Coalescent histories for discordant gene trees and species trees |
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Authors: | Noah A Rosenberg James H Degnan |
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Institution: | a Department of Human Genetics, University of Michigan, Ann Arbor, MI 48109, United States b Center for Computational Medicine and Bioinformatics, University of Michigan, Ann Arbor, MI 48109, United States c Life Sciences Institute, University of Michigan, Ann Arbor, MI 48109, United States d Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand |
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Abstract: | Given a gene tree and a species tree, a coalescent history is a list of the branches of the species tree on which coalescences in the gene tree take place. Each pair consisting of a gene tree topology and a species tree topology has some number of possible coalescent histories. Here we show that, for each n≥7, there exist a species tree topology S and a gene tree topology G≠S, both with n leaves, for which the number of coalescent histories exceeds the corresponding number of coalescent histories when the species tree topology is S and the gene tree topology is also S. This result has the interpretation that the gene tree topology G discordant with the species tree topology S can be produced by the evolutionary process in more ways than can the gene tree topology that matches the species tree topology, providing further insight into the surprising combinatorial properties of gene trees that arise from their joint consideration with species trees. |
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Keywords: | Coalescent history Gene tree Species tree |
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