Innovations in ancient DNA (aDNA) preparation and sequencing technologies have exponentially increased the quality and quantity of aDNA data extracted from ancient biological materials. The additional temporal component from the incoming aDNA data can provide improved power to address fundamental evolutionary questions like characterising selection processes that shape the phenotypes and genotypes of contemporary populations or species. However, utilising aDNA to study past selection processes still involves considerable hurdles such as how to eliminate the confounding effect of genetic interactions in the inference of selection. To circumvent this challenge, in this work we extend the method introduced by He et al. (2022) to infer temporally variable selection from the data on aDNA sequences with the flexibility of modelling linkage and epistasis. Our posterior computation is carried out through a robust adaptive version of the particle marginal Metropolis-Hastings algorithm with a coerced acceptance rate. Moreover, our extension inherits their desirable features like modelling sample uncertainties resulting from the damage and fragmentation of aDNA molecules and reconstructing underlying gamete frequency trajectories of the population. We assess the performance and show the utility of our procedure with an application to ancient horse samples genotyped at the loci encoding base coat colours and pinto coat patterns.

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 for detection and quantification of natural selection from ancient DNA (aDNA) data have been developed. However, most of the existing methods do not allow us to estimate the timing of natural selection along with its strength, which is key to understanding the evolution and persistence of organismal diversity. Additionally, most methods ignore the fact that natural populations are almost always structured, which can result in overestimation of the effect of natural selection. To address these issues, we propose a novel Bayesian framework for the inference of natural selection and gene migration from aDNA data with Markov chain Monte Carlo techniques, co-estimating both timing and strength of natural selection and gene migration. Such an advance enables us to infer drivers of natural selection and gene migration by correlating genetic evolution with potential causes such as the changes in the ecological context in which an organism has evolved. The performance of our procedure is evaluated through extensive simulations, with its utility shown with an application to ancient chicken samples.