On 2013 Jul 03, Joshua L Cherry commented:

This review, and the work on which it is based (Webster AJ, 2003, Pagel M, 2006), claim that speciation events are accompanied by bursts of protein sequence evolution. This claim is based on correlations between the total root-to-tip branch length and the number of nodes along this path in phylogenetic trees.

As the authors explain, in such analyses it is critical to account for what they call the node-density artifact. This effect can lead to an apparent correlation for the inferred branch lengths in the absence of a correlation for the true lengths. The authors claim to have accounted for this artifact, but there is reason to doubt this.

The authors attempt to detect the artifact through the concavity of the relationship between number of nodes and path length, and eliminate trees that appear to be affected. There are, however, several reasons to doubt the reliability of their test. The form of the expected relationship is not known. In fact the effect does not depend on only the number of nodes, but also on their position; an additional node in the middle of a long branch will have a large effect on the total calculated length, whereas an additional node near one end of the branch will have a small effect. The authors fit a power law to the data. This family of functions has unrealistic features. The true relationship is expected to approach a horizontal asymptote, whereas the power law increases without bound. Also, the power law artificially forces the curve through the origin. Furthermore, with finite data the downward concavity might not be detected due to chance, even with a perfect model. Because the concavity will be weak under some circumstances, this is an important concern.

I would suggest another type of test. Branch lengths can be recalculated with some species, and hence some nodes, omitted. The true branch lengths and speciation histories of course remain unchanged, but species originally separated from the root by many nodes are now just as vulnerable to branch shortening as species with fewer nodes. If the path shortens as a result, this is evidence of the node-density artifact. I suspect that many additional trees would be shown to suffer from the artifact by this type of test.

On 2013 Jul 03, Joshua L Cherry commented:

This review, and the work on which it is based (Webster AJ, 2003, Pagel M, 2006), claim that speciation events are accompanied by bursts of protein sequence evolution. This claim is based on correlations between the total root-to-tip branch length and the number of nodes along this path in phylogenetic trees.

As the authors explain, in such analyses it is critical to account for what they call the node-density artifact. This effect can lead to an apparent correlation for the inferred branch lengths in the absence of a correlation for the true lengths. The authors claim to have accounted for this artifact, but there is reason to doubt this.

The authors attempt to detect the artifact through the concavity of the relationship between number of nodes and path length, and eliminate trees that appear to be affected. There are, however, several reasons to doubt the reliability of their test. The form of the expected relationship is not known. In fact the effect does not depend on only the number of nodes, but also on their position; an additional node in the middle of a long branch will have a large effect on the total calculated length, whereas an additional node near one end of the branch will have a small effect. The authors fit a power law to the data. This family of functions has unrealistic features. The true relationship is expected to approach a horizontal asymptote, whereas the power law increases without bound. Also, the power law artificially forces the curve through the origin. Furthermore, with finite data the downward concavity might not be detected due to chance, even with a perfect model. Because the concavity will be weak under some circumstances, this is an important concern.

I would suggest another type of test. Branch lengths can be recalculated with some species, and hence some nodes, omitted. The true branch lengths and speciation histories of course remain unchanged, but species originally separated from the root by many nodes are now just as vulnerable to branch shortening as species with fewer nodes. If the path shortens as a result, this is evidence of the node-density artifact. I suspect that many additional trees would be shown to suffer from the artifact by this type of test.