Locating a Tree in a Reticulation-Visible Network in Cubic Time

系统发育网络的精确枚举：树孩子、网状可见和果园层次结构

Exact Enumeration of Phylogenetic Networks: The Tree-Child, Reticulation-Visible and Orchard Hierarchy

本文针对三类系统发育网络（树孩子、网状可见和果园网络）建立统一框架进行精确枚举和渐近分析，推导出差异的闭式恒等式，并证明果园网络满足超几何定律。

Normalising phylogenetic networks

Rooted phylogenetic networks provide a way to describe species' relationships when evolution departs from the simple model of a tree. However, networks inferred from genomic data can be highly tangled, making it difficult to discern the main reticulation signals present. In this paper, we describe a natural way to transform any rooted phylogenetic network into a simpler canonical network, which has desirable mathematical and computational properties, and is based only on the 'visible' nodes in the original network. The method has been implemented and we demonstrate its application to some exam…

On Tree Based Phylogenetic Networks

A large class of phylogenetic networks can be obtained from trees by the addition of horizontal edges between the tree edges. These networks are called tree based networks. Reticulation-visible networks and child-sibling networks are all tree based. In this work, we present a simply necessary and sufficient condition for tree-based networks and prove that there is a universal tree based network for each set of species such that every phylogenetic tree on the same species is a base of this network. The existence of universal tree based network implies that for any given set of phylogenetic tree…

On the Subnet Prune and Regraft Distance

Phylogenetic networks are rooted directed acyclic graphs that represent evolutionary relationships between species whose past includes reticulation events such as hybridisation and horizontal gene transfer. To search the space of phylogenetic networks, the popular tree rearrangement operation rooted subtree prune and regraft (rSPR) was recently generalised to phylogenetic networks. This new operation - called subnet prune and regraft (SNPR) - induces a metric on the space of all phylogenetic networks as well as on several widely-used network classes. In this paper, we investigate several probl…

基于μ-表示的半二元系统发育网络类别的度量

Metrics for classes of semi-binary phylogenetic networks using $μ$-representations

该研究针对系统发育网络的比较难题，基于μ-表示的变体推导了半二元约束下果园网络与强网状可见网络类的度量方法，为特定类别系统发育网络的比较提供了量化工具。

Phylogenetic networks that are their own fold-ups

Phylogenetic networks are becoming of increasing interest to evolutionary biologists due to their ability to capture complex non-treelike evolutionary processes. From a combinatorial point of view, such networks are certain types of rooted directed acyclic graphs whose leaves are labelled by, for example, species. A number of mathematically interesting classes of phylogenetic networks are known. These include the biologically relevant class of stable phylogenetic networks whose members are defined via certain "fold-up" and "un-fold" operations that link them with concepts arising within the th…

关于有根系统发育网络类中漏斗状定向的存在性

On the existence of funneled orientations for classes of rooted phylogenetic networks

本文修正了 Bulteau 等人关于漏斗状 tree-child 定向计算困难性的错误证明，并将困难性结果推广到漏斗状 normal 和漏斗状 reticulation-visible 等有根系统发育网络类，且结果对两种不同扎根方式均成立。

Tree-based networks: characterisations, metrics, and support trees

Phylogenetic networks generalise phylogenetic trees and allow for the accurate representation of the evolutionary history of a set of present-day species whose past includes reticulate events such as hybridisation and lateral gene transfer. One way to obtain such a network is by starting with a (rooted) phylogenetic tree $T$, called a base tree, and adding arcs between arcs of $T$. The class of phylogenetic networks that can be obtained in this way is called tree-based networks and includes the prominent classes of tree-child and reticulation-visible networks. Initially defined for binary phyl…

通过自同构权重的无限制二元系统发育网络的精确与渐近计数

Exact and asymptotic enumeration of unrestricted binary phylogenetic networks through automorphism weights

本文通过自同构权重对无限制二元系统发育网络进行精确与渐近计数，提出递归方法，给出k≤5的闭式计数，并证明非树-子网络占比及随机网络非平凡自同构概率的渐近结果。