Mar. 17 2011 10:00AM

Mar. 17 2011 11:30AM

Balanced minimum evolution (BME) is a statistically consistent distance-based method to reconstruct a phylogenetic tree from an alignment of molecular data. In 2000, Pauplin showed that the BME method is equivalent to optimizing a linear functional over the BME polytope, the convex hull of the BME vectors obtained from Pauplin’s formula applied to all binary trees. The BME method is related to the popular Neighbor Joining (NJ) algorithm, now known to be a greedy optimization of the BME principle. In this talk I will elucidate some of the structure of the BME polytope and strengthen the connection between the BME method and NJ Algorithm. I will show that any subtree-prune-regraft move from a binary tree to another binary tree corresponds to an edge of the BME polytope. Moreover, I will describe an entire family of faces parametrized by disjoint clades. Finally, given a phylogenetic tree T, I will show that the BME cone and every NJ cone of T have intersection of positive measure. No knowledge of biology will be required and all results will be explained using polyhedral geometry.

Pravidelný seminář Inteligentní systémy (Kontaktní osoba: Tomáš Kroupa)