Revisiting Shao and Sokal’s B2 index of phylogenetic balance

• Main Authors: Bienvenu, F. (Author), Cardona, G. (Author), Scornavacca, C. (Author)
• Format: Article
• Language: English
• Published: Springer Science and Business Media Deutschland GmbH 2021
• Subjects: algorithm; Algorithms; B2 index; Biological Evolution; Colless index; evolution; Phylogenetic balance; Phylogenetic networks; phylogeny; Phylogeny; Sackin index; Shannon entropy
• Online Access: View Fulltext in Publisher

 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 B2 index, was first proposed by Shao and Sokal (Syst Zool 39(3): 266–276, 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 B2 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. © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.