Estimation of Natural Selection and Allele Age from Time Series Allele Frequency Data Using a Novel Likelihood-Based Approach

Abstract

Temporally spaced genetic data allow for more accurate inference of population genetic parameters and hypothesis testing on the recent action of natural selection. In this work, we develop a novel likelihood-based method for jointly estimating selection coefficient and allele age from time series data of allele frequencies. Our approach is based on a hidden Markov model where the underlying process is a Wright-Fisher diffusion conditioned to survive until the time of the most recent sample. This formulation circumvents the assumption required in existing methods that the allele is created by mutation at a certain low frequency. We calculate the likelihood by numerically solving the resulting Kolmogorov backward equation backwards in time while re-weighting the solution with the emission probabilities of the observation at each sampling time point. This procedure reduces the two-dimensional numerical search for the maximum of the likelihood surface for both the selection coefficient and the allele age to a one-dimensional search over the selection coefficient only. We illustrate through extensive simulations that our method can produce accurate estimates of the selection coefficient and the allele age under both constant and non-constant demographic histories. We apply our approach to re-analyse ancient DNA data associated with horse base coat colours. We find that ignoring demographic histories or grouping raw samples can significantly bias the inference results.

Inferring the timing and strength of natural selection and gene migration in the evolution of chicken from ancient DNA data

“…Our approach is also readily applicable to the analysis of multiple (independent) loci, where we observe that updating the selection-related parameters for each locus can be proceeded in parallel on different cores. Additionally, it is possible to extend our procedure to handle the case of non-constant demographic histories like Schraiber et al (2016) and He et al (2020c). In order to achieve accurate estimation of relevant population genetic quantities of interest, it is important to taking into account local linkage among loci, which has been illustrated to be capable of further improving the inference of natural selection (He et al, 2020b).…”

“…Such an MCMC-based procedure can be easily extended to handle more complex demographic scenarios such as non-constant population sizes and general diploid models of natural selection. He et al (2020c) provided an alternative likelihood-based method for co-estimating the selection coefficient and the allele age, where they conditioned the Wright-Fisher diffusion to survive until the time of the most recent sample under the HMM framework of Bollback et al (2008). This conditioning takes advantage of the fact that aDNA samples are often collected from only those loci that are segregating in the most recent sample.…”

Allele frequency divergence reveals ubiquitous influence of positive selection in Drosophila

“…However, determining the full nature and extent of selective allele frequency change has been difficult. Numerous methods exist for inferring selection coefficients from allele frequency time series [10,[17][18][19][20][21][22][23][24], but are only reliable for selection that is strong relative to the intensity of random, non-selective allele frequency change (random genetic drift) and allele frequency measurement error (e.g. due to population sampling or limited sequencing read depth).…”

Moment-based approximations for the Wright-Fisher model of population dynamics under natural selection at two linked loci

“…However, with the exception of Terhorst et al (2015) and He et al (2020b), all existing methods built upon the Wright-Fisher model for estimating selection coefficients from temporally spaced genetic data are limited to either a single locus (e.g., Bollback et al, 2008;Malaspinas et al, 2012;Steinrücken et al, 2014;Lacerda & Seoighe, 2014;Schraiber et al, 2016;He et al, 2020c) or multiple independent loci (e.g., Ferrer-Admetlla et al, 2016;Paris et al, 2019), i.e., genetic recombination and local linkage are ignored in these approaches. Terhorst et al (2015), one of the exceptions amongst these methods, extended the momentbased approximation of the Wright-Fisher model introduced by Feder et al (2014) to the case of natural selection acting on multiple linked loci, where the Wright-Fisher model was approximated through a deterministic path with added Gaussian noises.…”

“…Properly modelling genetic recombination and local linkage has been shown to bring a significant improvement to the inference of natural selection from time series genetic data (He et al, 2020b). However, with the exception of Terhorst et al (2015) and He et al (2020b), all existing methods built upon the Wright-Fisher model for estimating selection coefficients from temporally spaced genetic data are limited to either a single locus ( e.g ., Bollback et al, 2008; Malaspinas et al, 2012; Steinrücken et al, 2014; Lacerda & Seoighe, 2014; Schraiber et al, 2016; He et al, 2020c) or multiple independent loci ( e.g ., Ferrer-Admetlla et al, 2016; Paris et al, 2019), i.e ., genetic recombination and local linkage are ignored in these approaches.…”