Model selection and model averaging in phylogenetics: Advantages of akaike information criterion and bayesian approaches over likelihood ratio tests

Systematic Biology

Volumn 53, Issue 5, 2004, Pages 793-808

  Posada, David ^a   Buckley, Thomas R ^b  

^a UNIVERSITY OF VIGO   (Spain)

^b LANDCARE RESEARCH   (New Zealand)

Author keywords

AIC; Bayes factors; BIC; Likelihood ratio tests; Model averaging; Model selection; Model uncertainty; Multimodel inference

Indexed keywords

MITOCHONDRIAL DNA;

ANIMAL; BAYES THEOREM; BEETLE; BIOLOGICAL MODEL; CLASSIFICATION; COMPARATIVE STUDY; GENETICS; METHODOLOGY; PHYLOGENY; REVIEW; STATISTICAL MODEL;

ANIMALS; BAYES THEOREM; BEETLES; CLASSIFICATION; DNA, MITOCHONDRIAL; LIKELIHOOD FUNCTIONS; MODELS, GENETIC; PHYLOGENY;

CARABIDAE; COLEOPTERA; OHOMOPTERUS;

EID: 9644301241     PISSN: 10635157     EISSN: None     Source Type: Journal    
DOI: 10.1080/10635150490522304     Document Type: Review

References (165)

1. Adachi, J., and M. Hasegawa. 1996. MOLPHY version 2.3: Programs for molecular phylogenetics based in maximum likelihood. Comput. Sci. Monogr. 28:1-150.
2. Agresti, A. 1990. Categorical data analysis, 2nd edition. Wiley, New York.
3. Akaike, H. 1973. Information theory and an extension of the maximum likelihood principle. Pages 267-281 in Second International Symposium on Information Theory. Akademiai Kiado, Budapest.
4. Akaike, H. 1974. A new look at the statistical model identification. IEEE Trans. Aut. Control 19:716-723.
5. Akaike, H. 1981. Likelihood of a model and information criteria. J. Econometrics 16:3-14.
6. Akaike, H. 1983. Information measures and model selection. Int. Stat. Inst. 22:277-291.
7. Anderson, D. R., K. P. Burnham, and W. L. Thompson. 2000. Null hypothesis testing: Problems, prevalence, and an alternative. J. Wildl. Manage 64:912-923.
8. Aris-Brosou, S., and Z. Yang. 2002. Effects of models of rate evolution on estimation of divergence dates with special reference to the metazoan 18S ribosomal RNA phylogeny. Syst. Biol. 51:703-714.
9. Bartlett, M. S. 1957. A comment on D. V. Lindley's statistical paradox. Biometrika 44:533-534.
10. Berger, J. O., and T. Sellke. 1987. Testing a point null hypothesis: The irreconcilability of P values and evidence. J. Am. Stat. Assoc. 82:112-122.
11. Bernardo, J. M., and A. F. M. Smith. 1994. Bayesian theory. Wiley and Sons, New York.
12. Bollback, J. P. 2002. Bayesian model adequacy and choice in phylogenetics. Mol. Biol. Evol. 19:1171-1180.
13. Box, G. E. P. 1976. Science and statistics. J. Am. Stat. Assoc. 71:791-799.
14. Bozdogan, H. 1987. Model selection and Akaike's information criterion (AIC): The general theory and its analytical extensions. Psychometrika 52:345-370.
15. Browne, M. 2000. Cross-validation methods. J. Math. Psychol. 44:108-132.
16. Bruno, W. J., and A. L. Halpern. 1999. Topological bias and inconsistency of maximum likelihood using wrong models. Mol. Biol. Evol. 16:564-566.
17. Buckley, T. R. 2002. Model misspecification and probabilistic tests of topology: Evidence from empirical data sets. Syst. Biol. 51:509-523.
18. Buckley, T. R., P. Arensburger, C. Simon, and G. K. Chambers. 2002. Combined data, Bayesian phylogenetics, and the origin of the New Zealand cicada genera. Syst. Biol. 51:4-18.
19. Buckland, S. T., K. P. Burnham, and N. H. Augustin. 1997. Model selection uncertainty: An integral part of inference. Biometrics 53:603-618.
20. Buckley, T. R., and C. W. Cunningham. 2002. The effects of nucleotide substitution model assumptions on estimates of nonparametric bootstrap support. Mol. Biol. Evol. 19:394-405.
21. Buckley, T. R., C. Simon, and G. K. Chambers. 2001. Exploring among-site rate variation models in a maximum likelihood framework using empirical data: The effects of model assumptions on estimates of topology, branch lengths, and bootstrap support. Syst. Biol. 50:67-86.
22. Burnham, K. P., and D. R. Anderson. 1998. Model selection and inference: A practical information-theoretic approach, 1st ed. Springer-Verlag, New York.
23. Burnham, K. P., and D. R. Anderson. 2003. Model selection and multimodel inference: A practical information-theoretic approach, 2nd ed. Springer-Verlag, New York.
24. Burnham, K. P., D. R. Anderson, and G. C. White. 1994. Evaluation of the Kullback-Leibler discrepancy for model selection in open population capture-recapture models. Biometrica J. 36:299-315.
25. Cavanaugh, J. E., and A. A. Neath. 1999. Generalizing the derivation of the Schwarz information criterion. Commun. Stat. Theory Methods 28:49-66.
26. Chamberlain, T. C. 1890. The method of multiple working hypotheses. Science 15:93.
27. Chatfield, C. 1995. Model uncertainty, data mining and statistical inference. J. R. Stat. Soc. A 158:419-466.
28. Churchill, G. A., A. Von Haeseler, and W. C. Navidi. 1992. Sample size for a phylogenetic inference. Mol. Biol. Evol. 9:753-769.
29. Deleeuw, J. 1992. Introduction to Akaike (1973) information theory and an extension of the maximum likelihood principle. Pages 599-609 in Breakthroughs in statistics (S. Kotz, and N. L. Johnson, eds.). Springer-Verlag, London.
30. Edwards, A. W. F. 1972. Likelihood. Cambridge University Press, Cambridge, UK.
31. Efron, B., and R. J. Tibshirani. 1993. An Introduction to the Bootstrap. Chapman and Hall, New York.
32. Felsenstein, J. 1978. Cases in which parsimony or compatibility methods will be positively misleading. Syst. Zool. 27:401-410.
33. Felsenstein, J. 1981a. Evolutionary trees from DNA sequences: A maximum likelihood approach. J. Mol. Evol. 17:368-376.
34. Felsenstein, J. 1981b. A likelihood approach to character weighting and what it tells us about parsimony and compatibility. Biol. J. Linnaean Soc. 16:183-196.
35. Findley, D. F. 1991. Counterexamples to parsimony and BIC. Ann. Inst. Stat. Math. 43:505-514.
36. Fisher, R. A. 1921. On the 'probable error' of a coefficient of correlation deduced from a small sample. Metron I, part 4:3-32.
37. Forster, M. R. 2000. Key Concepts in model selection: Performance and generalizability. J. Math. Psychol. 44:205-231.
38. Forster, M. R. 2001. The new science of simplicity. Pages 83-119 in Simplicity, inference and modeling (A. Zeller, H. A. Keuzenkamp, and M. McAleer, eds.). Cambridge University Press, Cambridge, UK.
39. Forster, M. R. 2002. Predictive accuracy as am achievable goal of science. Phil. Sci. 69:S124-S134.
40. Forster, M., and E. Sober. 1994. How to tell when simpler, more unified, or less ad hoc theories will provide more accurate predictions. Br. J. Phil. Sci. 45:1-35.
41. Forster, M. R., and E. Sober. 2004. Why likelihood? in Likelihood and Evidence (M. Taper, and S. Lele, eds.). University of Chicago Press, Chicago.
42. Foulds, L. R., M. D. Hendy, and D. Penny. 1979. A graph theoretic approach to the development of minimal phylogenetic trees. J. Mol. Evol. 13:127-149.
43. Foutz, R. V., and R. C. Srivastava. 1977. The performance of the likelihood ratio test when the model is incorrect. Ann. Stat. 5:1183-1194.
44. Frati, F., C. Simon, J. Sullivan, and D. L. Swofford. 1997. Gene evolution and phylogeny of the mitochondrial cytochrome oxidase gene in Collembola. J. Mol. Evol. 44:145-158.
45. Gelfand, A. E. 1996. Model determination using sampling-based methods. Pages 145-161 in Markov chain Monte Carlo in practice (W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, eds.). Chapman & Hall, London, New York.
46. Gilks, W. R., S. Richardson, and D. J. Spiegelhalter (eds.) 1996. Markov chain Monte Carlo in practice. Chapman & Hall, London, New York.
47. Golden, R. M. 1995. Making correct statistical inferences using a wrong probability model. J. Math. Psychol. 38:3-20.
48. Goldman, N. 1990. Maximum likelihood inference of phylogenetic trees, with special reference to a Poisson process model of DNA substitution and to parsimony analyses. Syst. Zool. 39:345-361.
49. Goldman, N. 1993. Statistical tests of models of DNA substitution. J. Mol. Evol. 36:182-198.
50. Goldman, N. 1998. Phylogenetic information and experimental design in molecular systematics. Proc. R. Soc. Lond. B Biol. Sci. 265:1779-1786.
51. Goldman, N., and S. Whelan. 2000. Statistical tests of gamma-distributed rate heterogeneity in models of sequence evolution in phylogenetics. Mol. Biol. Evol. 17:975-978.
52. Green, P. J. 1995. Reversible jump MCMC computation and Bayesian model determination. Biometrika 92:711-732.
53. Hasegawa, M. 1990a. Mitochondrial DNA evolution in primates: Transition rate has been extremely low in the lemur. J. Mol. Evol. 31:113-121.
54. Hasegawa, M. 1990b. Phylogeny and molecular evolution in primates. Jpn. J. Genet. 65:243-266.
55. Hasegawa, M., K. Kishino, and T. Yano. 1985. Dating the human-ape splitting by a molecular clock of mitochondrial DNA. J. Mol. Evol. 22:160-174.
56. Hastings, W. K. 1970. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57:97-109.
57. Hochberg, Y. 1988. A sharper Bonferroni procedure for multiple tests of significance. Biometrika 75:800-802.
58. Hoeting, J. A., D. Madigan, and A. E. Raftery. 1999. Bayesian model averaging: A tutorial. Stat. Sci. 14:382-417.
59. Holder, M., and P. O. Lewis. 2003. Phylogeny estimation: Traditional and Bayesian approaches. Nat. Rev. Genet. 4:275-284.
60. Hsiao, C. K. 1997. Approximate Bayes factors when a mode occurs on the boundary. J. Am. Stat. Assoc. 92:656-663.
61. Huelsenbeck, J. P., and K. A. Crandall. 1997. Phylogeny estimation and hypothesis testing using maximum likelihood. Annu. Rev. Ecol. Syst. 28:437-466.
62. Huelsenbeck, J. P., and D. M. Hillis. 1993. Success of phylogenetic methods in the four-taxon case. Syst. Biol. 42:247-264.
63. Huelsenbeck, J. P., and N. S. Imennov. 2002. Geographic origin of human mitochondrial DNA: Accommodating phylogenetic uncertainty and model comparison. Syst. Biol. 51:155-165.
64. Huelsenbeck, J. P., B. Larget, and M. E. Alfaro. 2004. Bayesian phylogenetic model selection using reversible jump Markov chain Monte Carlo. Mol. Biol. Evol. 21:1123-1133.
65. Huelsenbeck, J. P., B. Larget, R. E. Miller, and F. Ronquist. 2002. Potential applications and pitfalls of Bayesian inference of phylogeny. Syst. Biol. 51:673-688.
66. Huelsenbeck, J. P., B. Rannala, and B. Larget. 2000. A Bayesian framework for the analysis of cospeciation. Evol. Int. J. Org. Evol. 54:352-364.
67. Huelsenbeck, J. P., F. Ronquist, R. Nielsen, and J. P. Rollback. 2001. Bayesian inference of phylogeny and its impact on evolutionary biology. Science 294:2310-2314.
68. Hurvich, C. M., and C.-L. Tsai. 1989. Regression and time series model selection in small samples. Biometrika 76:297-307.
69. Jeffreys, H. 1939. Theory of probability. Oxford University Press, Oxford.
70. Jermiin, L. S., G. J. Olsen, K. L. Mengersen, and S. Easteal. 1997. Majority-rule consensus of phylogenetic trees obtained by maximum-likelihood analysis. Mol. Biol. Evol. 14:1296-1302.
71. Johnson, J. B., and K. S. Omland. 2003. Model selection in ecology and evolution. Trends Ecol. Evol. 19:101-108.
72. Jukes, T. H., and C. R. Cantor. 1969. Evolution of protein molecules. Pages 21-132 in Mammalian protein metabolism (H. M. Munro, ed.) Academic Press, New York.
73. Kadane, J. B., and L. J. Wolfson. 1998. Experiencies in elicitation. J. R. Stat. Soc. D 47 Part 1:3-19.
74. Kass, R. E., and A. E. Raftery. 1995. Bayes factors. J. Am. Stat. Assoc. 90:773-795.
75. Kass, R. E., and L. Wasserman. 1995. A reference Bayesian test for nested hypotheses and its relationship to the Schwarz criterion. J. Am. Stat. Assoc. 90:928-934.
76. Kelsey, C. R., K. A. Crandall, and A. F. Voevodin. 1999. Different models, different trees: The geographic origin of PTLV-I. Mol. Phylogenet. Evol. 13:336-347.
77. Kendall, M., and A. Stuart. 1979. The advanced theory of statistics, 4th edition. Charles Griffin, London.
78. Kent, J. T. 1982. Robust properties of likelihood ratio tests. Biometrika 69:19-27.
79. Keuzenkamp, H., and M. McAleer. 1995. Simplicity, scientific inference and economic modeling. Econ. J. 105:1-21.
80. Kieseppä, I. A. 2002. Statistical model selection and Bayesianism. Phil. Sci. 68:S141-S152.
81. Kimura, M. 1980. A simple method for estimating evolutionary rate of base substitutions through comparative studies of nucleotide sequences. J. Mol. Evol. 16:111-120.
82. Kimura, M. 1981. Estimation of evolutionary distances between homologous nucleotide sequences. Proc. Nat. Acad. Sci. USA 78:454-458.
83. Kishino, H., and M. Hasegawa. 1989. Evaluation of the maximum likelihood estimate of the evolutionary tree topologies from DNA sequence data, and the branching order in Hominoidea. J. Mol. Evol. 29:170-179.
84. Kuha, J. 2003. AIC and BIC: Comparisons of assumptions and performance. Sociol. Methods Res. Submitted.
85. Kullback, S., and R. A. Leibler. 1951. On information and sufficiency. Ann. Math. Stat. 22:79-86.
86. Larget, B., and D. Simon. 1999. Markov chain Monte Carlo algorithms for the Bayesian analysis of phylogenetic trees. Mol. Biol. Evol. 16:750-759.
87. Lindley, D. V. 1957. A statistical paradox. Biometrika 44:187-192.
88. Linhart, H. 1988. A test whether two AIC's differ significantly. S. Afr. Stat. J. 22:153-161.
89. Linhart, H., and W. Zucchini. 1986. Model selection. Wiley, New York.
90. Madigan, D., J. Gavrin, and A. E. Raftery. 1995. Eliciting prior information to enhance the predictive performance of Bayesian graphical models. Commun. Stat. Theory Methods 24:2271-2292.
91. Madigan, D. M., and A. E. Raftery. 1994. Model selection and accounting for model uncertainty in graphical models using Occam's Window. J. Am. Stat. Assoc. 89:1335-1346.
92. Mau, B., and M. A. Newton. 1997. Phylogenetic inference for binary data on dendrograms using Markov chain Monte Carlo. J. Comp. Grap. Stat.
93. Mau, B., M. A. Newton, and B. Larget. 1999. Bayesian phylogenetic inference via Markov chain Monte Carlo methods. Biometrics 55:1-12.
94. Metropolis, N., A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller. 1953. Equations of state calculations by fast computing machines. J. Chem. Phys. 21:1087-1092.
95. Miller, A. J. 2002. Subset Selection in Regression, 2nd edition edition. Chapman & Hall/CRC, New York.
96. Minin, V., Z. Abdo, P. Joyce, and J. Sullivan. 2003. Performance-based selection of likelihood models for phylogeny estimation. Syst. Biol. 52:674-683.
97. Morozov, P., T. Sitnikova, G. Churchill, F. J. Ayala, and A. Rzhetsky. 2000. A new method for characterizing replacement rate variation in molecular sequences: Application of the Fourier and Wavelet models to Drosophila and mammalian proteins. Genetics 154:381-395.
98. Myrvold, W. C., and W. L. Harper. 2002. Model Selection, Simplicity, and Scientific Inference. Philos. Sci. 69:S135-S149.
99. Nishii, R. 1984. Asymptotic properties of criteria for selection of variables in multiple regression. Ann. Stat. 12:758-765.
100. Nishii, R. 1988. Maximum likelihood principle and model selection when the true model is unspecified. J. Multivar. Ana. 27.
101. Nylander, J. A. 2004. Bayesian Phylogenetics and the Evolution of Gall Wasps. Pages 43 in Acta Universitatis Upsaliensis. Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 937 Uppsala University, Uppsala, Sweden.
102. Nylander, J. A., F. Ronquist, J. P. Huelsenbeck, and J. L. Nieves-Aldrey. 2004. Bayesian phylogenetic analysis of combined data. Syst. Biol. 53:47-67.
103. Occam, W. ca. 1320. Scriptum in Librum Primum Sententiarum, Opera Theologica, I.
104. Ogishima, S., F. Ren, and H. Tanaka. 2000. Efficiencies of information criteria for topology selection in reconstructing molecular phylogenetic tree in Proceedings of International Symposium on Artificial Life and Robotics 2000:745-748.
105. Ota, R., P. J. Waddell, M. Hasegawa, H. Shimodaira, and H. Kishino. 2000. Appropriate likelihood ratio tests and marginal distributions for evolutionary tree models with constraints on parameters. Mol. Biol. Evol. 17:798-803.
106. Penny, D., P. J. Lockhart, M. A. Steel, and M. D. Hendy. 1994. The role of models in reconstructing evolutionary trees. Pages 211-230 in Models in Phylogenetic Reconstruction (R. W. Scotland, D. J. Siebert, and D. M. Williams, eds.). Clarendon Press, Oxford.
107. Pol, D. in press. Empirical problems of the hierarchical likelihood ratio test for model selection. Syst. Biol.
108. Popper, K. R. 1959. Logic of scientific discovery. Hutchinson, London.
109. Posada, D. 2001. The effect of branch length variation on the selection of models of molecular evolution. J. Mol. Evol. 52:434-444.
110. Posada, D. 2003. Using Modeltest and PAUP* to select a model of nucleotide substitution. Pages 6.5.1-6.5.14 in Current Protocols in Bioinformatics (A. D. Baxevanis, D. B. Davison, R. D. M. Page, G. A. Petsko, L. D. Stein, and G. D. Stormo, eds.). John Wiley & Sons, Inc.
111. Posada, D., and K. A. Crandall. 1998. Modeltest: Testing the model of DNA substitution. Bioinformatics 14:817-818.
112. Posada, D., and K. A. Crandall. 2001a. Selecting models of nucleotide substitution: An application to human immunodeficiency virus 1 (HIV-1). Mol. Biol. Evol. 18:897-906.
113. Posada, D., and K. A. Crandall. 2001b. Selecting the best-fit model of nucleotide substitution. Syst. Biol. 50:580-601.
114. Posada, D., and K. A. Crandall. 2001c. Simple (wrong) models for complex trees: Empirical Bias. Mol. Biol. Evol. 18:271-275.
115. Pupko, T., D. Huchon, Y. Cao, N. Okada, and M. Hasegawa. 2002. Combining multiple data sets in a likelihood analysis: Which models are the best? Mol. Biol. Evol. 19:2294-2307.
116. Raftery, A. E. 1996. Hypothesis testing and model selection. Pages 163-187 in Markov chain Monte Carlo in practice (W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, eds.). Chapman & Hall, London, New York.
117. Raftery, A. E. 1999. Bayes factors and BIC: Comment on "A critique of the Bayesian information criterion for model selection." Sociol. Methods Res. 27:411-427.
118. Robinson, D. F., and L. R. Foulds. 1981. Comparison of phylogenetic trees. Math. Biosci. 53:131-147.
119. Rzhetsky, A., and M. Nei. 1995. Tests of applicability of several substitution models for DNA sequence data. Mol. Biol. Evol. 12:131-151.
120. Sakamoto, Y., M. Ishiguro, and G. Kitagawa. 1986. Akaike information criterion statistics. Springer, New York.
121. Sanderson, M. J., and J. Kim. 2000. Parametric phylogenetics? Syst. Biol. 49:817-829.
122. Schwarz, G. 1978. Estimating the dimension of a model. Ann. Stat. 6:461-464.
123. Shafer, G. 1982. Lindley's paradox (with discussion). J. Am. Stat. Assoc. 77:325-351.
124. Shibata, R. 1986. Consistency of model selection and parameter estimation. J. Appl. Prob. 23A:127-141.
125. Shimodaira, H. 1997. Assessing the error probability of the model selection test. Ann. Inst. Stat. Math. 49:395-410.
126. Shimodaira, H. 1998. An application of multiple comparison techniques to model selection. Ann. Inst. Stat. Math. 1:1-13.
127. Shimodaira, H. 2001. Multiple comparisons of log-likelihoods and combining nonnested models with applications to phylogenetic tree selection. Commun. Stat. Theory Methods 30:1751-1772.
128. Shimodaira, H., and M. Hasegawa. 1999. Multiple comparisons of log-likelihoods with applications to phylogenetic inference. Mol. Biol. Evol. 16:1114-1234.
129. Sober, E. 2002a. Bayesianism - its scope and limits. Pages 21-38 in Bayes's Theorem (R. Swinburne, ed.). Oxford University Press, Oxford.
130. Sober, E. 2002b. Instrumentalism, parsimony, and the Akaike framework. Phil. Sci. 69:S112-S123.
131. Sober, E., and M. Steel. 2002. Testing the hypothesis of common ancestry. J. Theoret. Biol. 218:395-408.
132. Sota, T., and A. P. Vogler. 2001. Incongruence of mitochondrial and nuclear gene trees in the Carabid beetles Ohomopterus. Syst. Biol. 50:39-59.
133. Steel, M., and D. Penny. 2000. Parsimony, likelihood, and the role of models in molecular phylogenetics. Mol. Biol. Evol. 17:839-850.
134. Stone, M. 1977. An asymptotic equivalence of choice of model by cross-validation and Akaike's criterion. J. R. Stat. Soc. 39:44-47.
135. Strimmer, K. 2001. Model selection using expected likelihood weights: A Bayes-frequentist compromise. Technical Report available at http://www.stat.uni- muenchen.de/~strimmer/cv.html.
136. Strimmer, K., and A. Rambaut. 2001. Inferring confidence sets of possibly misspecified gene trees. Proc. R. Soc. Lond. B Biol. Sci. 269:137-142.
137. Suchard, M. A., C. M. Kitchen, J. S. Sinsheimer, and R. E. Weiss. 2003a. Hierarchical phylogenetic models for analyzing multipartite sequence data. Syst. Biol. 52:649-664.
138. Suchard, M. A., R. E. Weiss, K. S. Dorman, and J. S. Sinsheimer. 2002. Oh brother, where art thou? A Bayes factor test for recombination with uncertain heritage. Syst. Biol. 51:715-728.
139. Suchard, M. A., R. E. Weiss, and J. S. Sinsheimer. 2001. Bayesian selection of continuous-time Markov chain evolutionary models. Mol. Biol. Evol. 18:1001-1013.
140. Suchard, M. A., R. E. Weiss, and J. S. Sinsheimer. 2003b. Testing a molecular clock without an outgroup: Derivations of induced priors on branch-Length restrictions in a Bayesian framework. Syst. Biol. 52:48-54.
141. Sugiura, N. 1978. Further analysis of the data by Akaike's information criterion and the finite corrections. Commun. Stat. Theory Methods A7:13-26.
142. Sullivan, J., and D. L. Swofford. 1997. Are guinea pigs rodents? The importance of adequate models in molecular phylogenies. J. Mamm. Evol. 4:77-86.
143. Sullivan, J., and D. L. Swofford. 2001. Should we use model-based methods for phylogenetic inference when we know that assumptions about among-site rate variation and nucleotide substitution pattern are violated? Syst. Biol. 50:723-729.
144. Suzuki, Y., G. V. Glazko, and M. Nei. 2002. Overcredibility of molecular phylogenies obtained by Bayesian phylogenetics. Proc. Natl. Acad. Sci. USA 99:16138-16143.
145. Swofford, D. L. 1998. PAUP* Phylogenetic analysis using parsimony and other methods, version 4.0 beta. Sinauer Associates, Sunderland, Massachusetts.
146. Swofford, D. L. 2000. PAUP*. Phylogenetic analysis using parsimony (*and other methods), version 4. Sinauer Associates, Sunderland, Massachusetts.
147. Tamura, K. 1994. Model selection in the estimation of the number of nucleotide substitutions. Mol. Biol. Evol. 11:154-157.
148. Tamura, K., and M. Nei. 1993. Estimation of the number of nucleotide substitutions in the control region of mitochondrial DNA in humans and chimpanzees. Mol. Biol. Evol. 10:512-526.
149. Tanaka, H., F. Ren, T. Okayama, and T. Gojobori. 1999. Topology selection in unrooted molecular phylogenetic tree by minimum model-based complexity method. Pac. Symp. Biocomput. 4:326-337.
150. Tavaré, S. 1986. Some probabilistic and statistical problems in the analysis of DNA sequences. Pages 57-86 in Some mathematical questions in biology - DNA sequence analysis (R. M. Miura, ed.) American Mathematical Society, Providence, Rhode Island.
151. Van Den Bussche, R. A., R. J. Baker, J. P. Huelsenbeck, and D. M. Hillis. 1998. Base compositional bias and phylogenetic analyses: A test of the "flying DNA" hypothesis. Mol. Phylogenet. Evol. 10:408-416.
152. Verdinelli, I., and L. Wasserman. 1995. Computing Bayes factors using a generalization of the Savage-Dickey density ratio. J. Am. Stat. Assoc. 90:614-618.
153. Vuong, Q. H. 1989. Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica 57:307-333.
154. Wasserman, L. 2000. Bayesian model selection and model averaging. J. Math. Psychol. 44:92-107.
155. Weakliem, D. L. 1999. A critique of the Bayesian information criterion for model selection. Sociol. Methods Res. 27:359-397.
156. Whelan, S., and N. Goldman. 1999. Distributions of statistics used for the comparison of models of sequence evolution in phylogenetics. Mol. Biol. Evol. 16:1292-1299.
157. Woodroofe, M. 1982. On the model selection and the arc sine laws. Ann. Stat. 10:1182-1194.
158. Yang, Z. 1996a. Among-site rate variation and its impact on phylogenetic analysis. Trends Ecol. Evol. 11:367-372.
159. Yang, Z. 1996b. Maximum-likelihood models for combined analyses of multiple sequence data. J. Mol. Evol. 42:587-596.
160. Yang, Z., N. Goldman, and A. Friday. 1995. Maximum likelihood trees from DNA sequences: A peculiar statistical estimation problem. Syst. Biol. 44:384-399.
161. Yang, Z., R. Nielsen, N. Goldman, and A.-M. K. Pedersen. 2000. Codon-substitution models for heterogeneous selection pressure at amino acid sites. Genetics 155:431-449.
162. Yang, Z., and B. Rannala. 1997. Bayesian phylogenetic inference using DNA sequences: A Markov chain Monte Carlo method. Mol. Biol. Evol. 14:717-724.
163. Zhang, J. 1999. Performance of likelihood ratio tests of evolutionary-hypotheses under inadequate substitution models. Mol. Biol. Evol. 16:868-875.
164. Zharkikh, A. 1994. Estimation of evolutionary distances between nucleotide sequences. J. Mol. Evol. 39:315-329.
165. Zucchini, W. 2000. An introduction to model selection. J. Math. Psychol. 44:41-46.