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

Abstract

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 under a Wright-Fisher model. Existing approaches that can take genetic recombination effect and local linkage information into account are built upon either the diffusion approximation or the moment-based approximation of the Wright-Fisher model. However, such approximations are either limited to the increased computational cost like the diffusion approximation or suffer from the distribution support issue like the normal approximation, which can seriously affect computational efficiency and accuracy. In this work, we propose two novel moment-based approximations for the Wright-Fisher model of population dynamics subject to natural selection at a pair of linked loci. Our key innovation is that we extend existing approaches to calculate the mean and (co)variance of the two-locus Wright-Fisher model with selection and suggest a logistic normal distribution or a hierarchical beta distribution as a parametric continuous probability distribution to approximate the Wright-Fisher model by matching its first two moments to those of the Wright-Fisher model. Compared with the diffusion approximation, our approximations enable the computation of the transition probability distribution of the Wright-Fisher model at a far smaller computational cost and also allow us to avoid the distribution support issue found in the normal approximation.

Estimating Temporally Variable Selection Intensity from Ancient DNA Data

“…These methods have already been successfully applied in aDNA studies (e.g., Ludwig et al 2009 ; Sandoval-Castellanos et al 2017 ; Ye et al 2017 ; Wutke et al 2018 ). Moment-based approximations of the Wright–Fisher model, as tractable alternatives, are commonly used in the approaches tailored to experimental evolution (e.g., Feder et al 2014 ; Lacerda and Seoighe 2014 ; Terhorst et al 2015 ; Paris et al 2019 ) due to their poor performance for large evolutionary timescales ( He et al 2021 ).…”

Estimating temporally variable selection intensity from ancient DNA data

“…The copyright holder for this preprint this version posted August 2, 2022. ; https://doi.org/10.1101/2022.08.01.502345 doi: bioRxiv preprint used in the existing methods tailored to experimental evolution (e.g., Lacerda & Seoighe, 2014;Feder et al, 2014;Terhorst et al, 2015;Paris et al, 2019) owing to their poor performance for large evolutionary timescales (He et al, 2021).…”

“…Moment-based approximations of the Wright-Fisher model, as tractable alternatives, are usually used in the existing methods tailored to experimental evolution ( e . g ., Lacerda & Seoighe, 2014; Feder et al, 2014; Terhorst et al, 2015; Paris et al, 2019) owing to their poor performance for large evolutionary timescales (He et al, 2021).…”

“…These methods have already been successfully applied in aDNA studies ( e.g ., Ludwig et al, 2009; Sandoval-Castellanos et al, 2017; Ye et al, 2017; Wutke et al, 2018). Moment-based approximations of the Wright-Fisher model, as tractable alternatives, are commonly used in the approaches tailored to experimental evolution ( e.g ., Lacerda & Seoighe, 2014; Feder et al, 2014; Terhorst et al, 2015; Paris et al, 2019) due to their poor performance for large evolutionary timescales (He et al, 2021).…”