Counting phylogenetic networks (2015)
AuthorsMcDiarmid, C., Semple, C., Welsh, D.show all
We give approximate counting formulae for the numbers of labelled general, treechild, and normal (binary) phylogenetic networks on n vertices. These formulae are of the form 2 γnlogn+O(n) , where the constant γ is 32 for general networks, and 54 for tree-child and normal networks. We also show that the number of leaf-labelled tree-child and normal networks with ℓ leaves are both 2 2ℓlogℓ+O(ℓ) . Further we determine the typical numbers of leaves, tree vertices, and reticulation vertices for each of these classes of networks.
CitationMcDiarmid, C., Semple, C., Welsh, D. (2015) Counting phylogenetic networks. Annals of Combinatorics, 19(1), pp. 205-224.
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