# Isolating selective from non-selective forces using site frequency ratios

## TL;DR

A new method called SFRatios is introduced to better estimate the effects of natural selection on mutations by using frequency ratios of selected and neutral sites.

## Contribution

The novel approach avoids assumptions about non-selective factors by using frequency ratios and a Gaussian approximation for statistical analysis.

## Key findings

- The SFRatios method performs well in detecting selection effects across various demographic models.
- Applications to Drosophila populations show weak selection on synonymous sites and stronger selection on nonsynonymous sites.
- The method provides estimates consistent with previous studies for nonsynonymous variants.

## Abstract

A new method is introduced for estimating the distribution of mutation fitness effects using site frequency spectra. Unlike previous methods, which make assumptions about non-selective factors, or that try to incorporate such factors into the underlying model, this new method mostly avoids non-selective effects by working with the ratios of counts of selected sites to neutral sites. An expression for the likelihood of a set of selected/neutral ratios is found by treating the ratio of two Poisson random variables as the ratio of two gaussian random variables. This approach also avoids the need to estimate the relative mutation rates of selected and neutral sites. Simulations over a wide range of demographic models, with linked selection effects show that the new SFRatios method performs well for statistical tests of selection, and it performs well for estimating the distribution of selection effects. Performance was better with weak selection models and for expansion and structured demographic models than for bottleneck models. Applications to two populations of Drosophila melanogaster reveal clear but very weak selection on synonymous sites. For nonsynonymous sites, selection was found to be consistent with previous estimates and stronger for an African population than for one from North Carolina.

A new statistical method is presented for estimating the distribution of strengths of natural selection acting on mutations in natural populations using the distribution of polymorphic site allele frequencies. In order to isolate the impact of selection, separately from other demographic and genomic factors that can shape allele frequencies, our method uses the ratio of the frequency of candidate selected variants to the ratio of the frequency of neutral variants of the same frequency. An expression for the overall likelihood across the range of frequency ratios is developed using a gaussian approximation. Testing of the method, called SFRatios, finds that it performs reasonably well across a range of strengths of selection and demographic histories. Applications to two Drosophila populations find estimates of the strength of selection on nonsynonymous coding variants consistent with previous estimates and estimates for synonymous variation quite close to selectively neutral.