[R-sig-phylo] Pagel-type tree transformations

Luke Harmon lukeh at uidaho.edu
Wed Apr 8 18:43:58 CEST 2009

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?

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
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