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Evolution of molecular phenotypes under stabilizing selection

Molecular phenotypes are important links between genomic information and organismic functions, fitness, and evolution. Complex phenotypes, which are also called quantitative traits, often depend on multiple genomic loci. Their evolution builds on genome evolution in a complicated way, which involves selection, genetic drift, mutations and recombination. Here we develop a coarse-grained evolutionary statistics for phenotypes, which decouples from details of the underlying genotypes. We derive approximate evolution equations for the distribution of phenotype values within and across populations. This dynamics covers evolutionary processes at high and low recombination rates, that is, it applies to sexual and asexual populations. In a fitness landscape with a single optimal phenotype value, the phenotypic diversity within populations and the divergence between populations reach evolutionary equilibria, which describe stabilizing selection. We compute the equilibrium distributions of both quantities analytically and we show that the ratio of mean divergence and diversity depends on the strength of selection in a universal way: it is largely independent of the phenotype's genomic encoding and of the recombination rate. This establishes a new method for the inference of selection on molecular phenotypes beyond the genome level. We discuss the implications of our findings for the predictability of evolutionary processes.