Squaring within the Colless index yields a better balance index

The Colless index for bifurcating phylogenetic trees, introduced by (1982), is defined as the sum, over all internal nodes v of tree, absolute value difference sizes clades children v. It one most popular balance indices, because, in addition to measuring a tree very simple and intuitive way, it turns out be powerful discriminating shape indices. But has some drawbacks. On hand, although its minimum reached at so-called maximally balanced almost always also trees that are not balanced. other definition sum values differences makes difficult study analytically distribution under probabilistic models trees. In this paper we show if replace clade squares these differences, drawbacks overcome resulting still more than original index.