Hola Adrián,

Here is my grain of sand. The lambda parameter you estimate gives you an idea 
of the evolutionary co-variance between all the traits included in the model, 
its the same interpretation as for the single trait, but in the case of 
multiple traits it provides information on the evolutionary co-variance as 
lambda estimates the phylogenetic signal of the residuals of the regression. An 
important point to add is that it is the evolutionary co-variance given the 
model of evolution, in this case Brownian motion, which has its underlying 
assumptions. You can look at recent papers by Tomas Hansen on this issue.
 
There is quite a bit of literature on the subject, I can venture to recommend a 
few papers and maybe others in the list can add more:

Martins and Hansen 1997 Phylogenies and the comparative method: a general 
approach to incorporating phylogenetic information into the analysis of 
interspecific data. American Naturalist 149

Rholf 2006 A comment on phylogenetic correction. Evolution 60: 1509-1515

Revell 2010 Phylogenetic signal and linear regression on species data. Methods 
in Ecology and Evolution 1: 319-329

Revell et al 2008 Phylogenetic signal, evolutionary process and rate. 
Systematic Biology 57: 591-601

Freckleton et al 2002 Phylogenetic analysis and comparative data: a test and 
review of evidence American Naturalist 160: 712-726

Freckleton 2009 Seven deadly sins of comparative analysis. J Evol Biol  22: 
1367-1375


Cheers

Alejandro


On 8, Aug 2013, at 2:33 PM, Adrián Arellano Davín wrote:

> Hi all,
> 
> First of all, I am very much a newbie in phylogenetics, so the question I
> will ask may be a bit naïve. Here it is:
> 
> I want to correlate some phenotypic traits of several species of animals.
> Let's say, body mass and brain size. To account for the non-independence of
> the points, I must use PGLS. One way to do this is searching a lambda
> parameter that maximises the likelihood of my tree under a Brownian Model
> of evolution.
> 
> I think I can understand the meaning of having a lambda value for one
> phenotypic trait. And I think it makes sense because it gives you a rough
> idea of what kind of evolution is going on. But, what is the purpose of
> calculating a lambda for several traits at the same time? Does it make
> sense at all? Is it just a mathematical trick with no biological meaning?
> 
> Thanks in advance
> 
> Adri
> 
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> 
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__________________________________

Alejandro Gonzalez Voyer

Post-doc

Estación Biológica de Doñana
Consejo Superior de Investigaciones Científicas (CSIC)
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Spain

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