Counting Phylogenetic Networks

Counting Phylogenetic Networks

We give approximate counting formulae for the numbers of labelled general, tree-child, and normal (binary) phylogenetic networks on n vertices. These formulae are of the form 2 , where the constant γ is 32 for general networks, and 5 4 for tree-child and normal networks. We also show that the number of leaf-labelled tree-child and normal networks with ` leaves are both 2 log . Further we determ...

Constructing and Counting Phylogenetic Invariants

The method of invariants is an approach to the problem of reconstructing the phylogenetic tree of a collection of m taxa using nucleotide sequence data. Models for the respective probabilities of the 4m possible vectors of bases at a given site will have unknown parameters that describe the random mechanism by which substitution occurs along the branches of a putative phylogenetic tree. An inva...

Counting consistent phylogenetic trees is #P-complete

Reconstructing phylogenetic trees is a fundamental task in evolutionary biology. Various algorithms exist for this purpose, many of which come under the heading of ‘supertree methods.’ These methods amalgamate a collection P of phylogenetic trees into a single parent tree. In this paper, we show that, in both the rooted and unrooted settings, counting the number of parent trees that preserve al...

Counting phylogenetic invariants in some simple cases.

An informal degrees of freedom argument is used to count the number of phylogenetic invariants in cases where we have three or four species and can assume a Jukes-Cantor model of base substitution with or without a molecular clock. A number of simple cases are treated and in each the number of invariants can be found. Two new classes of invariants are found: non-phylogenetic cubic invariants te...

Phylogenetic Networks