On Sackin’s original proposal: the variance of the leaves’ depths as a phylogenetic balance index

摘要

In the last decades there has been an increasing interest in the definition and study of indices quantifying properties of trees. Besides the research on this topic carried out within the framework of [ ], the main motivation has come from the field of phylogenetics, through the application of such indices in the description and comparison of phylogenetic trees. In effect, there is the commonly accepted belief that the characteristics of the branching pattern of a phylogenetic tree reflect the properties and tendencies of the evolutionary processes that have produced it [ , ]. As a consequence, the shape of a phylogenetic tree is thought to offer clues to the features of the evolutionary processes underlying it and in particular to provide a ground to test hypothesis on these features [ ]. This has motivated the introduction of many on phylogenetic trees, related only to their topology and not taking into account branch lengths or the actual taxa on their leaves. These indices have then been used to test evolutionary hypothesis and models [ , , , , , , , , ] as well as in other applications [ , , , , ].