Asymptotic enumeration and distributional properties of galled networks

We show a first-order asymptotics result for the number of galled networks with n leaves. This is the first class of phylogenetic networks of large size for which an asymptotic counting result of such strength can be obtained. In addition, we also find the limiting distribution of the number of reti...

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Bibliographic Details
Published inJournal of combinatorial theory. Series A Vol. 189; p. 105599
Main Authors Fuchs, Michael, Yu, Guan-Ru, Zhang, Louxin
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.07.2022
Subjects
Asymptotic counting
Dup-tree
Galled network
Laplace method
Limit distribution
Phylogenetic network
Poisson law
Laplace method
Phylogenetic network
Dup-tree
Limit distribution
Galled network
Poisson law
Asymptotic counting
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Summary:We show a first-order asymptotics result for the number of galled networks with n leaves. This is the first class of phylogenetic networks of large size for which an asymptotic counting result of such strength can be obtained. In addition, we also find the limiting distribution of the number of reticulation nodes of galled networks with n leaves chosen uniformly at random. These results are obtained by performing an asymptotic analysis of a recent approach of Gunawan, Rathin, and Zhang (2020) [12] which was devised for the purpose of (exactly) counting galled networks. Moreover, an old result of Bender and Richmond (1984) [1] plays a crucial role in our proofs, too.
ISSN:0097-3165
1096-0899
DOI:10.1016/j.jcta.2022.105599