Nonadaptive Amino Acid Convergence Rates Decrease over Time

Convergence is a central concept in evolutionary studies because it provides strong evidence for adaptation. It also provides information about the nature of the fitness landscape and the repeatability of evolution, and can mislead phylogenetic inference. To understand the role of adaptive convergence, we need to understand the patterns of nonadaptive convergence. Here, we consider the relationship between nonadaptive convergence and divergence in mitochondrial and model proteins. Surprisingly, nonadaptive convergence is much more common than expected in closely related organisms, falling off as organisms diverge. The extent of the convergent drop-off in mitochondrial proteins is well predicted by epistatic or coevolutionary effects in our "evolutionary Stokes shift" models and poorly predicted by conventional evolutionary models. Convergence probabilities decrease dramatically if the ancestral amino acids of branches being compared have diverged, but also drop slowly over evolutionary time even if the ancestral amino acids have not substituted. Convergence probabilities drop-off rapidly for quickly evolving sites, but much more slowly for slowly evolving sites. Furthermore, once sites have diverged their convergence probabilities are extremely low and indistinguishable from convergence levels at randomized sites. These results indicate that we cannot assume that excessive convergence early on is necessarily adaptive. This new understanding should help us to better discriminate adaptive from nonadaptive convergence and develop more relevant evolutionary models with improved validity for phylogenetic inference.