Population genetic models of GERP scores suggest pervasive turnover of constrained sites across mammalian evolution

Comparative genomic approaches have been used to identify sites where mutations are under purifying selection and of functional consequence by searching for sequences that are conserved across distantly related species. However, the performance of these approaches has not been rigorously evaluated under population genetic models. Further, short-lived functional elements may not leave a footprint of sequence conservation across many species. Here, we use simulations to study how one measure of conservation, the GERP score, relates to the strength of selection (Nes). We show that the GERP score is related to the strength of purifying selection. However, changes in selection coefficients or functional elements over time (i.e. functional turnover) can strongly affect the GERP distribution, leading to unexpected relationships between GERP and Nes. Further, we show that for functional elements that have a high turnover rate, the optimal tree size is not necessarily the largest possible tree, and more turnover reduces the optimal tree size. Finally, we use the distribution of GERP scores across the human genome to compare models with and without turnover of sites where mutations under purifying selection. We show that mutations in 4.51% of the noncoding human genome are under purifying selection and that most of this sequence has likely experienced changes in selection coefficients throughout mammalian evolution.