关于系统发育网络的树状网络可区分性和完全可识别性
On Tree-Network Distinguishability and Full Identifiability of Phylogenetic Networks
中文总结 AI 辅助
研究在JC、K2P和K3P模型下系统发育网络拓扑的可识别性，证明一级网络半定向参数完全可识别，还区分了网络与树，表明网状进化在叶模式分布中多能产生可检测特征，对可识别性有广泛意义。
中文摘要 AI 辅助
系统发育网络将系统发育树推广到包含重组、水平基因转移和杂交等网状事件的进化历史。在核苷酸替换的马尔可夫模型下，系统发育网络决定叶模式的分布。本文研究在Jukes-Cantor（JC）、Kimura 2-参数（K2P）和Kimura 3-参数（K3P）模型下从该分布识别网络拓扑。首先，在一定生物合理参数空间中，一级系统发育网络的半定向网络参数（模重定向三角形）在这三种模型下都是完全可识别的。其次，在JC和K2P下，在相同参数空间中能区分系统发育网络和系统发育树，除非网络是树或可能带有特定子结构，否则它们不会诱导相同叶模式分布。这些结果对可识别性有更广泛影响。
英文摘要
Phylogenetic networks generalize phylogenetic trees to evolutionary histories that include reticulate events such as recombination, horizontal gene transfer, and hybridization. Under a Markov model of nucleotide substitution, a phylogenetic network determines a distribution of leaf-patterns. Here, we study the identifiability of the network topology from this distribution under the Jukes-Cantor (JC), Kimura 2-parameter (K2P), and Kimura 3-parameter (K3P) models. Our first result is that the semi-directed network parameter of a level-1 phylogenetic network (modulo redirecting triangles) is fully identifiable under all three models, on a biologically reasonable parameter space in which substitution rates are probabilistic and mixing parameters are non-trivial (i.e., not 0 or 1). In contrast to the generic identifiability established in prior work, this holds at every point of the parameter space, not merely off of a measure-zero subset. Our second result distinguishes phylogenetic networks from phylogenetic trees, on the same parameter space, under JC. We prove that no phylogenetic network and phylogenetic tree can induce the same leaf-pattern distribution unless the network is a tree, possibly augmented with certain substructures called 2-blobs. This means the presence of reticulate evolution creates, in most cases, a detectable signature in the leaf-pattern distribution. More broadly, these results have consequences for identifiability beyond the models and network classes studied here, including for several coalescent-based models.
