A few months ago, walking in the woods near our house, I came up with what I thought would be the phylogenetic equivalent of the trait-based metric functional dispersion (FDis, Laliberte & Legendre 2010). The metric would be the mean distance of a sample of taxa to their most recent common ancestor (MRCA). Almost as soon as the idea crossed my mind, I realized this new measure, let's call it distMRCA, was not exactly analogous to FDis. Given that in an ultrametric tree, a sample of species are all equally distant from their MRCA, distMRCA would be the same for one species or when averaged across all species in a sample. Kind of boring. Also, in many empirical cases, given a sample of taxa, it's likely their MRCA is the root (or near it) of the phylogeny in question. So I let the idea walk to the other side of my mind and forgot about it.
A few weeks ago I noticed that two different folks (one, two) have implemented (with attribution--thanks!) a mean root distance (MRD) function from my now defunct U. of Missouri, St. Louis webpage. Since it fits within the framework introduced in our recent paper, I decided to include MRD in the metricTester package.
While updating the MRD code, a variant of the distMRCA function occurred to me. Rather than simply finding the distance of the set of taxa from their MRCA, perhaps the mean of all distances between all pairwise MRCAs and the root would provide a better measurement of subtle variation in the arrangement of present taxa across a phylogeny. For instance, given three species (s1, s2, and s3), the original idea would have simply found the distance of those taxa from their MRCA. The updated idea would be to find the distance of the MRCA of each taxon-pair (s1-s2, s1-s3, s2-s3) from the root. Sounded promising. Maybe you already see where this is going. It took me coding the whole thing out and testing how it behaved until I realized I'd re-invented the wheel (admission: my version is extra heavy and slow rolling). Specifically, I'd come up with a new way of calculating phylogenetic species variability (Helmus et al. 2007), which was really just a new flavor of mean pairwise phylogenetic distance (Webb 2000), which was just a new way of calculating Δ+ (Warwick and Clarke 1995). And so on and so forth. Maybe there are no new phylogenetic community structure metrics under the sun.
In retrospect, it's quite obvious why these things should be equivalent. Given an ultrametric tree, the pairwise distance between two taxa is related to their distance from the root. By that, I mean that if the total tree height is 10 mya, and two taxa are separated by a "pairwise" distance of 4 mya, then we know they shared a MRCA 8 mya (10 - 4/2). Obviously, taking the averages of these distMRCA and these MPD values are going to be closely correlated.
On the plus side, I thought of a way of abundance-weighting MRD. That is incorporated into metricTester now too. Given my experience with re-inventing the MPD wheel, I figured it would be related to IAC (Cadotte et al. 2010), but an initial test showed that not to be the case. Since it's just a node-based measure, it seems likely it's not of great use to empiricists in today's age of dated phylogenies, but it's there in case someone would like to experiment with it.
Cadotte, M. W., T. Jonathan Davies, J. Regetz, S. W. Kembel, E. Cleland, and T. H. Oakley. 2010. Phylogenetic diversity metrics for ecological communities: integrating species richness, abundance and evolutionary history. Ecology Letters 13:96–105. 10.1111/j.1461-0248.2009.01405.x
Helmus, M. R., T. J. Bland, C. K. Williams, and A. R. Ives. 2007. Phylogenetic measures of biodiversity. The American Naturalist 169:E68–E83. 10.1086/511334
Laliberté, E., and P. Legendre. 2010. A distance-based framework for measuring functional diversity from multiple traits. Ecology 91:299–305. 10.1890/08-2244.1
Miller, E. T., D. R. Farine, and C. H. Trisos. 2016. Phylogenetic community structure metrics and null models: a review with new methods and software. Ecography:In press. 10.1111/ecog.02070
Warwick, R. M., and K. R. Clarke. 1995. New "biodiversity’ measures reveal a decrease in taxonomic distinctness with increasing stress. Marine Ecology Progress Series 129:301–305. 10.3354/meps129301
Webb, C. O. 2000. Exploring the phylogenetic structure of ecological communities: an example for rain forest trees. The American Naturalist 156:145–155. 10.1086/303378