Averaging metric phylogenetic trees

摘要: This paper investigates the computational geometry relevant to calculations of Frechet mean and variance for probability distributions on phylogenetic tree space Billera, Holmes Vogtmann, using theory measures spaces nonpositive curvature developed by Sturm. We show that combinatorics geodesics with a specified fixed endpoint in are determined location varying certain polyhedral subdivision space. The function associated finite subset is continuously differentiable within each cell corresponding subdivision. use this establish two iterative methods producing sequences converge mean: one based Sturm's Law Large Numbers, another descent algorithms finding optima smooth functions convex polyhedra. present properties biological applications means extend our main results more general globally nonpositively curved composed Euclidean orthants.