Mutation bias shapes the spectrum of adaptive substitutions

Evolutionary adaptation often occurs by the fixation of beneficial mutations. This mode of adaptation can be characterized quantitatively by a spectrum of adaptive substitutions, i.e., a distribution for types of changes fixed in adaptation. Recent work establishes that the changes involved in adaptation reflect common types of mutations, raising the question of how strongly the mutation spectrum shapes the spectrum of adaptive substitutions. We address this question with a codon-based model for the spectrum of adaptive amino acid substitutions, applied to three large datasets covering thousands of amino acid changes identified in natural and experimental adaptation in Saccharomyces cerevisiae, Escherichia coli, and Mycobacterium tuberculosis. Using species-specific mutation spectra based on prior knowledge, we find that the mutation spectrum has a proportional influence on the spectrum of adaptive substitutions in all three species. Indeed, we find that by inferring the mutation rates that best explain the spectrum of adaptive substitutions, we can accurately recover the species-specific mutation spectra. However, we also find that the predictive power of the model differs substantially between the three species. To better understand these differences, we use population simulations to explore the factors that influence how closely the spectrum of adaptive substitutions mirrors the mutation spectrum. The results show that the influence of the mutation spectrum decreases with increasing mutational supply (N mu) and that predictive power is strongly affected by the number and diversity of beneficial mutations.