Multimodal pattern formation in phenotype distributions of sexual populations

During bouts of evolutionary diversification, such as adaptive radiations, the emerging species cluster around different locations in phenotype space, How such multimodal patterns in phenotype space can emerge from a single ancestral species is a fundamental question in biology. Frequency-dependent competition is one potential mechanism for such pattern formation, as has previously been shown in models based on the theory of adaptive dynamics. Here we demonstrate that also in models similar to those used in quantitative genetics, phenotype distributions can split into multiple modes under the force of frequency-dependent competition. In sexual populations, this requires assortative mating, and we show that the multimodal splitting of initially unimodal distributions occurs over a range of assortment parameters. In addition, assortative mating can be favoured evolutionarily even if it incurs costs, because it provides a means of alleviating the effects of frequency dependence. Our results reveal that models at both ends of the spectrum between essentially monomorphic (adaptive dynamics) and fully polymorphic (quantitative genetics) yield similar results. This underscores that frequency-dependent selection is a strong agent of pattern formation in phenotype distributions, potentially resulting in adaptive speciation.

💡 Research Summary

The paper addresses a central problem in evolutionary biology: how a single ancestral species can give rise to multiple distinct phenotypic clusters during episodes of rapid diversification such as adaptive radiations. While adaptive‑dynamics models have long demonstrated that frequency‑dependent competition can generate multiple evolutionary stable strategies (ESS), it has remained unclear whether similar multimodal patterns can arise in quantitative‑genetics frameworks that treat phenotypes as continuous distributions. The authors bridge this gap by constructing and analysing two related models—one for asexual (clonal) populations and one for sexual populations—both incorporating a Gaussian competition kernel and, in the sexual case, assortative mating.

In the asexual model, the density p(x,t) of individuals with phenotype x evolves according to a reaction‑diffusion equation. The reaction term reflects logistic growth reduced by competition, which is a function of the phenotypic distance between individuals (K(x,y)=exp