Counting Coalescent Histories

@article{Rosenberg2007CountingCH,
  title={Counting Coalescent Histories},
  author={Noah A. Rosenberg},
  journal={Journal of computational biology : a journal of computational molecular cell biology},
  year={2007},
  volume={14 3},
  pages={360-77}
}
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… CONTINUE READING
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