Evolution of molecular phenotypes under stabilizing selection

∗ Authors with equal contributions Molecular phenotypes are important links between genomic information and or-ganismic 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, mu-tations 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 re-combination rates, that is, it applies to sexual and asexual populations. In a fitness landscape with a single optimal phenotype value, the phenotypic diversity within pop-ulations and the divergence between populations reach evolutionary equilibria, which describe stabilizing selection. We compute the equilibrium distributions of both quan-tities 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 pheno-type’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.