Abstract
We study the evolution of quantitative molecular traits in the absence of selection. Using a simple theory based on Felsenstein’s 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 the widely-used OU model for stabilizing selection. We confirm the predictions empirically using additive molecular phenotypes calculated from ancestral reconstructions of putatively unconstrained DNA sequences in primate genomes. We show that the OU model is favoured by inference software even when applied to GC content of unconstrained sequences or simulations of DNA evolution. 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 non-additive 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.
