Mathematics Colloquia and Seminars

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A phylogeny is mathematical model of the common evolutionary history of a group of species. A tree metric is a distance function on a set of species realized by a tree graph with edge weights. Dissimilarity maps computed from biological sequence data are uniquely identified as vectors in a Euclidean space properly containing the space of all tree metrics as a polyhedral fan. Distance-based phylogenetic methods project such dissimilarity maps onto tree metrics, dividing the space of all dissimilarity maps into regions based upon which combinatorial tree is reconstructed by the method. We explore the combinatorial geometry of the subdivision of Euclidean space induced by the distance-based methods UPGMA, Neighbor-Joining, and Least-Squares Phylogeny and the statistical properties of inputs computed from aligned sequences. The geometry and statistical properties of the input and output spaces of these methods can give insight into their observed behavior on biological data. We show that this perspective informs the individual suitability of a biological dataset as an input for a chosen phylogenetic or phylogenomic inference method. This talk includes results from joint work with Joe Rusinko, Seth Sullivant, Zoe Vernon, and Jing Xi, and assumes no previous exposure to phylogenies or the relevant geometry.