Ted wrote: > Following on that, various papers (I can't remember the references) > have argued that imagining Brownian-like evolution of body size on a > log scale seems reasonable. That is, it should be equally easy for an > elephant's body size to evolve 10% as for a mouse's body size to > evolve 10%, and to analyze that you want everybody on a log scale. > Extending this, you would want to use log(Y/X) or log(Y/[X raised to > some allometric slope]).
It's just easier to put all variables onto their log scales, so you have log(X), log(Y), log(Z) and then the allometric stuff just corresponds to linear combinations there, which you already have machinery to do. The recommendation to use log scales is a very old one: I talk about it in my "Theoretical Evolutionary Genetics" free e-text. But is older than that. Falconer has a whole chapter on "Scale" in his 1960 "Introduction of Quantitative Genetics". Sewall Wright has a discussion of it in Chapter 10 of his 1968 first volume of "Evolution and the Genetics of Populations" (see pages 227ff.). But it is older than those -- for Wright also says (p. 228): "Galton, as long ago as 1879, noted that the logarithms of measurements of organisms may be more appropriate than the measurements themselves on the hypothesis that growth factors tend to contribute constant percentage increments rather than constant absolute ones." The old biometrical types of the 1930s and 1940s knew all about this (though taking logarithms was tedious). It is only the more recent researchers who don't know it. Joe ---- Joe Felsenstein 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
