### Reconstructing the parameters of a network from its tree-average distances

**Willson, S ***(Iowa State)*

Tuesday 21 June 2011, 12:10-12:30

Seminar Room 1, Newton Institute

#### Abstract

A phylogenetic network is a rooted acyclic directed graph with labeled leaves which correspond to extant species. The network depicts the course of evolutionary history as species mutate and hybridize. Often each arc is weighted by a nonnegative real number measuring the amount of genetic change along the arc. A "tree-average distance" is defined which tells the average of the distances between the leaves in each displayed tree using these weights. Given a normal network N with certain restrictions, we show how the weights may be reconstructed from the tree-average distances. With additional assumptions we also indicate how the network N itself may be reconstructed.

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