论文标题
累积网络的渐近枚举和分布特性
Asymptotic Enumeration and Distributional Properties of Galled Networks
论文作者
论文摘要
我们显示了带有$ n $叶子的累积网络数量的一阶渐近学结果。这是{\ IT}大小的第一类系统发育网络，可以为其获得这种强度的渐近计数结果。此外，我们还发现了$ n $叶子随机选择的累积网络的网络的网络节点数量的限制分布。这些结果是通过对Gunawan，Rathin和Zhang（2020）的最新方法进行渐近分析来获得的，该方法是为了（准确）计数累积的网络而设计的。此外，本德和里士满（1984）的旧结果在我们的证明中也起着至关重要的作用。
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 {\it 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 a 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) which was devised for the purpose of (exactly) counting galled networks. Moreover, an old result of Bender and Richmond (1984) plays a crucial role in our proofs, too.
