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.

Mutation rate, selection, and epistasis inferred from RNA virus haplotypes via neural posterior estimation

“…This model is simple enough to simulate efficiently but complex enough to capture the genome frequency dynamics. Furthermore, SNPE is also computationally more efficient than sampling methods such as REJ-ABC due to its application of neural density estimators as well as amortization (Avecilla et al, 2021).…”

“…We used a recently developed neural-network-assisted likelihood-free inference method, sequential neural posterior estimation (SNPE) (Greenberg et al, 2019), or specifically, the SNPE-C implementation in the Python package sbi (Tejero-Cantero et al, 2020). SNPE has been recently applied for inferring the formation rate and fitness effect of copy number variation in populations of yeast evolving under nutrient limitation in a chemostat (Avecilla et al, 2021). Briefly, SNPE trains an artificial neural network on a training set of parameters (generated from the prior distribution) and simulated data (generated from the evolutionary model) to estimate the joint density of model parameters and data (conditioned on the prior distribution).…”

“…applied for inferring the formation rate and fitness effect of copy number variation in populations of yeast evolving under nutrient limitation in a chemostat (Avecilla et al, 2021)…”

“…Importantly, MS2 has a particularly short genome of about 3,500 bases, allowing us to obtain reads that cover the entire genome.Here, we develop and test an approach to jointly infer both the mutation rate and selection parameters from sequencing data of MS2. Our approach relies on key methodological novelties: (a) long-read sequencing that covers the full length of the viral genome (i.e., haplotypes) (Callahan et al, 2021); (b) a multi-locus evolutionary model that captures the multitude of segregating haplotypes in the population; and (c) deep artificial neural networks and simulation-based inference that allow efficient and high-dimensional inference of model parameters (Avecilla et al, 2021; Cranmer et al, 2020). We applied this approach to infer the MS2 mutation rate and selection parameters from long-read haplotype sequences sampled from populations evolving in the lab.…”

Simulation Intelligence: Towards a New Generation of Scientific Methods

“…In physics, SBI is useful from the smallest scales in particle colliders [165,166,167], where it allows us to measure the properties of the Higgs boson with a higher precision and less data, to the largest scales in the modeling of gravitational waves [168,169], stellar streams [170], gravitational lensing [171], and the evolution of the universe [172]. These methods have also been applied to study the evolutionary dynamics of protein networks [173] and in yeast strains [174]. In neuroscience, they have, e.g., been used to estimate the properties of ion channels from high-throughput voltage-clamp, and properties of neural circuits from observed rhythmic behaviour in the stomatogastric ganglion [133], to identify network models which can capture the dynamics of neuronal cultures [175], to study how the connectivity between different cell-types shapes dynamics in cortical circuits [176], and to identify biophysically realistic models of neurons in the retina [177,178].…”