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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