系统发生树的随机模型

基于拉普拉斯变换的临界情况随机系统发生树模型

Critical case stochastic phylogenetic tree model via the Laplace transform

死亡模型现在是一种常见的数学工具，用来描述在真实世界的系统发育树中观察到的分支模式。Liggett和Schinazi（2009）就是这样一个例子。作者提出了一个简单的出生和死亡模型，该模型与流感和HIV的系统发育树兼容，取决于出生率参数。这个模型的一个有趣的特例是出生率等于死亡率的临界情况。这是一个非平凡的情况，并研究其渐近行为，我们采用了拉普拉斯变换。在临界情况下，我们修正了Liggett和Schinazi（2009）的证明。

Identifiability of tree-child phylogenetic networks under a probabilistic recombination-mutation model of evolution

Phylogenetic networks are an extension of phylogenetic trees which are used to represent evolutionary histories in which reticulation events (such as recombination and hybridization) have occurred. A central question for such networks is that of identifiability, which essentially asks under what circumstances can we reliably identify the phylogenetic network that gave rise to the observed data? Recently, identifiability results have appeared for networks relative to a model of sequence evolution that generalizes the standard Markov models used for phylogenetic trees. However, these results are…

Phylogenetic diversity and biodiversity indices on phylogenetic networks

In biodiversity conservation it is often necessary to prioritize the species to conserve. Existing approaches to prioritization, e.g. the Fair Proportion Index and the Shapley Value, are based on phylogenetic trees and rank species according to their contribution to overall phylogenetic diversity. However, in many cases evolution is not treelike and thus, phylogenetic networks have come to the fore as a generalization of phylogenetic trees, allowing for the representation of non-treelike evolutionary events, such as horizontal gene transfer or hybridization. Here, we extend the concepts of phy…

高阶分类群系统发育树的随机模型

Stochastic Models for Phylogenetic Trees on Higher-order Taxa

简单的随机模型的系统发育树的物种已经得到了很好的研究。但是，许多古生物学数据关注的是更高级分类群的时间序列或树木，而任何关于现存群体之间关系的广泛图景都需要使用更高级分类群。一个连贯的模型，树（说）属应该包括一个物种水平的模型和一个模型的分类方案，物种被分配到属。我们提出了一个这样的模型的一般框架，并描述了三种替代的分类方案。结合Aldous-Popovic（2005）的种级模型，得到了高阶树的模型，并对高阶树模型进行了分析研究。特别是，我们推导出公式的寿命属，每属的物种数的分布，并为后代结构的树属。

系统发生树中物种形成事件的随机模型

Stochastic Models for Speciation Events in Phylogenetic trees

在系统发育树中，我们通常没有关于物种形成事件（内部节点）发生时间的信息。在一个中性的物种形成模型下，我开发了快速算法来计算内部节点i是第k个物种形成事件的概率。对于Yule和聚结模型，我也开发了一个边长估计。Yule模型的各种性质在整个论文中进行了讨论。

On asymptotic joint distributions of cherries and pitchforks for random phylogenetic trees

Tree shape statistics provide valuable quantitative insights into evolutionary mechanisms underpinning phylogenetic trees, a commonly used graph representation of evolution systems ranging from viruses to species. By developing limit theorems for a version of extended Pólya urn models in which negative entries are permitted for their replacement matrices, we present strong laws of large numbers and central limit theorems for asymptotic joint distributions of two subtree counting statistics, the number of cherries and that of pitchforks, for random phylogenetic trees generated by two widely use…