title: Counting coalescent histories.
abstract: Given a species tree and a gene tree, a valid coalescent history is a list of the branches of the species tree on which coalescences in the gene tree take place. I develop a recursion for the number of valid coalescent histories that exist for an arbitrary gene tree/species tree pair, when one gene lineage is studied per species. The result is obtained by defining a concept of m-extended coalescent histories, enumerating and counting these histories, and taking the special case of m = 1. As a sum over valid coalescent histories appears in a formula for the probability that a random gene tree evolving along the branches of a fixed species tree has a specified labeled topology, the enumeration of valid coalescent histories can considerably reduce the effort required for evaluating this formula.
authors.affiliation: Department of Human Genetics, Bioinformatics Program, and the Life Sciences Institute, University of Michigan, Ann Arbor, Michigan 48109-2218, USA. rnoah@umich.edu
authors.forename: Noah A
authors.initials: NA
authors.lastname: Rosenberg
mesh_terms: D016013:Likelihood Functions; D008957:Models, Genetic; D008962:Models, Theoretical; D010802:Phylogeny