Laplacian Matrices for Extremely Balanced and Unbalanced Phylogenetic Trees

基于半正定规划的平衡最小进化准则下的系统发育推断

Phylogenetic Inference under the Balanced Minimum Evolution Criterion via Semidefinite Programming

本文提出结合半正定规划放松与迭代舍入方案的算法，用于解决平衡最小进化问题，实现准确的系统发育重构。

Challenges of sampling and how phylogenetic comparative methods help: With a case study of the Pama-Nyungan laminal contrast

Phylogenetic comparative methods are new in our field and are shrouded, for most linguists, in at least a little mystery. Yet the path that led to their discovery in comparative biology is so similar to the methodological history of balanced sampling, that it is only an accident of history that they were not discovered by a typologist. Here we clarify the essential logic behind phylogenetic comparative methods and their fundamental relatedness to a deep intellectual tradition focussed on sampling. Then we introduce concepts, methods and tools which will enable typologists to use these methods …

Squaring within the Colless index yields a better balance index

The Colless index for bifurcating phylogenetic trees, introduced by Colless (1982), is defined as the sum, over all internal nodes $v$ of the tree, of the absolute value of the difference of the sizes of the clades defined by the children of $v$. It is one of the most popular phylogenetic balance indices, because, in addition to measuring the balance of a tree in a very simple and intuitive way, it turns out to be one of the most powerful and discriminating phylogenetic shape indices. But it has some drawbacks. On the one hand, although its minimum value is reached at the so-called maximally b…

Polyhedral geometry of Phylogenetic Rogue Taxa

It is well known among phylogeneticists that adding an extra taxon (e.g. species) to a data set can alter the structure of the optimal phylogenetic tree in surprising ways. However, little is known about this "rogue taxon" effect. In this paper we characterize the behavior of balanced minimum evolution (BME) phylogenetics on data sets of this type using tools from polyhedral geometry. First we show that for any distance matrix there exist distances to a "rogue taxon" such that the BME-optimal tree for the data set with the new taxon does not contain any nontrivial splits (bipartitions) of the …

系统发育树中的幂律与偏好性合并

Power-laws in phylogenetic trees and the preferential coalescent

本研究提出一个基于偏好性合并的生成模型，通过广义Smoluchowski方程解释系统发育树中观测到的幂律标度，揭示其数学起源并提供新分析工具。

Stochastic safety radius on Neighbor-Joining method and Balanced Minimal Evolution on small trees

A distance-based method to reconstruct a phylogenetic tree with $n$ leaves takes a distance matrix, $n \times n$ symmetric matrix with $0$s in the diagonal, as its input and reconstructs a tree with $n$ leaves using tools in combinatorics. A safety radius is a radius from a tree metric (a distance matrix realizing a true tree) within which the input distance matrices must all lie in order to satisfy a precise combinatorial condition under which the distance-based method is guaranteed to return a correct tree. A stochastic safety radius is a safety radius under which the distance-based method i…