Limit distribution of the quartet balance index for Aldous's b>=0-model

A balance index for phylogenetic trees based on rooted quartets

We define a new balance index for rooted phylogenetic trees based on the symmetry of the evolutive history of every set of 4 leaves. This index makes sense for multifurcating trees and it can be computed in time linear in the number of leaves. We determine its maximum and minimum values for arbitrary and bifurcating trees, and we provide exact formulas for its expected value and variance on bifurcating trees under Ford's $α$-model and Aldous' $β$-model and on arbitrary trees under the $α$-$γ$-model.

快速容错四元组生成算法

Fast error-tolerant quartet phylogeny algorithms

我们提出了一种算法，系统发育重建使用四重奏，返回正确的拓扑结构$n$类群在$O(n \log n)$时间与高概率，在一个概率模型，其中一个四重奏是不符合真实的拓扑结构的树与恒定的概率，独立于其他四重奏。我们的增量算法依赖于一个搜索树结构的平衡，具有很高的概率，无论真正的拓扑结构。我们的实验结果表明，我们的方法是在运行时最快的算法相媲美，同时仍然提供一致性保证。