Inference of distribution of fitness effects and proportion of adaptive substitutions from polymorphism data

The distribution of fitness effects (DFE) encompasses deleterious, neutral and beneficial mutations. It conditions the evolutionary trajectory of populations, as well as the rate of adaptive molecular evolution ( α ). Inference of DFE and α from patterns of polymorphism (SFS) and divergence data has been a longstanding goal of evolutionary genetics. A widespread assumption shared by numerous methods developed so far to infer DFE and α from such data is that beneficial mutations contribute only negligibly to the polymorphism data. Hence, a DFE comprising only deleterious mutations tends to be estimated from SFS data, and α is only predicted by contrasting the SFS with divergence data from an outgroup. Here, we develop a hierarchical probabilistic framework that extends on previous methods and also can infer DFE and α from polymorphism data alone. We use extensive simulations to examine the performance of our method. We show that both a full DFE, comprising both deleterious and beneficial mutations, and α can be inferred without resorting to divergence data. We demonstrate that inference of DFE from polymorphism data alone can in fact provide more reliable estimates, as it does not rely on strong assumptions about a shared DFE between the outgroup and ingroup species used to obtain the SFS and divergence data. We also show that not accounting for the contribution of beneficial mutations to polymorphism data leads to substantially biased estimates of the DFE and α . We illustrate these points using our newly developed framework, while also comparing to one of the most widely used inference methods available.