Bayesian reversible-jump MCMC: deflating inflated support values

Recently, on the Botanical Society of America Student ListServ, commonly-used phylogenetic methods were being discussed, and a specific problem was raised with regard to Bayesian phylogenetic inference: it has been documented that, within a Bayesian framework, support values (in the form of posterior probabilities) can become inflated or skewed.  This is an issue of special interest to me, since I commonly use Bayesian inference alongside other phylogenetic methods in my research (e.g., Hodkinson & Lendemer 2010, Hodkinson & Lutzoni 2009, Miadlikowska et al. 2006).  I decided to contribute to the discussion by sending the following message to the ListServ:

"
I have found that Bayesian phylogenetic inference methods can do amazing things (like finding the same topology with one gene that only emerges with two or three genes in an analysis based on maximum parsimony (MP) or maximum likelihood (ML)).  However, this problem of Bayesian methods inflating support (especially at short internodes) makes me feel very suspicious of any given Bayesian posterior probability value. Therefore, if I want to evaluate support, I always look at MP- and/or ML-bootstrap proportions.  The Bayesian problem that we're talking about has been discussed by Lewis et al. (2005), and they state that the solution is to use reversible-jump MCMC (rjMCMC).  However, I have wondered myself how I could actually implement this.

I recently found an article that clearly stated the fact that MrBayes and BEAST cannot perform rjMCMC (Kodandaramaiah et al. 2010): http://dx.doi.org/10.1016/j.ympev.2009.08.012
In this article, they used Phycas for their rjMCMC analyses.

So I went to the Phycas manual (Lewis et al. 2010), and found that it does give the nitty-gritty of how to implement this (see section 2.3 on 'Polytomy Priors'):
http://phylo.bio.ku.edu/phycas/manual.pdf
I have not yet done it myself, but I am very excited to try it out!  Perhaps now I will have more faith in my posterior probabilities!
"

The Phycas manual gives the best, most concise summary of the issue that I have seen anywhere:

"
A solution to the 'Star Tree Paradox' problem was proposed by Lewis, Holder, and Holsinger (2005). Their solution was to use reversible-jump MCMC to allow unresolved tree topologies to be sampled during the course of a Bayesian phylogenetic analysis in addition to fully-resolved tree topologies. If the time between speciation events is so short (or the substitution rate so low) that no substitutions occurred along a particular internal edge in the true tree, then use of the polytomy prior proposed by Lewis, Holder, and Holsinger (2005) can improve inference by giving the Bayesian model a 'way out.' That is, it is not required to find a fully resolved tree, but is allowed to place a lot of posterior probability mass on a less-than-fully-resolved topology. Please refer to the Lewis, Holder, and Holsinger (2005) paper for details.
"

Please post comments here if you have performed these types of analyses and have any additional insights!

-Brendan

P.S. Please see my more recent posts for the details of using Phycas:
http://squamules.blogspot.com/2011/06/installing-and-running-phycas.html
http://squamules.blogspot.com/2011/06/writing-phycas-script.html

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Works Cited:

Hodkinson, B. P., and J. C. Lendemer. 2011. Molecular analyses reveal semi-cryptic species in Xanthoparmelia tasmanica. Bibliotheca Lichenologica 106: 115-126.
Download draft (PDF file)
Download alignment (NEXUS file)

Hodkinson, B. P., and F. Lutzoni. 2009. A microbiotic survey of lichen-associated bacteria reveals a new lineage from the Rhizobiales. Symbiosis 49: 163-180.
Download publication (PDF file)
Download alignment (NEXUS file)

Kodandaramaiah U., C. Pena, M. F. Braby, R. Grund, C. J. Muller, S. Nylin, and N. Wahlberg. 2010. Phylogenetics of Coenonymphina (Nymphalidae: Satyrinae) and the problem of rooting rapid radiations. Molecular Phylogenetics and Evolution 54(2): 386-394.
View Publication (webpage)

Lewis, P. O., M. T. Holder, and K. E. Holsinger. 2005. Polytomies and Bayesian phylogenetic inference. Systematic Biology 54(2): 241-253
View Publication (webpage)

Lewis, P. O., M. T. Holder, and D. L. Swofford. 2010. Phycas User Manual, Version 1.2.0.
View Manual (PDF file)

Miadlikowska, J., F. Kauff, V. Hofstetter, E. Fraker, M. Grube, J. Hafellner, V. Reeb, B. P. Hodkinson, M. Kukwa, R. Lücking, G. Hestmark, M. Garcia Otalora, A. Rauhut, B. Büdel, C. Scheidegger, E. Timdal, S. Stenroos, I. Brodo, G. Perlmutter, D. Ertz, P. Diederich, J. C. Lendemer, P. May, C. L. Schoch, A. E. Arnold, C. Gueidan, E. Tripp, R. Yahr, C. Robertson, and F. Lutzoni. 2006. New insights into classification and evolution of the Lecanoromycetes (Pezizomycotina, Ascomycota) from phylogenetic analyses of three ribosomal RNA- and two protein-coding genes. Mycologia 98: 1088-1103.
Download publication (PDF file)
Download supplement (PDF file)
Download alignment (zipped NEXUS file)