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Likelihood Maximization on Phylogenic Trees

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Polynomial Optimisation

The problem of inferring the phylogenic tree of $n$ extant species from their genome is treated via mainly two approaches, the maximum parsimony and the maximum likelihood approach. While the latter is thought to produce more meaningful results, it is harder to solve computationally. We show that under a molecular clock assumption, the maximum likelihood model has a natural formulation that can be approached via branch-and-bound and polynomial optimization. Using this approach, we produce a counterexample to a conjecture relating to the reconstruction of an ancestral genome under the maximum parsimony and maximum likelihood approaches.

This talk is part of the Isaac Newton Institute Seminar Series series.

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