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Invariants of phylogenies in a simple case with discrete states

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Abstract

Under a simple model of transition between two states, we can work out the probabilities of different data outcomes in four species with any given phylogeny. For a given tree topology, if all characters are evolving under the same probabilistic model, there are two quadratic forms in the frequencies of outcomes that must be zero. It may be possible to test the null hypothesis that the tree is of a particular topology by testing whether these quadratic forms are zero. One of the tests is a test for independence in a simple 2×2 contingency table. If there are differences of evolutionary rate among characters, these quadratic forms will no longer necessarily be zero.

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The authors wish to thank Thomas Haigh and an anonymous reviewer for helpful comments on the manuscript. Work by J. Felsenstein was supported in part by task agreement number DE-AT06-76EV71005 of contract number DE-AM06-76RL02225 between the U.S. Department of Energy and the University of Washington.

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Cavender, J.A., Felsenstein, J. Invariants of phylogenies in a simple case with discrete states. Journal of Classification 4, 57–71 (1987). https://doi.org/10.1007/BF01890075

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  • DOI: https://doi.org/10.1007/BF01890075

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