论文标题
重新访问Shao和Sokal的$ B_2 $系统发育平衡索引
Revisiting Shao and Sokal's $B_2$ index of phylogenetic balance
论文作者
论文摘要
系统发育平衡的测量，例如胶囊指数，在系统发育学中起着重要作用。不幸的是，这些指数是专门为系统发育树设计的，并且不会自然地扩展到系统发育网络（越来越多地用于描述网状演化）。这使我们考虑了鲜为人知的平衡索引，其定义基于同样适用于树木和网络的概率解释。该索引被称为$ b_2 $索引，是Shao and Sokal在1990年首次提出的。令人惊讶的是，从那以后，它似乎并没有进行数学研究。同样，它仅在生物学文献中偶尔使用，在生物学文献中倾向于将其视为奥术。在本文中，我们研究了$ b_2 $的数学特性，例如在最常见的随机树模型及其在各种系统发育网络上的最常见模型中的期望和差异。我们还评估了它在生物应用中的相关性，并发现它与colless和sackin指数相当。总的来说，我们的结果要求重新评估这种遗忘的系统发育平衡的措施。
Measures of phylogenetic balance, such as the Colless and Sackin indices, play an important role in phylogenetics. Unfortunately, these indices are specifically designed for phylogenetic trees, and do not extend naturally to phylogenetic networks (which are increasingly used to describe reticulate evolution). This led us to consider a lesser-known balance index, whose definition is based on a probabilistic interpretation that is equally applicable to trees and to networks. This index, known as the $B_2$ index, was first proposed by Shao and Sokal in 1990. Surprisingly, it does not seem to have been studied mathematically since. Likewise, it is used only sporadically in the biological literature, where it tends to be viewed as arcane. In this paper, we study mathematical properties of $B_2$ such as its expectation and variance under the most common models of random trees and its extremal values over various classes of phylogenetic networks. We also assess its relevance in biological applications, and find it to be comparable to that of the Colless and Sackin indices. Altogether, our results call for a reevaluation of the status of this somewhat forgotten measure of phylogenetic balance.
