An ABC method for estimating the rate and distribution of effects of beneficial mutations

Determining the distribution of adaptive mutations available to natural selection is a difficult task. These are rare events and most of them are lost by chance. Some theoretical works propose that the distribution of newly arising beneficial mutations should be close to exponential. Empirical data are scarce and do not always support an exponential distribution. Analysis of the dynamics of adaptation in asexual populations of microorganisms has revealed that these can be summarized by two effective parameters, the effective mutation rate, Ue, and the effective selection coefficient of a beneficial mutation, Se. Here, we show that these effective parameters will not always reflect the rate and mean effect of beneficial mutations, especially when the distribution of arising mutations has high variance, and the mutation rate is high. We propose a method to estimate the distribution of arising beneficial mutations, which is motivated by a common experimental setup. The method, which we call One Biallelic Marker Approximate Bayesian Computation, makes use of experimental data consisting of periodic measures of neutral marker frequencies and mean population fitness. Using simulations, we find that this method allows the discrimination of the shape of the distribution of arising mutations and that it provides reasonable estimates of their rates and mean effects in ranges of the parameter space that may be of biological relevance.