MBE Advance Access published online on February 2, 2005
Molecular Biology and Evolution, doi:10.1093/molbev/msi097
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1 Department of Biology, University College London, London, UK
* To whom correspondence should be addressed. Codon-based substitution models have been widely used to identify amino acid sites under positive selection in comparative analysis of protein-coding DNA sequences. The nonsynonymous/synonymous substitution rate ratio (dN/dS, denoted
Accepted January 25, 2005
Research Article
Bayes Empirical Bayes Inference of Amino Acid Sites under Positive Selection
2 Department of Biological Statistics and Computational Biology, Cornell University, Ithaca, NY 14850, USA
3 Department of Biological Statistics and Computational Biology, Cornell University, Ithaca, NY 14850, USA; Center for Bioinformatics, University of Copenhagen, Universitetsparken 15, 2100 Kbh 
, Denmark
Rasmus Nielsen, E-mail: rasmus{at}binf.ku.dk
Abstract 
) is used as a measure of selective pressure at the protein level, with > 1 indicating positive selection. Statistical distributions are used to model the variation in among sites, allowing a subset of sites to have > 1 while the rest of the sequence may be under purifying selection with < 1. An Empirical Bayes (EB) approach is then used to calculate posterior probabilities that a site comes from the site class with > 1. Current implementations, however, use the naïve EB (NEB) approach and fail to account for sampling errors in maximum likelihood estimates of model parameters, such as the proportions and ratios for the site classes. In small data sets lacking information, this approach may lead to unreliable posterior probability calculations. In this paper, we develop a Bayes Empirical Bayes (BEB) approach to the problem, which assigns a prior to the model parameters and integrates over their uncertainties. We compare the new and old methods on real and simulated data sets. The results suggest that in small data sets the new BEB method does not generate false positives as did the old NEB approach, while in large data sets it retains the good power of the NEB approach for inferring positively selected sites.
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T. Hernandez-Hernandez, L. P. Martinez-Castilla, and E. R. Alvarez-Buylla Functional Diversification of B MADS-Box Homeotic Regulators of Flower Development: Adaptive Evolution in Protein-Protein Interaction Domains after Major Gene Duplication Events Mol. Biol. Evol., February 1, 2007; 24(2): 465 - 481. [Abstract] [Full Text] [PDF]
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M. L. Porter, T. W. Cronin, D. A. McClellan, and K. A. Crandall Molecular Characterization of Crustacean Visual Pigments and the Evolution of Pancrustacean Opsins Mol. Biol. Evol., January 1, 2007; 24(1): 253 - 268. [Abstract] [Full Text] [PDF]
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 S. Cohen, J. Tirindelli, M. Gomez-Chiarri, and D. Nacci Functional implications of Major Histocompatibility (MH) variation using estuarine fish populations Integr. Comp. Biol., December 1, 2006; 46(6): 1016 - 1029. [Abstract] [Full Text] [PDF]
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L. Yu and Y.-p. Zhang The Unusual Adaptive Expansion of Pancreatic Ribonuclease Gene in Carnivora Mol. Biol. Evol., December 1, 2006; 23(12): 2326 - 2335. [Abstract] [Full Text] [PDF]
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M. R. Pie The Influence of Phylogenetic Uncertainty on the Detection of Positive Darwinian Selection Mol. Biol. Evol., December 1, 2006; 23(12): 2274 - 2278. [Abstract] [Full Text] [PDF]
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Z. Yang On the Varied Pattern of Evolution of 2 Fungal Genomes: A Critique of Hughes and Friedman Mol. Biol. Evol., December 1, 2006; 23(12): 2279 - 2282. [Abstract] [Full Text] [PDF]
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S. Foret and R. Maleszka Function and evolution of a gene family encoding odorant binding-like proteins in a social insect, the honey bee (Apis mellifera) Genome Res., November 1, 2006; 16(11): 1404 - 1413. [Abstract] [Full Text] [PDF]
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T. H. M. Mes and M. Doeleman Positive Selection on Transposase Genes of Insertion Sequences in the Crocosphaera watsonii Genome. J. Bacteriol., October 1, 2006; 188(20): 7176 - 7185. [Abstract] [Full Text] [PDF]
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G. Hall Selective constraint and genetic differentiation in geographically distant barley yellow dwarf virus populations. J. Gen. Virol., October 1, 2006; 87(Pt 10): 3067 - 3075. [Abstract] [Full Text] [PDF]
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L. M. Turner and H. E. Hoekstra Adaptive Evolution of Fertilization Proteins within a Genus: Variation in ZP2 and ZP3 in Deer Mice (Peromyscus) Mol. Biol. Evol., September 1, 2006; 23(9): 1656 - 1669. [Abstract] [Full Text] [PDF]
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I. Dupanloup and H. Kaessmann Evolutionary simulations to detect functional lineage-specific genes Bioinformatics, August 1, 2006; 22(15): 1815 - 1822. [Abstract] [Full Text] [PDF]
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T. M. Panhuis and W. J. Swanson Molecular Evolution and Population Genetic Analysis of Candidate Female Reproductive Genes in Drosophila Genetics, August 1, 2006; 173(4): 2039 - 2047. [Abstract] [Full Text] [PDF]
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L. Conde, J. M. Vaquerizas, H. Dopazo, L. Arbiza, J. Reumers, F. Rousseau, J. Schymkowitz, and J. Dopazo PupaSuite: finding functional single nucleotide polymorphisms for large-scale genotyping purposes. Nucleic Acids Res., July 1, 2006; 34(Web Server issue): W621 - W625. [Abstract] [Full Text] [PDF]
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M. Benderoth, S. Textor, A. J. Windsor, T. Mitchell-Olds, J. Gershenzon, and J. Kroymann Positive selection driving diversification in plant secondary metabolism PNAS, June 13, 2006; 103(24): 9118 - 9123. [Abstract] [Full Text] [PDF]
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