McDiarmid, C.Semple, C.Welsh, D.2016-02-012016-02-012015McDiarmid, C., Semple, C., Welsh, D. (2015) Counting phylogenetic networks. Annals of Combinatorics, 19(1), pp. 205-224.http://hdl.handle.net/10092/11741We 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.enJournal ArticleFields of Research::49 - Mathematical sciences::4901 - Applied mathematics::490102 - Biological mathematicshttps://doi.org/10.1007/s00026-015-0260-2