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.

由Colless（1982）引入的分支系统树的Colless索引定义为所有内部节点的总和。 $v$ 的大小，由树的子代定义的进化枝的大小之差的绝对值 $v$。它是最流行的系统发育平衡指数之一，因为除了以非常简单和直观的方式测量树木的平衡之外，它还被证明是最强大，最有区别的系统发育形状指数之一。但是它有一些缺点。一方面，尽管在所谓的最大平衡树上达到了最小值，但是在没有最大平衡的树上几乎总是达到了最小值。另一方面，其定义为差值的绝对值之和，使得很难在分叉的系统发育树的概率模型下分析地研究其分布。在本文中，我们表明，如果用定义差异的平方代替进化枝大小差异的绝对值，