Abstract: The modeling of evolutionary dynamics of populations as random graphs offers a new direction of exploration. We also introduce the notion of a minimal descriptor of an Ancestral Recombination Graph (ARG) that can be used for measuring redundancy as well as extent-of-reconstructability of ARGs. I will discuss how we have used ARGs, constructed from extant samples (using a pipeline called IRiS), to address many fascinating questions ranging from human migration paths, to genetic diversity study in plant cultivars. The combinatorial viewpoint also paves the way for exltremely fast, as well as accurate, ARG sampling algorithms (called SimRA). I will conclude with a discussion of our exploration of persistent homology on ARGs to study admixture in populations: both on SimRA samples and plant cultivars.
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