Formal methods for evolutionary inference using ancient DNA

Ancient DNA has revolutionised our ability to study past evolutionary processes by enabling direct observation of genetic variation in past populations. However, current formal methods for evolutionary inference are challenged by the sparse and heterogeneous distribution of data in space and in time, typical of ancient DNA datasets, as well as sample age uncertainty. In this thesis, I introduce analytical approaches that explicitly address these problems and show how inference from ancient DNA can greatly benefit from analysis that formally compares different evolutionary and demographic scenarios. I apply these approaches to three different cases that represent a range of demographic histories and evolutionary questions spanning different time- scales, species and types of data. The first approach combines space and time into a single matrix that can be used to estimate levels of past within population mobility. I apply this method to human ancient DNA data spanning the last 35 thousand years to recover changes in mobility over this time period. The second approach combines spatially and temporally explicit simulations with ancient mitochondrial genome data, spanning the Northern hemisphere and the last 50 thousand years to reconstruct large- scale population dynamics in Grey wolves over this time period. The third approach uses likelihood-based analysis to reconstruct episodes of past selection from time series of ancient DNA data. I apply this method to genotype data spanning two thousand years from two loci in domestic chicken to estimate a number of selection parameters including the starting time of the selection. These case studies all illustrate how formal hypothesis testing in spatially and temporally explicit frameworks make it possible to directly link evolutionary histories to the climatic and archaeological records as well as historical sources and show how identifying potential drivers of evolution allow building a more detailed and complete picture of the past.