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PICs are a popular phylogenetic comparative method and I was wondering what units the actual contrasts are in. I want to say they are unitless but I am not entirely sure.

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  • $\begingroup$ Are you scaling the data? $\endgroup$ – Oreotrephes Jul 8 '15 at 2:57
  • $\begingroup$ @Oreotrephes Yes, I'm scaling it by the branch lengths $\endgroup$ – C_Z_ Jul 8 '15 at 14:08
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From what I understand, the answer is; it depends. As you point out in the comment to Remi.b, contrasts are standardized by branch lengths (which are assumed to be proportional to "evolutionary time") before they are analysed (to obtain standardized independent contrasts). However, branch lengths can be come from a number of different sources (divergence times, genetic similarity etc), can be based on different evolutionary models, and can also be transformed (log etc). Therefore, you cannot say what the units of standardized independent contrasts are in general. They would probably not be dimensionless though, since branch lenghts are seldomly (if ever?) expressed in the same units as the raw contrasts. Units such as log(kg)/year or kg/log(year) are more likely. Ultimately, in the usual case, the point of standardizing is to assure that all contrasts receive equal weight in the the analysis, and the creation of suitable branch lengths can be a trial-and-error process, where you e.g. study the relationship between standardized contrasts and the standard deviation of contrasts to see if they have been adequately standardized.

I guess you could describe the process as:

  1. calculate contrasts
  2. calculate standardized contrasts (using branch lengths)
  3. when the contrasts are appropriately standardized, you have obtained phylogenetically independent contrasts.

Here are a couple of relevant quotes from Garland et al., 1992:

...independent contrasts must be adequately standardized so that they will receive equal weighting in subsequent correlation or regression analyses.

also

Second, the statistical adequacy of any proposed branch lengths should be viewed as an empirical issue (cf. Grafen, 1989, 1992; Harvey and Pagel, 1991; Pagel and Harvey, 1992). Third, different transformations - and indeed entirely different branch lengths, based on different information - can be used for different characters. The use of different branch lengths for different characters would be analogous to using different transformations for the two variables in an ordinary correlation or regression.

finally

Standardized independent contrasts essentially indicate minimum average "rates" (or, in Bookstein's [1988] terminology, "reduced speeds") of character change occurring along two branches deriving from a common ancestor (Garland, 1992). Because they are standardized, they do not indicate absolute amounts of change. For example, a large contrast (absolute difference) between two species at the tips of a phylogeny may yield a small standardized contrast if the branch lengths of that contrast are long.

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  • $\begingroup$ Thanks for your answer. I thought it might be (units of measurement)/(units of time), but that seemed strange to me because those are the same units as rates. Thinking of contrasts as being rates is not intuitive to me, but based on that last paragraph I guess that's what they are. How about that! $\endgroup$ – C_Z_ Aug 7 '15 at 14:29
  • $\begingroup$ Good answer that proved me wrong. +1 I deleted my answer. $\endgroup$ – Remi.b Aug 7 '15 at 16:30

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