Limits to the evolution of assortative mating by female choice under restricted gene flow

Abstract

The evolution of assortative mating is a key component of the process of speciation with gene flow. Several recent theoretical studies have pointed out, however, that sexual selection which can result from assortative mating may cause it to plateau at an intermediate level; this is primarily owing to search costs of individuals with extreme phenotypes and to assortative preferences developed by individuals with intermediate phenotypes. I explore the limitations of assortative mating further by analysing a simple model in which these factors have been removed. Specifically, I use a haploid two-population model to ask whether the existence of assortative mating is sufficient to drive the further evolution of assortative mating. I find that a weakening in the effective strength of sexual selection with strong assortment leads to the existence of both a peak level of trait differentiation and the evolution of an intermediate level of assortative mating that will cause that peak. This result is robust to the inclusion of local adaptation and different genetic architecture of the trait. The results imply the existence of fundamental limits to the evolution of assortment via sexual selection in this situation, with which other factors, such as search costs, may interact.

Figure 1.

Equilibrium frequencies of sexually selected traits in population 2 as α increases, from expression (2.1). The top curve corresponds to the frequency of the trait characteristic of this population, while the bottom curve corresponds to the frequency of the trait characteristic of population 1. Solid lines (grey plus black) show stable equilbria and dashed lines show unstable equilibria with the assumption of symmetry. Black solid lines on the curves show the equilibria reached in simulations of the asymmetrical model for that value of α, starting from the assumption of secondary contact (t₂ ≈ 0 in population 1 and t₂ ≈ 1 in population 2 or vice versa, with offsets of 0.001 and 0.002). The values of α_opt are marked in each graph. In (b) the thin dashed arrows show a potential series of steps in the evolution of assortative mating, as described in the text. (a) m = 0.001, (b) m = 0.01, (c) m = 0.03.

Figure 2.

Change in α_opt with changing migration rate.

Figure 3.

Change in α_opt with changing selection on the trait. The migration rate m = 0.01.

Figure 4.

Summaries of evolutionary trajectories of the frequency of allele N₂ and the linkage disequilibrium D across various values of α with m = 0.01 and free recombination between the M and N loci. Each line summarizes an evolutionary trajectory by drawing a line from values at the start of a simulation (shown by the regularly spaced dots) to the equilibrium points, seen as the points of convergence. (a) α = 0.01; (b) α = 0.15; (c) α_opt = 9; (d) α = 65; (e) α = 70; (f) α = 75.

Figure 5.

Evaluation of the strength of selection on T₂ in a single population. (a) Strength of selection on T₂ in males (a_0,T) as α changes, for different values of t₂, when s = 0. Black: t₂ = 0.5, red: t₂ = 0.6, green: t₂ = 0.7, blue: t₂ = 0.8, pink: t₂ = 0.9, light blue: t₂ = 0.95, yellow: t₂ = 0.99. (b) The value of α that leads to the peak strength of selection in males (a_0,T) with increasing t₂, with s = 0. (c) The value of α that leads to the peak strength of selection in males (a_0,T) with increasing s, with t₂ = 0.95.