Inference of selection from genetic time series using various parametric approximations to the Wright-Fisher model

Abstract

Detecting genomic regions under selection is an important objective of population genetics.Typical analyses for this goal are based on exploiting genetic diversity patterns in present time data but rapid advances in DNA sequencing have increased the availability of time series genomic data. A common approach to analyze such data is to model the temporal evolution of an allele frequency as a Markov chain. Based on this principle, several methods have been proposed to infer selection intensity. One of their differences lies in how they model the transition probabilities of the Markoiv chain. Using the Wright-Fisher model is a natural choice but its computational cost is prohibitive for large population sizes so approximations to this model based on parametric distributions have been proposed. Here, we compared the performance of some of these approximations with respect to their power to detect selection and estimation of the selection coefficient. We developped a new generic Hidden Markov Model likelihood calculator and applied it on genetic time series simulated under various evolutionary scenarios. The Beta-with-Spikes approximation, which combines discrete fixation probabilities with a continuous Beta distribution, was found to perform consistently better than the others. This distribution provides an almost perfect fit to the Wright-Fisher model in terms of selection inference, for a computational cost that does not increase with population size. We further evaluate this model for population sizes not accessible to the Wright-Fisher model and illustrate its performance on a dataset of two divergently selected chicken populations.Under the null, λ asymptotically follows a χ 2 with one degree of freedom, a property that allows to 107 derive p-values which are useful quantities in particular in a multiple testing context. 108Having described the general framework used in this study, we now turn to its implementation that 109 requires specifying the transition kernel Q k (x, .). One objective of this work was to investigate differ-110 ent models for this transition kernel. A reference model in this context is the one-locus Wright-Fisher 111 (WF) model under diploid selection pressure (Ewens, 2004). However, this model has computational 112 limitations and, in the HMM famework, must generally be approximated. We first present the WF 113 model and then several continuous approximations of this model based on a common approach: the 114 method-of-moments. 115 Wright-Fisher transition model 116The WF model is a discrete time model that assumes random mating and non overlapping generations. 117Let N e be the haploid (constant) effective population size. Under this model, X (t) can take a discrete 118 number of values in {0, 1 Ne , . . . , Ne−1 Ne , 1} and the transition kernel of this process is a transition matrix 119 130 very costly for large N e and large intersample time. To overcome this issue, one approach is to ap-131 proximate the Wright-Fisher process with a continuous space process such that integral calculati...

Detecting and quantifying natural selection at two linked loci from time series data of allele frequencies with forward-in-time simulations

“…There has been a growing literature on the statistical inference of natural selection from time series data of allele frequencies over the past decade (e.g., Bollback et al, 2008;Malaspinas et al, 2012;Mathieson & McVean, 2013;Steinrücken et al, 2014;Lacerda & Seoighe, 2014;Feder et al, 2014;Foll et al, 2014Foll et al, , 2015Terhorst et al, 2015;Schraiber et al, 2016;Shim et al, 2016;Ferrer-Admetlla et al, 2016;Paris et al, 2019;He et al, 2019), reviewed in Bank et al (2014) and Malaspinas (2016). A common approach to analysing time series data of allele frequencies is based upon the hidden Markov model (HMM) framework of Williamson & Slatkin (1999),…”

“…Properly accounting for genetic recombination and local linkage can be expected to provide more precise estimates for the selection coefficient and more accurate hypothesis testing on the recent action of natural selection since genetic recombination may either reinforce or oppose changes in allele frequencies caused by natural selection according to the levels of linkage disequilibrium (He et al, 2020). However, with the exception of Terhorst et al (2015), all existing methods built on the Wright-Fisher model for inferring natural selection from allele frequency time series data are limited to either a single locus (e.g., Bollback et al, 2008;Malaspinas et al, 2012;Steinrücken et al, 2014;Schraiber et al, 2016;Paris et al, 2019;He et al, 2019) or multiple independent loci (e.g., Foll et al, 2014Foll et al, , 2015Shim et al, 2016;Ferrer-Admetlla et al, 2016), i.e., genetic recombination effect and local linkage information are ignored in these methods.…”

Genomic characterization and conservation of genetic diversity in cattle

“…As a last example, Paris et al [358] identified selection signatures from 25 years of gene bank data of the Spanish Asturiana de los Valles beef cattle breed. The authors used a method based on allele frequency trajectories [359], which could only be applied because of the availability of genomic time series data provided through the gene bank. These (and many other) case studies illustrate the value of gene bank collections for a wide range of objectives, including research and the (re)introduction of genetic diversity.…”

Using whole-genome sequencing data for demographic and functional evaluations of small managed populations

“…Genetic load approximated using the GERP score information of each homozygous damaging mutation (GERP > 1.0). c. Genetic load approximated from all variants independently of their coding potential using the chCADD scoreSignatures of selection and phenotype dataTo test whether the two breeds were interested by artificial selection since the start of the conservation programme, we decided to identify genomic regions under selection using the new generic Hidden Markov Model likelihood calculator developed byParis et al (2019) [230].…”

“…Genomic regions under selection were identified using the new generic Hidden Markov Model (HMM) likelihood calculator developed byParis et al (2019). This HMM model approximate the Wright-Fisher model implementing a Beta with spikes approximation, which combines discrete fixation probabilities with a continuous Beta distribution[230]. The advantage of this model over existing ones is its applicability to time series genomic data.…”