New Tools to model Dynamics of Population Evolution
One of the major contributions of the field of Statistics has been in the area of population genetics, whose foundations were laid down over the last century. With the availability of genomic data, the subject of population genetics has undergone transformational changes. I will talk about the contribution of ideas from discrete algorithms to this fascinating subject. The modeling of evolutionary dynamics of populations as random graphs offers a new direction of exploration [1]. Can we estimate the extent of (mathematical) reconstruction of genetic history of a population ? In our earlier work, we introduced the notion of a minimal descriptor [2] of an Ancestral Recombination Graph (ARG) that can be used for measuring redundancy as well as extent-of-reconstructability of ARGs [3]. 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 [4], to genetic diversity study in plant cultivars [5]. The combinatorial viewpoint also paves the way for extremely fast, as well as accurate, ARG sampling algorithms (called SimRA) [6]. I will also discuss some very recent work based on using topological data analysis (in particular persistent homology) on ARGs to study admixture in populations: both on SimRA samples and plant cultivars [7].
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