Runaway ornament diversity caused by Fisherian sexual selection

Abstract

Fisher's runaway process of sexual selection is potentially an important force generating character divergence between closely related populations. We investigated the evolution of multiple female preferences by Fisher's runaway process. There are two outcomes of runaway. The first is the evolution of mate preference to a stable equilibrium. This evolution occurs if the benefits of mate choice are sufficiently large relative to the cost of choice. Alternatively, mate preferences evolve cyclically. The rate and pattern of cyclic evolution depends primarily on the individual cost of choice and epistasis in the joint cost of choice. If there are small differences in natural selection (e.g., predation risk) between populations, cyclic evolution quickly leads to divergence in mate preferences and sexual ornaments and so to sexual isolation.

Figure 1

Evolution of the mean male ornament size (t̄) through time (mean female preference p̄ follows a similar path). The population is plotted every 40 generations. Two conditions varying in the degree of mutation bias are shown leading to a stable equilibrium (u = 0.0001) (a) and cyclic evolution (u = 0) (b). Other parameter values are a = 0.4, b = 0.001, c = 0.05, G_t = 0.5, and G_p = 0.5.

Figure 2

Coevolution of two preferences for separate male ornaments as a function of epistasis in the joint cost of choice θ. Evolution is represented in two ways. First as a phase-space of the mean male ornaments (t̄₁ and t̄₂) every 20 generations; second as t̄₁ (black) and t̄₂ (gray) values through time. The mean female preferences are not shown because they follow similar evolutionary trajectories. The cost of choosing t₁ is set to be larger than the cost of choosing t₂ (λ₁ = 1.0 and λ₂ = 0.6). Four values of the joint cost of choice are shown: (a) θ = 0.05, t̄₁ and t̄₂ show equal rates of change and entrained cycles; (b) θ = 0.2, t̄₁ changes three times more quickly than t̄₂ and cycles are entrained; (c) θ = 0.8, t̄₁ changes more quickly than t̄₂ and cycles are not entrained, the phase-space shows the first 8,000 generations; and (d) θ = 1.2, females only show preference for t̄₂ and progressively ignore t̄₁. Parameter values are a₁ = a₂ = 0.4, b = 0.001, c₁ = c₂ = 0.05, and all G = 0.5.

Figure 3

Length of an evolutionary cycle plotted against epistasis in the joint cost of choice (θ) when the individual cost of choice is higher for p₁ than for p₂ (λ₁ = 1, λ₂ = 0.6). Plots are given for the number of generations per cycle (p₁ diamonds, p₂ crosses) (a) and the ratio of p₁ cycle time to p₂ cycle time (b). Other parameter values as in Fig. 2.

Figure 4

Male ornament divergence in two allopatric populations subject to different selection pressures. Selection on female preference is set to be 20% weaker in population 2, both for the individual cost of choice and epistasis in the joint cost of choice (population 1 b = 1.0, θ = 0.6; population 2 b = 0.8, θ = 0.48). Otherwise selection in the two populations is identical. There are two male ornaments, so there are four possible character states: gray, t̄₁ < 0, t̄₂ < 0; stipple, t̄₁ > 0, t̄₂ < 0; blank, t̄₁ > 0, t̄₂ > 0; and stripe, t̄₁ < 0, t̄₂ > 0. The sequence in which these character states evolve is shown through time. The two populations start with the same strength of preferences and ornament sizes. Other parameter values as in Fig. 2.