Abstract
DNA sequence data provide a good source of information on the evolutionary history of organisms. Among the proposed methods, the maximum likelihood methods require an explicit probabilistic model of nucleotide substitution that makes the assumption clear. However, procedures for testing hypotheses on topologies have not been well developed. We propose a revised version of the maximum likelihood estimator of a tree and derive some of its properties. Then we present tests to compare given trees and to derive the most likely candidates for the true topology, applying to maximum likelihoods the notion of contrast, as defined in the framework of the analysis of variance, and the procedures used in multiple comparison. Finally, an example is presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barry, D. and Hartigan, J. A. (1987). Statistical analysis of hominoid molecular evolution, Statist. Sci., 2, 191–210.
Churchill, G. A., van Haeseler, A. and Navidi, W. C. (1992). Sample size for a phylogenetic inference, Molecular Biology and Evolution, 9, 753–769.
Cox, D. R. (1961). Tests of separate families of hypotheses, Proc. 4th Berkeley Symp. on Math. Statist. Prob., Vol. 1, 105–123, University of California Press, Berkeley.
Edwards, D. G. and Hsu, J. C. (1983). Multiple comparisons with the best treatment, J. Amer. Statist. Assoc., 78, 965–971.
Felsenstein, J. (1978). Cases in which parismony or competibility methods will be positively misleading, Systematic Zoology, 27, 401–410.
Felsenstein, J. (1981). Evolutionary trees from DNA sequences: a maximum likelihood approach, Journal of Molecular Evolution, 17, 368–376.
Felsenstein, J. (1983). Statistical inference of phylogenies, J. Roy. Statist. Soc. Ser. A, 146, 246–272.
Felsenstein, J. (1985). Confidence limits on phylogenies: an approach using the bootstrap, Evolution, 39, 783–791.
Felsenstein, J. and Kishino, H. (1993). Is there something wrong with the bootstrap on phylogenies?, A reply to Hillis and Bull, Systematic Biology, 42, 193–200.
Goldman, N. (1993). Statistical tests of models of DNA substitution, Journal of Molecular Evolution, 36, 182–198.
Grad, A. and Solomon, H. (1955). Distribution of quadratic forms and some applications, Ann. Math. Statist., 26, 464–477.
Hasegawa, M. and Yano, T. (1984). Phylogeny and classification of Hominoidea as inferred from DNA sequence data, Proceedings of the Japan Academy, B60, 389–392.
Hillis, D. M. and Bull, J. J. (1993). An empirical test of bootstrapping as a method for assessing confidence in phylogenetic analysis, Systematic Biology, 42, 182–192.
Hochberg, Y. and Tamhane, A. C. (1987). Multiple Comparison Procedures, Wiley, New York.
Horai, S., Hayaska, K., Kondo, R., Tsugane, K. and Takahata, N. (1995). Recent African origin of modern humans revealed by complete sequences of hominoid mitochondrial DNAs, Proc. Nat. Acad. Sci. U.S.A., 92, 532–536.
Hsu, J. C. (1984). Constrained simultaneous confidence intervals for multiple comparisons with the best, Ann. Statist., 12, 1136–1144.
Johnson, N. L. and Kotz, S. (1970). Continuous Univariate Distributions, Wiley, New York.
Kimura, M. (1983). The Neutral Theory of Molecular Evolution, Cambridge University Press, Cambridge.
Kishino, H. and Hasegawa, M. (1989). Evaluation of the maximum likelihood estimate of the evolutionary tree topologies from DNA sequence data, and the branching order in hominoidea, Journal of Molecular Evolution, 29, 170–179.
Kishino, H., Miyata, T. and Hasagewa, M. (1990). Maximum likelihood inference of protein phylogeny and the origin of chloroplasts, Journal of Molecular Evolution, 31, 151–160.
Kullback, S. (1959). Information Theory and Statistics, Dover, New York.
Linhart, H. (1988). A test whether two AIC's differ significantly, South African Statist. J., 22, 153–161.
Martin, L. (1985). Significance of enamel thickness in hominoid evolution, Nature, 314, 260–263.
Navidi, W. C., Churchill, G. A. and von Haeseler, A. (1993). Phylogenetic inference: linear invariants and maximum likelihood, Biometrics, 49, 543–555.
Rao, C. R. (1973). Linear Statistical Inference and Its Applications, 2nd ed., Wiley, New York.
Sibley, C. G. and Ahlquist, J. E. (1984). The phylogeny of the hominoid primates, as indicated by DNA-DNA hybridization, Journal of Molecular Evolution, 20, 2–15.
Sitnikova, T., Rzhetsky, A. and Nei, M. (1995). Interior-branch and bootstrap tests of phylogenetic trees, Molecular Biology and Evolution, 12, 319–333.
Steiger, J. H., Shapiro, A. and Browne, M. W. (1985). On the multivariate asymptotic distribution of sequential chi-square statistics, Psychometrika, 50, 253–264.
Swofford, D. L. and Olsen, G. J. (1990). Phylogeny reconstruction, Molecular Systematics (eds. D. M. Hillis and C. Moritz), 411–501, Sinauer, Sunderland, Massachusetts.
Templeton, A. R. (1983). Phylogenetic inference from restriction endonuclease cleavage site maps with particular reference to the evolution of humans and the apes, Evolution, 37, 221–244.
Ueda, S., Takenaka, O. and Honjo, T. (1985). A truncated immunoglobulin \(\varepsilon\) pseudogene is found in gorilla and man but not in chimpanzee, Proc. Nat. Acad. Sci. U.S.A., 82, 3712–3715.
Vuong, Q. H. (1989). Likelihood ratio tests for model selection and non nested hypotheses, Econometrica, 57, 307–333.
White, H. (1981). Consequences and detection of misspecified nonlinear regression models, J. Amer. Statist. Assoc., 76, 419–433.
White, H. (1982). Maximum likelihood estimation of misspecified models, Econometrica, 50, 253–264.
Zharkikh, A. and Li, W. H. (1992a). Statistical properties of bootstrap estimation of phylogenetic variability from nucleotide sequences: four taxa with a molecular clock, Molecular Biology and Evolution, 9, 1119–1147.
Zharkikh, A. and Li, W. H. (1992b). Statistical properties of bootstrap estimation of phylogenetic variability from nucleotide sequences: four taxa without molecular clock, Journal of Molecular Evolution, 35, 356–366.
Author information
Authors and Affiliations
About this article
Cite this article
Bar-Hen, A., Kishino, H. Comparing the Likelihood Functions of Phylogenetic Trees. Annals of the Institute of Statistical Mathematics 52, 43–56 (2000). https://doi.org/10.1023/A:1004180831122
Issue Date:
DOI: https://doi.org/10.1023/A:1004180831122