Given a species tree and a gene tree, a 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 coalescent histories appears in the Degnan & Salter (2005) 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 coalescent histories can reduce the effort required for evaluating this formula.
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