Triallelic Population Genomics for Inferring Correlated Fitness Effects of Same Site Nonsynonymous Mutations

Abstract

The distribution of mutational effects on fitness is central to evolutionary genetics. Typical univariate distributions, however, cannot model the effects of multiple mutations at the same site, so we introduce a model in which mutations at the same site have correlated fitness effects. To infer the strength of that correlation, we developed a diffusion approximation to the triallelic frequency spectrum, which we applied to data from Drosophila melanogaster. We found a moderate positive correlation between the fitness effects of nonsynonymous mutations at the same codon, suggesting that both mutation identity and location are important for determining fitness effects in proteins. We validated our approach by comparing it to biochemical mutational scanning experiments, finding strong quantitative agreement, even between different organisms. We also found that the correlation of mutational fitness effects was not affected by protein solvent exposure or structural disorder. Together, our results suggest that the correlation of fitness effects at the same site is a previously overlooked yet fundamental property of protein evolution.KEYWORDS diffusion approximation; distribution of fitness effects; Drosophila melanogaster; nonsynonymous mutations; triallelic sites M UTATIONS create genetic variation within populations, some of which causes differential fitness among individuals upon which natural selection operates. The effects of mutations on fitness range from strongly deleterious to strongly beneficial, and the distribution of fitness effects (DFE) is key for many problems in genetics, from the evolution of sex (Barton and Charlesworth 1998) to the architecture of human disease (Di Rienzo 2006). For protein-coding regions, there are generally many strongly deleterious or lethal mutations, a similar number of moderately deleterious or nearly neutral mutations, and a small number of beneficial mutations . The DFE may be determined experimentally through direct measurements of mutation fitness effects in clonal populations of viruses, bacteria, or yeast (Wloch et al. 2001;Sanjuán et al. 2004), and recent studies have provided high-resolution DFEs for single genes (Bank et al. 2014; and for beneficial mutations (Levy et al. 2015). The DFE may also be inferred from comparative (Nielsen and Yang 2003;Tamuri et al. 2012) or population genetic (Williamson et al. 2005;Eyre-Walker et al. 2006; Keightley and EyreWalker 2007;Boyko et al. 2008) data, although these approaches have little power for strongly deleterious mutations.In the typical population genetic approach for estimating the DFE, the population demography is first inferred using a putatively neutral class of mutations, and the DFE for another class of mutations is inferred by modeling the distribution of allele frequencies expected under a model of demography plus selection. Most population genetic inference has focused on biallelic loci, for which the ancestral allele and a single mutant (derived) allele are segregating in the population. When many indi...

Inference of the distribution of selection coefficients for new nonsynonymous mutations using large samples

“…To infer the DFE, we developed fit∂a∂i, which utilizes ∂a∂i and some of the methodological improvements of Ragsdale et al (2016). ∂a∂i is able to compute a distribution of allele frequencies f(x; ϴ D , γ), where ϴ D is a vector containing the demographic parameters inferred from synonymous sites and γ is a single population-scaled selection coefficient.…”

“…This process can be especially slow for large ranges of γ and for large sample sizes. Therefore, similar to (Ragsdale et al 2016), we initially computed the SFS for a range of selection coefficients, then cached these results to avoid re-computing the frequency spectra. In addition, we computed the many frequency spectra in parallel to save time; added compatibility for userdefined DFEs; modified the optimization routines available in ∂a∂i to work with cached spectra; and added the option to use constrained optimization for the inference of complex mixture distributions.…”

Perspective: Genomic inference using diffusion models and the allele frequency spectrum

“…∂a∂i also implements likelihood-based optimization package to perform inference on observed data. It is still commonly used to infer demographic histories (e.g., Mondal et al, 2016)) and patterns of selection for new mutations (e.g., (Ragsdale et al, 2016;Kim et al, 2017;Huber et al, 2017)). Spectral approaches for solving Eq.…”

“…Even though the frequency spectrum of synonymous variants is possibly skewed by background selection, it can still be used as a control if we assume that the demographic model fitted to the synonymous variants captures the effects of both demography and background selection acting on coding regions. This is the most commonly used approach for estimating DFEs for nonsynonymous variants (Ragsdale et al, 2016;Kim et al, 2017). In the direct selection case, , after controlling for demography using intergenic loci (Fig.…”

Haplotype-based inference of the distribution of fitness effects

“…2017). Two other extensions have been taken to model the correlation between the fitness effects of multiple nonsynonymous alleles at a particular position (Ragsdale et al . 2016) and to calculate the joint DFE between pairs of populations (Fortier et al .…”