Journal of Combinatorial Theory Series A ( IF 1.1 ) Pub Date : 2022-02-14 , DOI: 10.1016/j.jcta.2022.105599 Michael Fuchs , Guan-Ru Yu , Louxin Zhang
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.
中文翻译:
阻塞网络的渐近枚举和分布特性
我们展示了具有n 个叶子的阻塞网络数量的一阶渐近结果。这是第一类能够获得这种强度的渐近计数结果的大型系统发育网络。此外,我们还发现了随机均匀选择n个叶子的galled网络的网状节点数量的限制分布。这些结果是通过对 Gunawan、Rathin 和 Zhang (2020) [12] 最近的一种方法进行渐近分析获得的,该方法旨在(准确地)计算阻塞网络。此外,Bender 和 Richmond (1984) [1] 的一个旧结果在我们的证明中也起着至关重要的作用。