2020/07/29 by Tomás M. Coronado, Coronado, Tomás M., Arnau Mir +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Earth and Planetary Sciences · #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #Evolution and Paleontology Studies #FOS: Biological sciences #FOS: Computer and information sciences #FOS: Mathematics #Genomics and Phylogenetic Studies #Geochemistry and Geologic Mapping #Populations and Evolution (q-bio.PE)
paper · pdf · doi:10.48550/arxiv.2007.14731
openalex publication_date 2020/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 balanced trees, it is almost always reached also at trees that are not maximally balanced. On the other hand, its definition as a sum of absolute values of differences makes it difficult to study analytically its distribution under probabilistic models of bifurcating phylogenetic trees. In this paper we show that if we replace in its definition the absolute values of the differences of clade sizes by the squares of these differences, all these drawbacks are overcome and the resulting index is still more powerful and discriminating than the original Colless index.