Hi David.
> Poaching Intensity = beta0 + beta1*Body Size + e
I think it depends on how the residual error in the model is distributed
(esp. correlated) among species. It seems possible to invent
hypothetical scenarios (as I did in my previous email) about how the
residual error in poaching intensity given body size could be
phylogenetically autocorrelated, but this is fundamentally an empirical
question. If the residual error of poaching intensity given body size
is phylogenetically correlated and we ignore this then we risk
overestimating the predictive value of our model.
In addition, the residual error is likely/guaranteed to be non-Brownian
if the response variable is binary (e.g., extant v. extinct). For these
type of data the tree should not be ignored, but simple GLS regression
is probably not appropriate. One option might be the phylogenetic
logistic regression of Ives & Garland (2009), but I'm not too familiar
with this method.
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 11/14/2011 3:54 PM, David Bapst wrote:
Liam, Joe, Pasquale, all-
Thank you for your kind input.It seems that I am not the only one who
considers this issue at length.
There is just one point I'd like clarification of. Liam, in my first
example which you used, the inherited trait is the response and the
not-directly-inheritable trait the predictor, such that:
Growth Rate = beta0 + beta1*Habitat Degradation + e
What if we were to switch these? It seems to me this is the only real
difference in the extinction example. To make a neontological example,
let's say we were interested in whether larger mammals were more likely
to experience higher levels of poaching. The response here would be the
poaching intensity and body size the predictor, such that:
Poaching Intensity = beta0 + beta1*Body Size + e
Would your argument still apply? (It seems to me that it should.) If so,
then it would seem your explanation should equally apply to extinction
selectivity cases.
-Dave
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
--
David Bapst
Dept of Geophysical Sciences
University of Chicago
5734 S. Ellis
Chicago, IL 60637
http://home.uchicago.edu/~dwbapst/ <http://home.uchicago.edu/%7Edwbapst/>
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