Counting General Phylogenetic networks

TL;DR

This paper develops precise asymptotic estimates for counting general phylogenetic networks using analytic combinatorial methods, extending previous work on specific subclasses to the general case.

Contribution

It introduces a method to enumerate general phylogenetic networks asymptotically, broadening the scope beyond previously studied subclasses.

Findings

Derived asymptotic formulas for network counts

Extended enumeration techniques to general networks

Built on prior subclass enumeration results

Abstract

We provide precise asymptotic estimates for the number of general phylogenetic networks by using analytic combinatorial methods. Recently, this approach is studied by Fuchs, Gittenberger, and the author himself (Australasian Journal of Combinatorics 73(2):385-423, 2019), to count networks with few reticulation vertices for two subclasses: tree-child and normal networks. We follow this line of research to show how to obtain results on the enumeration of general phylogenetic networks.