HXH5@PSUVM.PSU.EDU (05/26/90)
I read one of those papers once and it seemed to me that the covariance between ecology and phylogeny was (arbitrarily) added to the phylogenetic variance--then the paper concluded that phylogeny accounted for whatever it was, mating systems and dimorphism or something. I never followed up on it. Is this part of the same thing??
rogers@ARSUN.UTAH.EDU (Alan R. Rogers) (05/27/90)
I've been trying to figure out the Cheverud-Dow-Leutenegger (CDL) method of
phylogenetic autocorrelation, and am stuck. I am posting my confusion in
the hope of generating a dialogue about (1) whether the problem I perceive is
real or not (2) how well the method works.
The aim of the method is to estimate the correlation, over several species,
of two characters. This is not a trivial problem because the data points are
not independent: closely related species tend to be more similar than random
pairs of species. CDL develop their method in two stages, the first of
which estimates the "phylogenetic constraint" involved in each character,
and the second of which attempts to estimate the correlation between what
are called the "specific components" of each character. It all boils down
to a path analysis problem which, in simplified form, looks something like
this:
s1
/- S1 -------\
| X1
/---+- P2 -------/
| rS| q1
| |
| | s2
rP| \- S2 -------\
| X2
\----- P2 -------/
q2
Here, Si and Pi represent the "phylogenetic" and "specific" components of Xi,
and si and pi are the corresponding path coefficients. rS and rP are the
correlations between specific and phylogenetic components, respectively.
The equations implied by this path diagram are
r = s1 s2 rS + q1 q2 rP
1 = s1^2 + q1^2
1 = s2^2 + q2^2
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
an additional equation that might give this system a sensible answer?
CDL, by the way, study systems with more than two variables. The problem
would appear to be even worse there, since each new variable adds more
parameters than it adds observable correlations. For example, adding one
more variable to a system of K variables would add K observable correlations
(one with each of the original variables), but 2K unobservable parameters
that must be estimates (K correlations between specific values, and K
between phylogenetic values).
Help!!
Alan Rogers
INTERNET: rogers@arsun.utah.edu
USMAIL : Dept. of Anthropology, Univ. of Utah, S.L.C., UT 84112
PHONE : (801) 581-5529rogers@ARSUN.UTAH.EDU (Alan R. Rogers) (05/31/90)
I share Felsenstein's skepticism about the method, but that skepticism does
not seem to be supported by the simulations I have been doing. Cheverud,
Dow, and Leutenegger do argue that all the information will be in the
specific component, and none in the phylogenetic component. I didn't believe
this either, but the results are as they claim. Here is a plot of the
estimated phylogenetic correlation against the true value:
1 ......................................................................
. . ****** ****** **** ********************************************* .
0 . * * ***** ** ** ** ************** **** *********** **** * .
0 . ** * * * * * * ** ** * * ** *** **** * * * * * .
. . ** *** * * *** * ** * * ** ** * * .
r 5 . * ** ** *** ** * * * * * ** *** ** * ** * .
. 0 . ** ** * ** ** * * ***** * * * ******** * .
p . . * * *** * * ** ** ****** * * *** ** * * .
h 0 . ** *** ** *** *** * ** * * * * ** * * .
y . ******* ** * * ** ** * * * * .
. * * * ** * * * *** * *** *** ** * ** * * * .
. ** ** ****** * ** * ** *** *** ** ** * ** * ** * .
- . ****** ** ********** ***** * **** ************* *** ** * .
1 . ********************************** ***** *********** *** ******* .
. ......................................................................
0 -1.0 -0.5 0.0 0.5 1.0
rho
Alan Rogers
INTERNET: rogers@arsun.utah.edu
USMAIL : Dept. of Anthropology, Univ. of Utah, S.L.C., UT 84112
PHONE : (801) 581-5529joe@GENETICS.WASHINGTON.EDU (Joe Felsenstein) (05/31/90)
Alan Rogers writes: > > I share Felsenstein's skepticism about the method, but that skepticism does > not seem to be supported by the simulations I have been doing. Cheverud, > Dow, and Leutenegger do argue that all the information will be in the > specific component, and none in the phylogenetic component. I didn't believe > this either, but the results are as they claim. Here is a plot of the > estimated phylogenetic correlation against the true value: I don't get it -- your plot is pure noise, so what does it prove? I think maybe it is a plot of residuals or something. You must have meant something by it that wasn't explained. As for your statement that "I didn't believe this either but the results are as they claim," Well, I STILL don't believe that all of the information is in the specific component. Successful estimation of rho from that component does not prove that it has all the information, just that it has some. ----- 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
rogers@ARSUN.UTAH.EDU (Alan R. Rogers) (05/31/90)
Joe Felsenstein comments: >I don't get it -- your plot is pure noise, so what does it prove? I think >maybe it is a plot of residuals or something. You must have meant something >by it that wasn't explained. So let me explain. The vertical axis of the "pure noise" plot was the correlation between the estimated phylogenetic values of X1 and X2, and the horizontal axis is the true correlation (rho) of X1 and X2. Cheverud, Dow, and Leutenegger claim that the phylogenetic component carries no information about rho, and that claim is supported by the graph. >As for your statement that "I didn't believe this either but the results are >as they claim," Well, I STILL don't believe that all of the information is >in the specific component. Successful estimation of rho from that component >does not prove that it has all the information, just that it has some. Me neither, but I am also at a loss to explain my own simulations. Alan Rogers INTERNET: rogers@arsun.utah.edu USMAIL : Dept. of Anthropology, Univ. of Utah, S.L.C., UT 84112 PHONE : (801) 581-5529