Figure 1.

Models of stabilizing selection in two sexes and peak shifts induced by sexual selection. Panels illustrate the natural selection (e.g. viability) adaptive landscape, the function ${\overline{W}}_m{\overline{W}}_f$_. In Lande's [12] original model of the evolution of sexual dimorphism by natural and sexual selection, a single multivariate optimum, corresponding to one optimum for the male trait and one for the female trait, is assumed (a). In this model, sexual selection leads to a displacement of males from their optimum (inset trajectories are shown starting from the optimum; one where r_mf = 0, blue and one where r_mf = 0.9, red), the magnitude of which is proportional to the strength of stabilizing natural selection. Extending the Lande and twin peaks model to both sexes results in two optima for each trait, or four multivariate optima on the two-sex adaptive landscape (b). As parameterized in this manuscript, the two-sex twin peaks model contains two sexually monomorphic optima, and two sexually dimorphic optima. Of interest is when and how peak shifts from an ancestral monomorphic optimum occur; (c) shows two deterministic trajectories, starting from the lower left optimum, corresponding to two different values of the cross-sex genetic correlation r_mf. Although the sexual selection is strong enough to induce a peak shift, which new optimum reached depends upon the value of r_mf; (d) illustrates 20 replicates of stochastic evolution (i.e. with drift; see electronic supplementary material for details) under the same parameter values as C and assuming female demographic dominance $(N_{t+1}=k\hspace{0.17em}{\overline{W}}_f{N}_t)$. Round circles illustrate the mean values after 10 000 generations of evolution; extinction events are denoted with a crossed circle; (e) contrasts trajectories under two strengths of sexual selection c_m, with otherwise identical parameter values; (f) illustrates stochastic evolution under the same parameter values as (e). White dashed line illustrates the line of sexual monomorphism, for reference. In (e,d), c_m = 0.2; (e,f) r_mf = 0.8; other parameter values as described in text.