Aloha all, Iʻm still reeling from the Atlanta murders and the rise of hate in general, so I may not be thinking straight, but if weʻre talking about Brownian motion, Iʻm not sure this is quite right.
If the trait is log(grams) then the trait is unit-free. > First - Joe - what do you mean by log(grams) has no units? The units of grams is a unit, so log(mass) will have units of log-gm. As log is not the same as 1/gm, log(gm) cannot be unit-free. > The "time" > is probably branch length from a phylogeny. That in turn (from DNA > data) is usually DNA substitutions per site. > > So the units of the standard deviation are sites per substitution. > But this is not the standard deviation, it is its square. > > So (wait for it ...) square sites per square substitution > We worked out the units of BM and OU parameters in Cressler et al (2015). We parameterized it this way. If we have a trait X evolving under a Brownian motion, we can write the change in X per unit time as: dX(t) = sigma*dB(t) Where dX(t) (the change in X) will have the same units as X (in this case log-gm). and dB or a draw from the white noise distribution has units of time to the 1/2 power. Therefore sigma must have units of trait*time^(-1/2), and sigma^2 would have units of trait^2/time, or we will not obtain the correct units for X. Ted - yes, I agree with Joe - the matrix version of sigma and sigma^2 on a element-by-element basis will have the same units as the univariate case, except that you will have to substitute the units of each trait, as appropriate, if they are measured in different units. Marguerite > So (wait for it ...) square sites per square substitution > > Now that is pretty weird. But years ago people pointed out to me that > quantitative geneticists were accustomed to inferring variance > components of crop yield. The yield might be in bushels per acre. > So the units of its variance was: square bushels per square acre. > Don't even try to think about how you square a bushel, or how many > dimensions you have to go into to square an acre. Actually, you can > think about them: a bushel is three-dimensional volume, and an acre is > two dimensional area. So crop yield has units of meters, and > variance of crop yield should have units of square meters. > > That way lies madness ... > > Joe > ----- > Joe Felsenstein felse...@gmail.com, j...@gs.washington.edu > Department of Genome Sciences and Department of Biology, > University of Washington, Box 355065, Seattle, WA 98195-5065 USA > > _______________________________________________ > R-sig-phylo mailing list - R-sig-phylo@r-project.org > https://stat.ethz.ch/mailman/listinfo/r-sig-phylo > Searchable archive at > http://www.mail-archive.com/r-sig-phylo@r-project.org/ > -- ____________________________________________ Marguerite A. Butler Professor Department of Biology 2538 McCarthy Mall, Edmondson Hall 216 Honolulu, HI 96822 Office: 808-956-4713 Dept: 808-956-8617 Lab: 808-956-5867 FAX: 808-956-4745 http://butlerlab.org http://manoa.hawaii.edu/biology/people/marguerite-butler http://www2.hawaii.edu/~mbutler [[alternative HTML version deleted]] _______________________________________________ R-sig-phylo mailing list - R-sig-phylo@r-project.org https://stat.ethz.ch/mailman/listinfo/r-sig-phylo Searchable archive at http://www.mail-archive.com/r-sig-phylo@r-project.org/
