Evolution of frequency-dependent mate choice: keeping up with fashion trends

Abstract

The diversity of sexual traits favoured by females is enormous and, curiously, includes preferences for males with rare or novel phenotypes. We modelled the evolution of a preference for rarity that yielded two surprising results. First, a Fisherian 'sexy son' effect can boost female preferences to a frequency well above that predicted by mutation-selection balance, even if there are significant mortality costs for females. Preferences do not reach fixation, however, as they are subject to frequency-dependent selection: if choosy females are too common, then rare genotypes in one generation become common, and thus unattractive, in the offspring generation. Nevertheless, even at relatively low frequency, preferences maintain polymorphism in male traits. The second unexpected result is that the preferences can evolve to much higher frequencies if choice is hindered, such that females cannot always express their preferences. Our results emphasize the need to consider feedback where preferences determine the dynamics of male genotypes and vice versa. They also highlight the similarity between the arbitrariness of behavioural norms in models of social evolution with punishment (the so-called 'folk theorem') and the diversity of sexual traits that can be preferred simply because deviating from the norm produces unattractive offspring and is, in this sense, 'punished'.

Figure 1

Mutation–selection balance histogram of preference frequencies when k=1, μ=0.0002 and cost c=0.01, obtained sampling a simulated population every 500 generations for 1.5 million generations. The mean of the distribution is 0.022. Repeating this procedure for other cost values gives the mean values 0.50 (for c=0), 0.46 (c=0.0001) and 0.35 (for c=0.001).

Figure 2

Example trajectories of the frequencies of the female preference (dots) and male types (lines) when preferences are initially (a) absent or (b) fixed. The examples use strict preferences with no temporal variation in viability selection. Parameters used are N=1000, n=50, c=0.01, k=5, y=1 and μ=0.0002. The dynamics of male genotypes are characterized by drift when female preferences are absent and much tighter regulation when a fraction of females prefer rare males. Where preferences are fixed (i.e. up to generation 100 in (b)), the rarest male types are the most common in the next generation, leading to sharp fluctuations in male frequencies.

Figure 3

Evolution of fully expressed (y=1) female preferences, with different numbers of male types k in the population. Data are presented as mean±s.e. (boxes) and ±95% CI for the mean (whiskers) for the frequency of the female preference allele after T generations. The expected frequency under mutation–selection balance is indicated by a dashed horizontal line (not visible in (a), where it is 0.5). It was numerically derived (figure 1). Populations started with either the preference allele absent (open boxes) or fixed (shaded boxes). (a) Strict preference for rarity with cost c=0 and no temporal variation in viability. (b) Strict preference for rarity with c=0.01 and no temporal variation in viability. (c) The same as for (b), but females have a threshold preference for rarity, mating with any male whose type frequency in her sample of n is below 5%. (d) The same as for (c), but the threshold frequency is 10%. (e) The same as for (b), but with frequency-independent viability selection using d_I=0.5. (f) The same as for (b), but with frequency-dependent viability selection, d_D=0.5. In all the examples, n=50, N=1000, μ=0.0002 and T=2500, except in (c) and (d) where T=5000 due to slower convergence between populations with different initial frequencies.

Figure 4

The effect of changes in the fraction y of females that fully express their mating preferences on the frequency of the preference after 7500 generations. The mean and 95% CI are based on 50 replicates per scenario, and populations started with the preference allele either absent (open bars) or fixed (shaded bars). The black horizontal lines give the expected frequency under mutation–selection balance for a given cost c of the female preference. Cost is indicated on the x axis. The effect of a greater ability of females to express preferences can be seen by noting the trend from (A) y=0.1, (B) y=1/3, (C) y=0.5, (D) y=2/3 to (E) y=1. For the sake of visual clarity, these labels are omitted in the case where the cost c=0.01. Other parameter values are k=10, n=50, N=1000 and μ=0.0002.