Abstract
Convergent and parallel amino acid substitutions in protein evolution, collectively referred to as molecular convergence here, have small probabilities under neutral evolution. For this reason, molecular convergence is commonly viewed as evidence for similar adaptations of different species. The surge in the number of reports of molecular convergence in the last decade raises the intriguing question of whether molecular convergence occurs substantially more frequently than expected under neutral evolution. We here address this question using all one-to-one orthologous proteins encoded by the genomes of 12 fruit fly species and those encoded by 17 mammals. We found that the expected amount of molecular convergence varies greatly depending on the specific neutral substitution model assumed at each amino acid site and that the observed amount of molecular convergence is explainable by neutral models incorporating site-specific information of acceptable amino acids. Interestingly, the total number of convergent and parallel substitutions between two lineages, relative to the neutral expectation, decreases with the genetic distance between the two lineages, regardless of the model used in computing the neutral expectation. We hypothesize that this trend results from differences in the amino acids acceptable at a given site among different clades of a phylogeny, due to prevalent epistasis, and provide simulation as well as empirical evidence for this hypothesis. Together, our study finds no genomic evidence for higher-than-neutral levels of molecular convergence, but suggests the presence of abundant epistasis that decreases the likelihood of molecular convergence between distantly related lineages.