Willis, AmyValdez Cabrera, Maria Alejandra2024-10-162024-10-162024-10-162024ValdezCabrera_washington_0250E_27431.pdfhttps://hdl.handle.net/1773/52431Thesis (Ph.D.)--University of Washington, 2024Phylogenetic trees, which describe shared ancestry between organisms through their branching structure (topology) and branch lengths, are a fundamental tool for analyzing evolutionary relationships. However, limited statistical tools exist for analyzing collections of phylogenetic trees with non-identical leaf sets. Here we present the first algorithm for computing distances between any pair of phylogenetic trees via Billera-Holmes-Vogtmann (BHV) extension spaces. Extension spaces represent trees with fewer leaves within the metric space of a larger leaf set, thus enabling comparisons in a common metric space. Motivated by limitations of extension spaces, we introduce the "towering" tree space, a metric space defined by transitions between nested BHV spaces. We describe an algorithm for computing distances within towering tree space, and propose Fréchet means to summarize collections of trees. We illustrate our proposed methods on gene trees spanning multiple domains of life.application/pdfen-USnoneBHV SpaceMetric SpaceObject Oriented Data AnalysisPhylogeneticsBiostatisticsBiostatisticsThesis