Evolutionary dynamics of neutral phenotypes under DNA substitution models

Abstract

We study the evolution of quantitative molecular traits in the absence of selection. Using Felsensteins 1981 DNA substitution model, we predict a linear restoring force on the mean of an additive phenotype. Remarkably, the mean dynamics are independent of the effect sizes and genotype and are similar to those predicted by the widely-used OU model for stabilizing selection and the house-of-cards model for phenotype evolution. We confirm the predictions empirically using additive molecular phenotypes calculated from ancestral reconstructions of putatively unconstrained DNA sequences in primate genomes. We predict and confirm empirically that the dynamics of the variance are more complicated than those predicted by the OU model, and show that our results for the restoring force of mutation hold even for nonadditive phenotypes, such as number of transcription factor binding sites, longest encoded peptide and folding propensity of the encoded peptide. Our results have implications for efforts to infer selection based on quantitative phenotype dynamics as well as to understand long-term trends in evolution of quantitative molecular traits.