One thing that is a bit odd, to me, about applying these Pagel-type
transformations is that the parameters interact, as you suggest. This
means that you can't compare parameter values across different models
- so that a lambda from a lambda+delta model is a different thing from
a lambda from a lambda-alone model. Additionally, parameters can
affect estimates of the rate parameter, because they change the time
scale of the tree; so you can't compare sigma-squared values
(continuous characters) or q-matrices (discrete characters) between
different models. Finally, I think that the order that you apply these
transformations probably matters, so that if you "lambda" the matrix
first, then "delta" it, you will get a different result from the
alternative order.
I do think Pagel's transformations are valuable, and give us
information about macroevolution. But, as Dan suggests, perhaps models
that have more straightforward, biological interpretations won't
exhibit these types of behaviors?
Luke
On Apr 8, 2009, at 5:50 AM, Dan Rabosky wrote:
Hi Folks-
Many thanks for the thoughtful and informative discussion of
phylogeny-based size and shape transformations for morphometric
analyses. I have another discussion question!
I'd be really interested to hear what others think about conducting
and/or interpreting multiple Pagel-type tree transformations (lambda,
kappa, delta) during a single analysis. For example Pagel (2002,
chapter in morphometrics book, title escaping me at the moment) fits,
simultaneously, all three of these parameters to a hominid cranial
capacity dataset. I have seen this done by others, and I think
Bayestraits explicitly enables you to do this.
In general, I am a fan of these transformations in the univariate
case. But I find that my ability to interpret these parameters goes
out the window when considering pairwise and higher-order tree
transformations. If you find that the best fit model has delta=0.25
with all internal branches multiplied by lambda=0.5, what does this
mean? And how do you interpret this if you are fitting lambda and
delta onto a speciational tree (kappa=0)?
Likewise, the idea of finding the ML lambda estimate, then rescaling
the tree by this value, then estimating delta etc also leaves me
unsettled. It seems like with a preliminary lambda transformation,
you are warping the tree in a way that may not correspond to a
biologically relevant model of trait evolution. What sort of
biologically-relevant processes are we then inferring if we use this
warped tree to make inferences about other parameters that entail
further tree transformation?
Thoughts appreciated.
~Dan
Dan Rabosky
Department of Ecology and Evolutionary Biology &
Fuller Evolutionary Biology Program
Cornell Lab of Ornithology
Cornell University
http://www.eeb.cornell.edu/Rabosky/dan/main.html
[[alternative HTML version deleted]]
_______________________________________________
R-sig-phylo mailing list
[email protected]
https://stat.ethz.ch/mailman/listinfo/r-sig-phylo
_______________________________________________
R-sig-phylo mailing list
[email protected]
https://stat.ethz.ch/mailman/listinfo/r-sig-phylo
