Likelihood Versus Bayesian Results

Given that Bayesian methods are relatively new in phylogenetics, it is reassuring that independent Bayesian runs with the full data set resulted in trees that are topologically identical to each other and to the maximum likelihood tree when analyses were performed under the GTR + r + I model of sequence evolution. Maximum likelihood bootstrap percentages were generally lower than Bayesian posterior probabilities. The observation that bootstrap support proportions are lower than Bayesian posterior probabilities has now become common (Douady et al., 2003; Huelsenbeck et al., 2002). As noted by Murphy et al. (2001b), this result is consistent with the suggestion of Hillis and Bull (1993) that nonparametric bootstrap support may be too conservative. Specifically, Hillis and Bull (1993) found that bootstrap proportions > 70% almost always defined a true clade in their study of a known bacteriophage T7 phylogeny. In our maximum likelihood bootstrap analysis, only four clades had support percentages below 70%. Efron et al. (1996) showed that bootstrap proportions (to a first approximation) are unbiased, but also that properties of the bootstrap underlie results like those of Hillis and Bull (1993). In an analysis using computer simulations, Wilcox et al. (2002) concluded that posterior probabilities are more reliable indicators of statistical confidence than bootstrap proportions. Huelsenbeck et al. (2002) suggested that the discrepancy between bootstrap proportions and posterior probabilities may reflect a statistical bias in uncorrected bootstrap proportions.

Whether or not bootstrap proportions are too conservative (for the best supported clades), other authors have concluded that Bayesian posterior probabilities may be too high (Suzuki et al., 2002; Waddell et al., 2001). Waddell et al. (2001) cautioned that Bayesian results are less robust than nonparametric bootstrap results in the face of model-violations. Elevated posterior probabilities may also result if Markov chain Monte Carlo runs fail to incorporate adequate mixing. In this context, it may be important to distinguish between posterior probabilities that are calculated analytically versus posterior probabilities that are estimated using MCMC (with or without Metropolis-coupling). Given that Bayesian phylogenetics is in its infancy, we can almost certainly expect improvements in methods that estimate posterior probabilities. Even if we ignore posterior probabilities, maximum likelihood bootstrap percentages above 90% occur over most of the tree and allow for only localized rearrangements. Maximum likelihood bootstrap support values for the four major groups (Xenarthra, Afrotheria, Laurasiatheria, Euarchontoglires), as well as for Boreoeutheria, were all 100%.

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