I would argue against using Mahalanobis D or D squared. It is a statistical test metric which is a legitimate measure when the null hypothesis is true that the taxa are identical but because it is a ratio that depends upon the variability of the divisor, it explodes when the two taxa are different and thus the large numerator is divided by an unstable variance type denominator. That would make deep bifurcations in the tree even more unstable than they are traditionally and even intermediate bifurcations much more unstable. A simpler direct measure of the distance, Euclidean or Manhattan, would be preferable and more interpretable to me.
Cheers, Joe Kunkel. On May 1, 2005, at 7:19 PM, morphmet wrote: > > Hi all, > > in literature, several people have been using Procrustes distances as > the data for a cluster-analysis, more specifically UPGMA. When doing > so, > the Procrustes distances between the consensus configurations of each > OTU are used to calculate a tree based on shape similarities between > the > consensusses. However, when using Procrustes distances, one is ignoring > possible differences in the amount of within-group variation (or is > assuming it is the same for all the OTUâs), not? The Procrustes > distance > between the means of three groups can be the identical, but because of > overlapping variations within two of them, the shape distance will in > many cases be much lower. > > So my question is, whether it is not wiser to use the Squared > Mahalanobis distances of a canonical variate analysis (based on weight > matrix), as a measure of shape distance between group means for a > UPGMA, > as this does take into account the amount of within-group variation > (and > as I understood even standardises it). Does this make sense or is there > some mathematical-statistical pitfall behind it? > > cheers > Dominique Adriaens > > > Prof. Dr. Dominique Adriaens > Ghent University > Evolutionary Morphology of Vertebrates & Zoology Museum > K.L. Ledeganckstraat 35, B-9000 Gent > BELGIUM > tel: +32 9 264.52.19, fax: +32 9 264.53.44 > E-mail: [EMAIL PROTECTED] > URL: http://www.fun-morph.ugent.be/ > http://www.zoologymuseum.ugent.be/ > ---Â. . `Â. .><((((Â>`Â. . `Â. .><((((Â>`Â. . `Â. .><((((Â> .ÂÂ. >=- <Â}}}>< Joseph G. Kunkel, Professor Biology Department University of Massachusetts Amherst Amherst, MA 01003 http://www.bio.umass.edu/biology/kunkel/ -- Replies will be sent to the list. For more information visit http://www.morphometrics.org
