University of Oxford
Counting and typical parameters for phylogenetic networks
It is well known how to count phylogenetic trees (rooted binary trees, either fully labelled or with just the leaves labelled). But what about phylogenetic networks, where we allow reticulation nodes (with indegree 2 and outdegree 1), corresponding to evolutionary processes such as recombination and hybridisation? Tree-child and normal networks are subclasses of structured networks of particular interest.
We shall find approximate counting formulae for the numbers of labelled general, tree-child, and normal phylogenetic networks on n nodes; and corresponding results for leaf-labelled tree-child and normal networks with l leaves. Further we find the typical proportions of leaves, tree nodes, and reticulation nodes for each of these classes of networks.
These results are joint work with Charles Semple and Dominic Welsh.