Estimating the time since admixture from phased and unphased molecular data

After admixture, recombination breaks down genomic blocks of contiguous ancestry. The breakdown of these blocks forms a new `molecular clock', that ticks at a much faster rate than the mutation clock, enabling accurate dating of admixture events in the recent past. However, existing theory on the break down of these blocks, or the accumulation of delineations between blocks,  so called `junctions', has mostly been limited to using regularly spaced markers on phased data. Here, we present an extension to the theory of junctions using the Ancestral Recombination Graph that describes the expected number of junctions for any distribution of markers along the genome. Furthermore, we provide a new framework to infer the time since admixture using unphased data. We demonstrate both the phased and unphased methods on simulated data and show that our new extensions have improved accuracy with respect to previous methods, especially for smaller population sizes and more ancient admixture times. L...