Markov Chains on Phylogenetic Tree Spaces

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Phylogenetic trees are the fundamental mathematical representation ofevolutionary processes in biology. They are characterized by thechallenges associated with "big data," as well as the complication thattheir discrete geometric structure results in a non-Euclidean tree space,posing significant computational and statistical limitations. A theoreticalresult from pure mathematics establishes an algebraic geometric treespace, which has recently been shown to support rigorous statistical andprobabilistic studies. This project will practically implement such studiesby harnessing the structural and combinatorial properties of the algebraicgeometric tree space to characterize its information geometry and adaptMarkov chains for statistical inference.