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

Recent advances in DNA sequencing techniques have made it possible to monitor genomes in great detail over time. This improvement provides an opportunity for us to study natural selection based on time serial samples of genomes while accounting for genetic recombination effect and local linkage information. Such genomic time series data allow for more accurate estimation of population genetic parameters and hypothesis testing on the recent action of natural selection. In this work, we develop a novel Bayesian statistical framework for inferring natural selection at a pair of linked loci by capitalising on the temporal aspect of DNA data with the additional flexibility of modelling the sampled chromosomes that contain unknown alleles. Our approach is based on a hidden Markov model where the underlying process is a two-locus Wright-Fisher diffusion with selection, which enables us to explicitly model genetic recombination and local linkage. The posterior probability distribution for the selection coefficients is obtained by using the particle marginal Metropolis-Hastings algorithm, which allows us to efficiently calculate the likelihood. We evaluate the performance of our Bayesian inference procedure through extensive simulations, showing that our method can deliver accurate estimates of selection coefficients, and the addition of genetic recombination and local linkage brings about significant improvement in the inference of natural selection. We illustrate the utility of our approach on real data with an application to ancient DNA data associated with white spotting patterns in horses.