title: There are no caterpillars in a wicked forest.
abstract: Species trees represent the historical divergences of populations or species, while gene trees trace the ancestry of individual gene copies sampled within those populations. In cases involving rapid speciation, gene trees with topologies that differ from that of the species tree can be most probable under the standard multispecies coalescent model, making species tree inference more difficult. Such anomalous gene trees are not well understood except for some small cases. In this work, we establish one constraint that applies to trees of any size: gene trees with "caterpillar" topologies cannot be anomalous. The proof of this involves a new combinatorial object, called a population history, which keeps track of the number of coalescent events in each ancestral population.
authors.affiliation: Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131, USA. Electronic address: jamdeg@unm.edu.
authors.forename: James H
authors.initials: JH
authors.lastname: Degnan
authors.affiliation: Department of Mathematics and Statistics, University of Alaska Fairbanks, PO Box 756660, Fairbanks, AK 99775, USA. Electronic address: j.rhodes@alaska.edu.
authors.forename: John A
authors.initials: JA
authors.lastname: Rhodes
mesh_terms: D049810:Genetic Speciation; D006801:Humans; D008957:Models, Genetic; D010375:Pedigree
keywords: Anomalous gene tree; Coalescent history; Gene tree; Multispecies coalescent; Phylogeny; Species tree