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

Abstract

With the rapid growth of the number of sequenced ancient genomes, there has been increasing interest in using this new information to study past and present adaptation.Such an additional temporal component has the promise of providing improved power for the estimation of natural selection. Over the last decade, statistical approaches

Estimating temporally variable selection intensity from ancient DNA data

“…Many existing approaches define the Wright-Fisher diffusion X in terms of the partial differential equation (PDE) that characterises its transition probability density function ( e.g ., Bollback et al, 2008; Steinrücken et al, 2014; He et al, 2020b). Instead, like Schraiber et al (2016), He et al (2020a) and Lyu et al (2022), we characterise the Wright-Fisher diffusion X as the solution to the stochastic differential equation (SDE) for t ≥ t 0 with initial condition X ( t 0 ) = x 0 , where W represents the standard Wiener process.…”

“…Since the posterior p ( ϑ, x 1: K | r 1: K ) is not available in a closed form, we resort to the PMMH algorithm introduced by Andrieu et al (2010) in this work, which has already been successfully applied in population genetic studies (see, e.g ., He et al, 2020b; Lyu et al, 2022). The PMMH algorithm calculates the acceptance ratio with the estimate of the marginal likelihood p ( r 1: K | ϑ ) in the Metropolis-Hastings procedure and generates a new candidate of the population mutant allele frequency trajectory x 1: K from the approximation of the smoothing distribution p ( x 1: K | r 1: K , ϑ ), which can both be achieved through the bootstrap particle filter developed by Gordon et al (1993).…”

“…To remain computationally feasible, these methods typically work with the diffusion approximation of the Wright-Fisher model ( e . g ., Bollback et al, 2008; Malaspinas et al, 2012; Steinrücken et al, 2014; Schraiber et al, 2016; Ferrer-Admetlla et al, 2016; He et al, 2020a,b; Lyu et al, 2022). The diffusion approximation enables us to efficiently integrate over all possible underlying allele frequency trajectories, therefore producing substantial reductions in computational cost of the likelihood calculation.…”

Estimating temporally variable selection intensity from ancient DNA data with the flexibility of modelling linkage and epistasis

“…To our knowledge, most existing methods tailored to aDNA rely on the diffusion approximation of the Wright-Fisher model. By working with the diffusion approximation, its HMM framework permits efficient integration over the probability distribution of the underlying population allele frequencies and therefore the calculation of the likelihood based on the observed sample allele frequencies can be completed within a reasonable amount of time (e.g., Bollback et al, 2008;Malaspinas et al, 2012;Steinrücken et al, 2014;Schraiber et al, 2016;Ferrer-Admetlla et al, 2016;He et al, 2020b,c;Lyu et al, 2022;He et al, 2022). These approaches have already been successfully used in aDNA studies; e.g., the method of Bollback et al (2008) was applied in Ludwig et al (2009) to analyse the aDNA data associated with horse coat colouration and illustrated that positive selection acted on the derived ASIP and MC1R alleles, suggesting that domestication and selective breeding contributed to changes in horse coat colouration.…”

“…By working with the diffusion approximation, its HMM frame-work permits efficient integration over the probability distribution of the underlying population allele frequencies and therefore the calculation of the likelihood based on the observed sample allele frequencies can be completed within a reasonable amount of time ( e . g ., Bollback et al, 2008; Malaspinas et al, 2012; Steinrücken et al, 2014; Schraiber et al, 2016; Ferrer-Admetlla et al, 2016; He et al, 2020b,c; Lyu et al, 2022; He et al, 2022). These approaches have already been successfully used in aDNA studies; e .…”