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. Lastly, we demonstrate the applicability
of our method on three empirical datasets, including labcrosses of yeast
(Saccharomyces cerevisae) and two  case studies of hybridization
in swordtail fish and Populus trees.