Counting and Enumerating Galled Networks

2018/12/20 by Andreas D. M. Gunawan, Andreas DM Gunawan, Gunawan, Andreas DM +4 · 3 citations
Agricultural and Biological Sciences · Biochemistry, Genetics and Molecular Biology · #Genetic diversity and population structure #Genomics and Phylogenetic Studies #Plant and animal studies #q-bio.PE

paper · pdf · doi:10.48550/arxiv.1812.08569

7 figures, 2 tables

arxiv created 2018/12/20 · arxiv updated 2018/12/21

Abstract

Galled trees are widely studied as a recombination model in population genetics. This class of phylogenetic networks is generalized into galled networks by relaxing a structural condition. In this work, a linear recurrence formula is given for counting 1-galled networks, which are galled networks satisfying the condition that each reticulate node has only one leaf descendant. Since every galled network consists of a set of 1-galled networks stacked one on top of the other, a method is also presented to count and enumerate galled networks.

Cited by

• Counting Tree-Child Networks and Their Subclasses
• Beyond level-1: Identifiability of a class of galled tree-child networks
• Asymptotic Enumeration of Subclasses of Level-2 Phylogenetic Networks

Related

• Counting Tree-Child Networks and Their Subclasses
• Counting Phylogenetic Networks with Few Reticulation Vertices: Galled and Reticulation-Visible Networks
• Asymptotic Enumeration and Distributional Properties of Galled Networks
• Counting Phylogenetic Networks with Few Reticulation Vertices: Tree-Child and Normal Networks
• Enumerative combinatorics of unlabeled and labeled time-consistent galled trees