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Multiple Maxima of Likelihood in Phylogenetic Trees: An Analytic Approach

journal contribution
posted on 2023-05-17, 02:17 authored by Chor, B, Hendy, MD, Barbara HollandBarbara Holland, Penny, D
Maximum likelihood (ML) is a widely used criterion for selecting optimal evolutionary trees. However, the nature of the likelihood surface for trees is still not sufficiently understood, especially with regard to the frequency of multiple optima. Here, we initiate an analytic study for identifying sequences that generate multiple optima. We concentrate on the problem of optimizing edge weights for a given tree or trees (as opposed to searching through the space of all trees). We report a new approach to computing ML directly, which we have used to find large families of sequences that have multiple optima, including sequences with a continuum of optimal points. Such data sets are best supported by different (two or more) phylogenies that vary significantly in their timings of evolutionary events. Some standard biological processes can lead to data with multiple optima, and consequently the field needs further investigation. Our results imply that hill-climbing techniques as currently implemented in various software packages cannot guarantee that one will find the global ML point, even if it is unique.


Publication title

Molecular Biology and Evolution










School of Natural Sciences


Oxford Univ Press

Place of publication

Great Clarendon St, Oxford, England, Ox2 6Dp

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The definitive publisher-authenticated version is available online at:

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  • Restricted

Socio-economic Objectives

Expanding knowledge in the mathematical sciences

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