The contrasts returned by pic() should already be standardized.
Standardizing phylogenetic contrasts is performed by dividing each contrast (calculated between internal or terminal nodes) by a sum proportional to the square root of its expected variance. Assuming Brownian motion, for two sister terminal nodes, this is just the square root of the sum of their branch lengths to a common ancestor. (This is because the variance of a difference between two random variables is just the sum of their separate variances, and variance is accumulates in direct proportion to elapsed time under BM.) For contrasts that are deeper in the phylogeny, this sum has to be adjusted to account for uncertainty in the reconstructed values at internal nodes, which adds extra variance to the computed difference. This is described in great detail in Felsenstein (1985; Am Nat 125:1-15). However, as noted above - the values returned by pic() should have already been standardized in this way!
You should also not subtract the mean value of the contrasts. This is stated explicitly in Garland et al. (1992; Syst Biol 41:18-32): "The expected mean of any set of contrasts is zero because the direction of subtraction is arbitrary..., so only standard deviations are needed."
- Liam Liam J. Revell NESCent, Duke University web: http://anolis.oeb.harvard.edu/~liam/ NEW email: lrev...@nescent.org On Tue, 15 Sep 2009, Manabu Sakamoto wrote:
Dear list, I am trying to standardise independent contrasts following Garland et al. (1992), but I am unsure just how you would extract the "sum of it's [contrast's] branch lenghts" in R. I computed independent contrasts using the "pic" function in "ape". I then took the contrasts and subtracted the mean from each one and now I need to divide them by their standard deviations or the square root of the sum of their branch lengths (Garland et al., 1992). This is where I am stuck. I assume the sum of the branch lengths here refer to the sum of the two branch lengths that go into the computation of each contrast? I would greatly appreciate any kind support on this matter. Many thanks in advance, Manabu Sakamoto -- -------------------------------------- M. Sakamoto, PhD Department of Earth Sciences, University of Bristol, Wills Memorial Building, Queen's Road, Bristol BS8 1RJ, UK m.sakam...@bristol.ac.uk _______________________________________________ R-sig-phylo mailing list R-sig-phylo@r-project.org https://stat.ethz.ch/mailman/listinfo/r-sig-phylo
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