A Brief Introduction to Testing for Phylogenetic Signal in Comparative Data

Phylogenetic comparative methods (PCMs) were the subject of my last post. You can read it here (http://evolbiology.blogspot.ca/2012/09/phylogenetic-comparative-methods-some.html). It was a VERY brief description of two commonly employed PCMs (Phylogenetically Independent Contrasts and Phylogenetic Generalized Least Squares Regression). However, it is important to note that PCMs should not be applied unless their use is justified. It's true that the availability of phylogenies and the array of methods for reconstructing phylogenies has skyrocketed. As a result, reviewers are suggesting PCMs more and more. But it is important to consider whether PCMs are necessary and whether they add to your analysis or aid in the interpretation of your data. But how can you determine if your study needs PCMs?

One of the questions to ask is whether your data (rather the residuals; Revell 2010) are phylogenetically structured. In other words, do your data show phylogenetic signal? Two common methods are the K statistics of Blomberg et al. (2003) and Pagel's lambda (Pagel, 1999). The K statistic compares the observed and expected variance for calculated independent contrasts (Blomberg et al. 2009; Glor, 2009). Pagel's lambda is a multiplier of the off diagonal elements of the covariance matrix that varies between 0 and 1. Lambda transforms the phylogenetic tree with the purpose of comparing a complete lack of phylogenetic structure (lambda = 0; star phylogeny) to the untransformed topology and branch lengths of your original tree (lambda = 1) (Pagel, 1999; Gor, 2009). In other words, Pagel's lambda determines which situation, a star or structured phylogeny, fits your data best.

Here is some basic R code for using Blomberg et al.'s K:

require(picante)

# Help file http://127.0.0.1:17385/library/picante/html/phylosignal.html

kstat<-phylosignal(data,tree) 

# Your data must have matching taxon names or be sorted in the same order as the tip labels of the phylogeny

# This will return the K statistics and p value (as well as the variance of the independent contrasts and the associated z value)

Here is some basic R code for using Pagel's lambda:

require(phytools)
# Help file http://127.0.0.1:17385/library/phytools/html/phylosig.html
lamb<- phylosig(tree,data,method="lambda")
# Your data also require names that match the tip labels on the tree
# This will return a lambda value and log likelihood, values of lambda closer to 1 indicate singificant phylogenetic signal

Using the K statistic and Pagel's lambda, you can justify the use of PCMs or demonstrate that they are not necessary. Although I feel strongly that PCMs are powerful tools in comparative studies, I also feel they should only be used when it is statistically justifiable to do so.

You can follow the instructions of Glor (2009) to further understand Pagel's lambda. There are also other methods for testing for phylogenetic signal that I have not covered here.

References

Blomberg, S. P., T. Garland, Jr., and A. R. Ives. 2003. Testing for phylogenetic signal in comparative data: behavioral traits are more labile. Evolution 57:717-745.

Glor. 2009. IV. Testing Phylogenetic Signal in R. Bodega Phylogenetics Wiki.

Pagel, M. 1999. Inferring the historical patterns of biological evolution. Nature, 401, 877–884.

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