Nodes in phylogenetic trees: the relation between imbalance and number of descendent species

The imbalance of a node in a phylogenetic tree can be defined in terms of the relative numbers of species (or higher taxa) on the branches that originate at the node. Empirically, imbalance also turns out to depend on the absolute total number of species on the branches: in a sample of large trees, nodes with more descendent species tend to be more unbalanced. Subsidiary analyses suggest that this pattern is not a result of errors in tree estimation. Instead, the increase in imbalance with species is consistent with a cumulative effect of differences in diversification rates between branches. [Equal-rates Markov model; imbalance; phylogeny shape; proportional-to-distinguishable-arrangements model.].