[R-sig-phylo] Model-Selection vs. Finding Models that "Fit Well"

Joe Felsenstein joe at gs.washington.edu
Mon Jan 31 22:02:38 CET 2011

David Bapst and Cecile Ane noted that

> On Mon, Jan 31, 2011 at 12:45 PM, Cecile Ane <ane at stat.wisc.edu> wrote:
> > I don't find the white noise to be any good evolutionary scenario: it's
> > nowhere continuous. It just reduces to the assumption of normal,
> independent
> > observations at the tips. Nothing fancy, then :)
> I think it is a bit problematic that WN could fit equally well to a
> situation with zero heritability and an OU1 scenario with infinite alpha. I
> guess one could check if there is any relationship between the magnitude of
> evolutionary change and distance from the mean (as it is generally expected
> under OU that changes are more minor closer to the optima). But perhaps even
> that relationship goes away as alpha approaches infinity. It would also be
> difficult to assess, because phylogenetic signal would be too low for
> ancestral state reconstruction to work with confidence.

Lack of continuity does not worry me: if we have (say) discrete generations
as in annual plants, nothing is continuous anyway.  And our observations
are rarely closely-enough spaced to be sensitive to that issue anyway.

The problem with WN (i.e. tips i.i.d. and from multivariate normal) is that,
although it connects to OU and to other models, in each case that is in a 
limit as some parameter goes off to infinity.   In those cases I think WN
as a null hypothesis is going to be difficult, as it will not be
contained within the alternative hypotheses in a way that allows a
Likelihood Ratio Test.   And I suspect that it would give trouble also in
a Bayesian framework, though that is just a suspicion.

Joe Felsenstein         joe at gs.washington.edu
 Department of Genome Sciences and Department of Biology,
 University of Washington, Box 355065, Seattle, WA 98195-5065 USA

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