Hi David.
In general it is inconsequential whether X or Y are biologically
inherited traits; but whether the residual error in Y given X is
correlated or independent among species. In the case of "growth rate as
a function of habitat degradation" this corresponds to:
Growth Rate = beta0 + beta1*Habitat Degradation + e
It seems highly plausible that the residual error in Growth Rate (e),
that is error not explained by Habitat Degradation, is phylogenetically
correlated. This would imply only that closely related species have
growth rates that deviate from the mean relationship between growth rate
and habitat degradation in similar ways. In this case, PIC or some
other phylogenetic method should be used. To be clear also, contrasts
need to be computed for both X & Y regardless of whether or not there is
phylogenetic autocorrelation in both X & Y! (See Revell 2010, MEE; or,
better yet, Stone 2011, Syst. Biol. doi:10.1093/sysbio/syq098.)
Regarding extinction probability, perhaps someone else on the list can
address that specific example.
All the best, Liam
--
Liam J. Revell
University of Massachusetts Boston
web: http://faculty.umb.edu/liam.revell/
email: liam.rev...@umb.edu
blog: http://phytools.blogspot.com
On 11/10/2011 3:36 PM, David Bapst wrote:
Hello all,
A recent discussion set my mind thinking on a particular issue and, once
again, I decided to ask for the general opinion of R-Sig-Phylo denizens. It
may be easier to start with an example.
Let's say that there exists a worker who is measuring several different
traits across a number of species and then testing for correlations among
these traits. The first test is body size versus growth rate and they use
independent contrasts or PGLS to test for a the correlation, accounting for
phylogeny. Both of these traits are inherited, evolving variables. Now
let's say they'd like to test for the relationship between growth rate and
some metric of the anthropogenic degradation of that species' habitat. Now
what? It is even valid to apply PIC to the habitat degradation metric even
though it is not an inherited, evolving trait? It's unclear to me.
Let's consider a paleontological example, one which I have found myself
both strongly agreeing and disagreeing with at times. Essentially, how
should we test for extinction selectivity on some trait at a mass
extinction event? Let's say we think body size is a predictor of the risk
of extinction during that event and so we want to test for a correlation
between them (please ignore that extinction would be a discrete variable
for the moment). Do we treat these variable with PIC or PGLS? Is it really
proper to refer to the probability of going extinct during a mass
extinction as an evolving trait? Let's say we did and we got different
results than when we used an analysis which did not account for the
phylogenetic covariance. How should we interpret these results?
One explanation I know of is that when we apply phylogenetic comparative
methods to these quasi-traits to consider their relationship to another
trait, we are assuming that these variables are actually the result of some
underlying, unobserved set of traits which are evolving along the
phylogeny. This makes sense, maybe in the extinction event case, which
would mean that any PCM analysis would be testing for an evolutionary
relationship between body size and these unobserved traits which predict
extinction. Of course, if extinction risk is largely a function of
non-inherited traits, then the initial assumption may be incorrect (that
extinction risk itself is an evolving trait). Regardless, I don't see how
to apply that explanation to the habitat degradation example.
So, what do people think? How should we test for correlation when
non-evolving quasi-traits are involved? I'm very interested to hear
people's thoughts on this matter.
-Dave Bapst, UChicago
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