B1510
Title: Modeling phylogenetic trees in the wald space
Authors: Stephan Huckemann - University of Goettingen (Germany) [presenting]
Abstract: Most existing metrics between phylogenetic trees directly measure differences in topology and edge weights and are unrelated to the models of evolution used to infer trees. Instead, metrics are described based on distances between the probability models of discrete or continuous characters induced by trees. It describes how the construction of information-based geodesics leads to the recently proposed wald space of phylogenetic trees. It sits between the BHV space and the edge-product space as a point set. It has a natural embedding into the space of positive definite matrices, equipped with the information geometry. Thus, singularities such as overlapping leaves are infinitely far away; proper forests, however, comprising the 'BHV-boundary at infinity', are part of the wald space, adding boundary correspondences to groves (corresponding to orthants in the BHV space). The wald space contracts to a completely disconnected forest. Further, it is a geodesic space, exhibiting the structure of a Whitney stratified space of type (A) where strata carry compatible Riemannian metrics. Some more geometric properties are explored, but the full picture remains open. Interesting open problems are identified as a conclusion.
