Accommodating Phylogenetic Uncertainty in Evolutionary Studies
Abstract
Many evolutionary studies use comparisons across species to detect evidence of natural selection and to examine the rate of character evolution. Statistical analyses in these studies are usually performed by means of a species phylogeny to accommodate the effects of shared evolutionary history. The phylogeny is usually treated as known without error; this assumption is problematic because inferred phylogenies are subject to both stochastic and systematic errors. We describe methods for accommodating phylogenetic uncertainty in evolutionary studies by means of Bayesian inference. The methods are computationally intensive but general enough to be applied in most comparative evolutionary studies.
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REFERENCES AND NOTES
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The posterior probability of the ith phylogenetic tree, τi, given a matrix of aligned sequences, X, is
where f(X￨τi) is the likelihood and f(τi) is the prior probability of the ith tree [here, f(τi) = 1/B(s)]. The summation is over all B(s) trees possible for s species. The likelihood is an integral over all possible branch lengths (vi) and parameters of the substitution model (θ)
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The joint posterior probability of p and μ were calculated with a program written by J.P.H. The posterior probability is
where D is the aphid caste data and C is a normalizing constant. The posterior probability distribution was approximated with MCMC (11, 12). An exponential prior was placed on the rate of change (μ) and a uniform prior on p. The results for an exponential prior with mean 1.0 are shown. However, the posterior probability of p was not affected by the prior placed on μ, suggesting that the inferences of the direction of change (p) are robust to assumptions about the rate of evolution of the aphid caste character (μ).
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We thank D. Stern for providing the aphid data and G. Bharathan for constructive comments on the study. B.R. was supported by NIH grant R01-HG01988.
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Published In
Science
Volume 288 | Issue 5475
30 June 2000
30 June 2000
Submission history
Received: 9 March 2000
Accepted: 2 May 2000
Published in print: 30 June 2000
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- John P. Huelsenbeck et al.
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