Markov Chains on Phylogenetic Tree Spaces

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