Evaluating Phylogenetic Tree Shape: Two Modifications to Fusco & Cronkʹs Method

Measurement of the degree of asymmetry in phylogenetic trees is important because a treeʹs shape reflects the process by which it has grown. For example, highly asymmetric trees are evidence that species have had different potential for diversification. Of the tree shape measures in the literature, that proposed by Fusco & Cronk (J. theor. Biol.175, 235–243) appears to be particularly useful, because it does not require fully-resolved trees whose terminals are of equal taxonomic rank. The value of the asymmetry or imbalance at a node is intended to be independent of the number of species ultimately descended from the node. In this paper, however, we point out that the value does depend upon species number. We propose two modifications that remove the dependency and so increase the measureʹs usefulness. We illustrate the use of the modified measures, which are implemented in a freely-available program, MESA.