Abstract
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 \({2^{\gamma n {\rm log}n+O(n)}}\), where the constant \({\gamma}\) is \({\frac{3}{2}}\) for general networks, and \({\frac{5}{4}}\) for tree-child and normal networks. We also show that the number of leaf-labelled tree-child and normal networks with \({\ell}\) leaves are both \({{2}^{2 \ell {\rm log} \ell +O( \ell )}}\). Further we determine the typical numbers of leaves, tree vertices, and reticulation vertices for each of these classes of networks.
Mathematics Subject Classification
05C30 92D15 05C80Keywords
phylogenetic networks tree-child networks normal networksPreview
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