Potential Applications and Pitfalls of Bayesian Inference of Phylogeny

—Only recently has Bayesian inference of phylogeny been proposed. The method is now a practical alternative to the other methods; indeed, the method appears to possess advantages over the other methods in terms of ability to use complex models of evolution, ease of interpretation of the results, and computational efciency. However, the method should be used cautiously. The results of a Bayesian analysis should be examined with respect to the sensitivity of the results to the priors used and the reliability of the Markov chain Monte Carlo approximation of the probabilities of trees. [Bayesian inference; Markov chain Monte Carlo; phylogeny; posterior probability. ] In 1996, threegroups independently proposed using Bayesian inference of phylogeny. Rannala and Yang (1996), then at Berkeley, showed how posterior probabilities of trees, the central quantity in Bayesian inference of phylogeny, could be calculated under a birth–death prior for a small number of species. At about the same time, two groups of statisticians were doing much the same thing; Mau (1996) and Li (1996), at Wisconsin and Ohio State, respectively, published their dissertations that year, both showing how posterior probabilities of trees could be calculated under simple priors. The next few years saw the publication of a number of important papers, most of which concerned the nuts and bolts of calculating posterior probabilities for trees (Mau and Newton, 1997; Yang and Rannala, 1997; Larget and Simon, 1999; Mau et al., 1999; Newton et al., 1999). The method of choice for calculating posterior probabilities, in fact the only numerical method currently available that can approximate posterior probabilities for trees, is a technique rmly grounded in probability theory (Tierney, 1994) called Markov chain Monte Carlo (MCMC; Metropolis et al., 1953; Hastings, 1970; Green, 1995). The next few years also saw a number of papers that used Bayesian inference in a phylogenetic context to address questions such as “Is an amino acid under positive or diversifying selection? ” (Nielsen and Yang, 1998), “When did a group of species diverge? ” (Thorne et al., 1998; Huelsenbeck et al., 2000a), “Did hosts and parasites cospeciate? ” (Huelsenbeck et al., 2000b), and “What is the ancestral sequence for some clade? ” (Yang et al., 1995b; Huelsenbeck and Bollback, 2001). Once the theory had been described and a number of computer programs became available (BAMBE: Simon and Larget, 1998; MrBayes: Huelsenbeck and Ronquist, 2001), it was only amatter of time before the method became more widely used. The phylogenetics literature is full of new methods for estimating phylogeny, so the introduction of yet another method of phylogenetic inference does not seem like a portentous event. Moreover, Bayesian inference is not even new. Bayesian estimation is one of the oldest methods of statistical inference, dating back to the 18 century. A number of earlier papers had hinted at Bayesian inference of phylogeny. Felsenstein (1968), in his Ph.D. thesis, introduced a number of Bayesian ideas, such as posterior probabilities of trees (Felsenstein, 1968: 21–26) and a credible set of trees (Felsenstein, 1968:25–26; also see Wheeler, 1991). However, Felsenstein was not able to calculate posterior probabilities of trees at the time; Hastings’ seminal paper appeared two years later (1970), and it was another two decades before statisticians began to fully realize the power of the MCMC approach. Bayesian inference of phylogeny represents a signicant advance for a number of reasons. First, like the maximum likelihood method, Bayesian estimation of phylogeny is based on the likelihood function. The likelihood, a quantity that is proportional to the probability of observing the data conditional