论文标题
在面包指数内的平方会产生更好的平衡指数
Squaring within the Colless index yields a better balance index
论文作者
论文摘要
Colless（1982）引入的分叉的系统发育树的Colless指数被定义为在所有内部节点$ v $的总和，这是由$ V $的儿童定义的进化枝差的绝对值。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的平衡外，它还是最强大和最有区别的系统发育形状指数之一。但这有一些缺点。一方面，尽管在所谓的最大平衡的树木上达到了其最低价值，但几乎总是在不平衡的树木上达到。另一方面，其定义是差异的绝对值之和，因此很难在分叉的系统发育树的概率模型下分析研究其分布。在本文中，我们表明，如果我们在其定义中替换了进化枝大小差异的绝对值，则克服了所有这些缺点，并且所产生的索引仍然比原始的colless索引更强大，更有区分。
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.
