied dynamics near fixation at the trait locus. They found that the stability properties of the fixation boundaries were similar in their diploid model and the haplo...

The evolution of costly mate choice against segregation distorters

“…Joint evolution of trait t 1 and preference p 1 alleles in the absence (A–B) and presence (C) of a distorter. Center row panels (i) illustrate a scenario of a repelling line of quasi‐equilibria, lower row panels (ii) a scenario an attracting line of quasi‐equilibria (indicated by the red lines, based on Greenspoon and Otto ()). Top panels follow the allele frequency dynamics of a specific evolutionary trajectory of scenario (i) over time (shaded in blue).…”

“…However, sexual selection models are complicated considerably when a distorter is added. While most population genetics models of sexual selection are framed in terms of haploids (Kuijper et al 2012), segregation distortion requires the analysis of diploid organisms, which makes analysis much more intricate (Greenspoon and Otto 2009). Most previously published models focus on the interplay between female choice and sex-linked distorters.…”

On the logic of Fisherian sexual selection

“…The model we employ is the diploid version of the canonical two-locus model of Fisherian sexual selection (Kirkpatrick 1982), as studied, for instance, by Gomulkiewicz & Hastings (1990), Heisler & Curtsinger (1990), Otto (1991), and Greenspoon & Otto (2009). The organism is sexual, and both natural and sexual selection are restricted to the diploid phase of its life cycle.…”

“…Since we are usually interested in mate choice and sexual selection in diploid organisms, an important question is whether the population dynamics differs between the two-locus haploid model-studied by Kirkpatrick (1982) for its mathematical tractability-and the diploid analog. Previous work has uncovered differences, particularly in the structure of sets of equilibria possible under the two models (Heisler & Curtsinger 1990, Gomulkiewicz & Hastings 1990, Otto 1991, Greenspoon & Otto 2009). For example, stable paths of equilibria involving polymorphism at both loci are characteristic of the haploid model, but are not observed for most configurations of the diploid model (Heisler & Curtsinger 1990).…”

“…Our aim is to gain a conceptual understanding of the phenomena we discuss, and for this reason we first develop the logic of our arguments and then illustrate this logic with a few instructive simulations, rather than constructing the arguments on the basis of a simulation scan over the entire parameter space. Our primary focus is on the non-equilibrium dynamics of sexual selection, for several reasons: (i) the equilibria of the haploid and diploid models are well studied (Kirkpatrick 1982, Heisler & Curtsinger 1990, Gomulkiewicz & Hastings 1990, (ii) in many configurations of these models, the dynamics are sufficiently slow that non-equilibrium dynamics are important even on long timescales (e.g., Curtsinger 1990, Otto &Greenspoon 2009, andbelow), and (iii) as we show, the non-equilibrium dynamics are often more revealing of the mechanisms underlying Fisherian sexual selection.…”