T80SMS1@niu.bitnet (05/28/90)
>I've been trying to figure out the Cheverud-Dow-Leutenegger (CDL) method of >phylogenetic autocorrelation, and am stuck. >The equations implied by this path diagram are > > r = s1 s2 rS + q1 q2 rP > 1 = s12 + q12 > 1 = s22 + q22 > >where r is the correlation between X1 and X2. CDL's autocorrelation method >gives us the values of s1 and s2, and the 2nd and 3rd equations then tell us >q1 and q2. This leaves 1 equation in two unknowns (rS and rP), which would >appear to have no unique solution. Can anyone suggest where we might find >n additional equation that might give this system a sensible answer? My understanding is that rP is determined from independent information, ie. other characters are first used to determine the phylogeny. Thus, equation 1 has only 1 unknown and a unique solution. Sam Scheiner Northern Illinois University t80sms1@niu.bitnet
joe@GENETICS.WASHINGTON.EDU (Joe Felsenstein) (05/30/90)
In regard to Cheverud, Dow, and Leutenegger's method, I asked them when I was shown a preprint of their work to explain how it related to other methods such as my own contrasts method of 1985 (American Naturalist) but have never seen it adequately explained. One difficulty with their approach is that when two characters are evolving in a correlated fashion this should show up in BOTH the "phylogenetic" and "specific" components. I believe that their method assumes that only the latter is to be used to estimate the correlation. If so then it must lose some power. I think there may also be a degrees-of-freedom problem. If there are four species then my method forms three contrasts and estimates regressions, correlations, etc from those. Theirs seems to make the estimate from four specific components, which seems to me to be one too many. Alan's simulations seem to show reasonable behavior but I would be interested in seeing whether it really does have the postulated distribution. I would welcome being corrected on this. ----- Joe Felsenstein, Dept. of Genetics, Univ. of Washington, Seattle, WA 98195 Internet/ARPANet: joe@genetics.washington.edu (IP No. 128.208.128.1) BITNET/EARN: FELSENST@UWALOCKE UUCP: ... uw-beaver!uw-entropy!uw-evolution!joe