Counting coalescent histories. |
| |
Authors: | Noah A Rosenberg |
| |
Institution: | Department of Human Genetics, Bioinformatics Program, and the Life Sciences Institute, University of Michigan, Ann Arbor, Michigan 48109-2218, USA. rnoah@umich.edu |
| |
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. |
| |
Keywords: | |
|
|