Novel statistical techniques for joint estimation of selection and migration from time series genetic data

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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 to infer selection. Recently, statistical approaches for detection and quantification of selection from ancient DNA (aDNA) data have been developed. Most existing methods can only estimate one selection coefficient and possibly the age of the selected allele. Other important factors, e.g. additional selection coefficients at nearby loci, more complicated selection schemes, or time-varying selection, cannot be effectively estimated. Moreover, most existing approaches ignore the fact that natural population are almost always structured, which can result in the overestimation of the underlying selection coefficient. To address these issues, we aim to develop a novel Bayesian framework for the joint inference of multiple selection coefficients and migration from aDNA data. We aim to combine techniques from diffusion processes and Metropolis-Hastings type sampling schemes.