# PLG

## Seminar

### Glimpses from the strange world of phylogenetic mixtures

Seminar Room 1, Newton Institute

#### Abstract

Rates of evolution and evolutionary history may vary across the genome of a given organism. The standard way of modeling the resulting data is a "mixture model" where a given phylogenetic pattern comes from one of a collection of trees with fixed probabilities. In this talk I will focus on recent results (joint with Mike Steel and Elchanan Mossel) which investigate what pattern probabilities are and are not possible when rates of evolution vary on a single topology.

In particular, we have shown that a mixture of two processes on a tree of one topology can produce exactly the same expected site pattern frequencies (i.e. sequence data) as an unmixed process on a different topology. For mixtures of a number of processes the situation is even more dire: in a certain sense the topology is not uniquely determined for a majority of data vectors. I will also present other related results along with the associated mathematics and indicate some interesting future directions for research.

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