4 papers
Exact Counts of Binary Phylogenetic Networks with Four Reticulations
Hao Yu, Louxin Zhang
Phylogenetic networks provide a flexible framework for representing reticulate evolutionary processes, such as hybridization, introgression, recombination, and horizontal gene tran…
A Short Combinatorial Proof of the Pons-Batle Identity for Counting Tree-Child Networks
Hao Yu, Louxin Zhang
Tree-child networks are a useful class of binary phylogenetic networks. The Pons--Batle identity (Pons and Batle, \textit{Scientific Reports}, 2021) states that the number $a_{n,k}…
A cube-root phase transition in tree-child networks and the enumeration threshold for galled networks
Michael Fuchs, Hao Yu
We prove two surprising results about phylogenetic networks. First, we show that the structure of tree-child networks with leaves and reticulation nodes undergoes a sharp p…
Asymptotic Counting of Binary Phylogenetic Networks
Hao Yu, Louxin Zhang
Phylogenetic networks provide a general framework for modeling reticulate evolutionary processes such as hybridization, recombination, and horizontal gene transfer. In this paper,…