Simulation-based inference of evolutionary parameters from adaptation dynamics using neural networks

Abstract

The rate of adaptive evolution depends on the rate at which beneficial mutations are introduced into a population and the fitness effects of those mutations. The rate of beneficial mutations and their expected fitness effects is often difficult to empirically quantify. As these two parameters determine the pace of evolutionary change in a population, the dynamics of adaptive evolution may enable inference of their values. Copy number variants (CNVs) are a pervasive source of heritable variation that can facilitate rapid adaptive evolution. Previously, we developed a locus-specific fluorescent CNV reporter to quantify CNV dynamics in evolving populations maintained in nutrient-limiting conditions using chemostats. Here, we use the observed CNV adaptation dynamics to estimate the rate at which beneficial CNVs are introduced through de novo mutation and their fitness effects using simulation-based Bayesian likelihood-free inference approaches. We tested the suitability of two evolutionary models: a standard Wright-Fisher model and a chemostat growth model. We evaluated two likelihood-free inference algorithms: the well-established Approximate Bayesian Computation with Sequential Monte Carlo (ABC-SMC) algorithm, and the recently developed Neural Posterior Estimation (NPE) algorithm, which applies an artificial neural network to directly estimate the posterior distribution. By systematically evaluating the suitability of different inference methods and models we show that NPE has several advantages over ABC-SMC and that a Wright-Fisher evolutionary model suffices in most cases. Using our validated inference framework, we estimate the CNV formation rate at the GAP1 locus in yeast as 10-4.7 -10-4 per cell division, and a selection coefficient of 0.04 - 0.1 per generation for GAP1 CNVs in glutamine-limited chemostats. We experimentally validated our estimates using barcode lineage tracking and pairwise fitness assays. Our results are consistent with a high beneficial CNV supply rate that is 10-fold greater than the estimated rates of beneficial single-nucleotide mutations, explaining their outsized importance in rapid adaptive evolution. More generally, our study demonstrates the utility of novel simulation-based likelihood-free inference methods for inferring the rates and effects of evolutionary processes from empirical data.