Response to Comments on "Molecular Phylogenies Link Rates of Evolution and Speciation"

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Abstract
The node-density effect produces a curvilinear relationship between nodes n and path lengths x in the phylogenetic tree of the form n = xδ, such that δ > 1. Contrary to remarks by Witt and Brumfield (1), values of δ = 1 are not compatible with the artifact. We explained this point in (3) (supplementary online text), and it is easily proven mathematically. The paper by Fitch and Bruschi (4) cited in (1), which attempted to correct for the node density effect by adjusting paths using a linear rule of thumb (equivalent to δ =1), may have given the impression that the node density effect is expected to produce a linear relationship. It is not expected to, and Fitch and Bruschi did not suggest that it did. In a later paper, Fitch and Beintema (5) showed a clearer example of the curvilinear form of the relationship [see also (6)]. As stated in (3), we excluded all trees with δ > 1, regardless of whether the value of δ was statistically significant. Thus, we applied a conservative inclusion criterion and there is no reason to believe that the node density effect may have biased our results.