The disentangling number for phylogenetic mixtures

大型系统发育混合模型的可识别性：多种系统发育模型结构

Identifiability of Large Phylogenetic Mixtures for Many Phylogenetic Model Structures

该研究扩展了Rhodes和Sullivant的定理，证明了多种等变系统发育混合模型（如Jukes-Cantor、Kimura 2/3参数及Strand Symmetric模型）的可识别性，确保参数可从数据中唯一确定。

Identifiability in Phylogenetics using Algebraic Matroids

Identifiability is a crucial property for a statistical model since distributions in the model uniquely determine the parameters that produce them. In phylogenetics, the identifiability of the tree parameter is of particular interest since it means that phylogenetic models can be used to infer evolutionary histories from data. In this paper we introduce a new computational strategy for proving the identifiability of discrete parameters in algebraic statistical models that uses algebraic matroids naturally associated to the models. We then use this algorithm to prove that the tree parameters ar…

Quarnet inference rules for level-1 networks

An important problem in phylogenetics is the construction of phylogenetic trees. One way to approach this problem, known as the supertree method, involves inferring a phylogenetic tree with leaves consisting of a set $X$ of species from a collection of trees, each having leaf-set some subset of $X$. In the 1980's characterizations, certain inference rules were given for when a collection of 4-leaved trees, one for each 4-element subset of $X$, can all be simultaneously displayed by a single supertree with leaf-set $X$. Recently, it has become of interest to extend such results to phylogenetic …