• Investigations in phylogenetics: tree inference and model identifiability

      Yourdkhani, Samaneh; Rhodes, John A.; Allman, Elizabeth S.; McIntyre, Julie; Williams, Gordon (2020-05)
      This thesis presents two projects in mathematical phylogenetics. The first presents a new, statistically consistent, fast method for inferring species trees from topological gene trees under the multispecies coalescent model. The algorithm of this method takes a collection of unrooted topological gene trees, computes a novel intertaxon distance from them, and outputs a metric species tree. The second establishes that numerical and non-numerical parameters of a specic Prole Mixture Model of protein sequence evolution are generically identifiable. Algebraic techniques are used, especially a theorem of Kruskal on tensor decomposition.