Hadamard Conjugations and Modeling Sequence Evolution with Unequal Rates across Sites

Molecular Phylogenetics and Evolution

Volumn 8, Issue 1, 1997, Pages 33-50

  Waddell, Peter J ^a   Penny, David ^a   Moore, Terry ^a  

^a MASSEY UNIVERSITY   (New Zealand)

Author keywords

[No Author keywords available]

Indexed keywords

MITOCHONDRIAL DNA; PURINE DERIVATIVE; PYRIMIDINE DERIVATIVE; RIBOSOME RNA;

ALGORITHM; ANIMAL; ARTICLE; BIOLOGICAL MODEL; GENETIC VARIABILITY; GENETICS; HUMAN; MAMMAL; PHYLOGENY; STATISTICAL MODEL;

ALGORITHMS; ANIMALS; DNA, MITOCHONDRIAL; HUMANS; LIKELIHOOD FUNCTIONS; MAMMALS; MODELS, BIOLOGICAL; PHYLOGENY; PURINES; PYRIMIDINES; RNA, RIBOSOMAL; VARIATION (GENETICS);

EID: 0031202202     PISSN: 10557903     EISSN: None     Source Type: Journal    
DOI: 10.1006/mpev.1997.0405     Document Type: Article

References (51)

1. Adachi J., Hasegawa M. Tempo and mode of synonymous substitutions in mitochondrial DNA of primates. Mol. Biol. Evol. 13:1996;200-208.
2. Bandelt H.-J., Dress A. W. M. Split decomposition: A new and useful approach to phylogenetic analysis of distance data. Mol. Phylogenet. Evol. 1:1992;242-252.
3. Bull J. J., Huelsenbeck J. P., Cunningham C. W., Swofford D. L., Waddell P. J. Partitioning and combining data in phylogenetic analysis. Syst. Biol. 42:1993;384-397.
4. Cavalier-Smith T. Kingdom Protozoa and its 18 phyla. Microbiol. Rev. 57:1993;953-994.
5. Cavender J. A. Taxonomy with confidence. Math. Biosci. 40:1978;271-280.
6. Churchill G. A., von Haeseler A., Navidi W. C. Sample size for phylogenetic inference. Mol. Biol. Evol. 9:1992;753-769.
7. Evans S. N., Speed T. P. Invariants of some probability models used in phylogenetic inference. Anal. Stat. 21:1993;355-377.
8. Farris J. S. A probability model for inferring evolutionary trees. Syst. Zool. 22:1973;250-256.
9. Felsenstein J. Phylogenies from molecular sequences: Inference and reliability. Annu. Rev. Genet. 22:1988;521-565.
10. Fitch W. M., Markowitz E. An improved method for determining codon variability in a gene and its application to the rate of fixation of mutations in evolution. Biochem. Genet. 4:1970;579-593.
11. Gaut B. S., Lewis P. O. Success of maximum likelihood in the four-taxon case. Mol. Biol. Evol. 12:1995;152-162.
12. Golding G. B. Estimates of DNA and protein sequence divergence: An examination of some assumptions. Mol. Biol. Evol. 1:1983;125-142.
13. Gu X., Fu Y.-X., Li W.-H. Maximum likelihood estimation of the heterogeneity of substitution rate among nucleotide sites. Mol. Biol. Evol. 12:1995;546-557.
14. Hasegawa M., Fujiwara M. Relative efficiencies of the maximum likelihood, maximum parsimony, and neighbor-joining methods for estimating protein phylogeny. Mol. Phylogenet. Evol. 2:1993;1-5.
15. Hasegawa M., Kishino H., Yano T. Dating of the human-ape splitting by a molecular clock of mitochondrial DNA. J. Mol. Evol. 21:1985;160-174.
16. Hendy M. D. A combinatorial description of the closest tree algorithm for finding evolutionary trees. Discrete Math. 96:1991;51-58.
17. Hendy M. D., Penny D. A framework for the quantitative study of evolutionary trees. Syst. Zool. 38:1989;297-309.
18. Hendy M. D., Penny D. Spectral analysis of phylogenetic data. J. Classif. 10:1993;5-24.
19. Hendy M. D., Penny D., Steel M. A. Discrete Fourier analysis for evolutionary trees. Proc. Natl. Acad. Sci. USA. 91:1994;3339-3343.
20. Horai S., Satta Y., Hayasaka K., Kondo R., Inoue T., Ishida T., Hayashi S., Takahata N. Man's place in the Hominoidea revealed by mitochondrial DNA genealogy. J. Mol. Evol. 35:1992;32-43.
21. Jin L., Nei M. Limitations of the evolutionary parsimony method of phylogenetic analysis. Mol. Biol. Evol. 7:1990;82-102.
22. Kimura M. Estimation of evolutionary distances between homologous nucleotide sequences. Proc. Natl. Acad. Sci. USA. 78:1981;454-458.
23. Lake J. A. Eocytes: A new ribosome structure indicates a kingdom with a close relationship to eukaryotes. Proc. Natl. Acad. Sci. USA. 81:1986;3786-3790.
24. Lake J. A. Origin of the eukaryotic nucleus determined by rate-invariant analysis of rRNA sequences. Nature. 331:1988;184-186.
25. Lake J. A. Reconstructing evolutionary trees from DNA and protein sequences: Paralinear distances. Proc. Natl. Acad. Sci. USA. 91:1994;1455-1459.
26. Lanave C., Preparata G., Saccone C., Serio G. A new method for calculating evolutionary substitution rates. J. Mol. Evol. 20:1984;86-93.
27. +Hexamita inflata. Mol. Biochem. Parisitol. 59:1993;41-48.
28. Lockhart P. J., Larkum A. W., Steel M. A., Waddell P. J., Penny D. Evolution of chlorophyll and bacteriochlorophyll: The problem of invariant sites in sequence analysis. Proc. Natl. Acad. Sci. USA. 93:1996;1930-1934.
29. Lockhart P. J., Steel M. A., Hendy M. D., Penny D. Recovering evolutionary trees under a more realistic model of evolution. Mol. Biol. Evol. 11:1996;605-612.
30. M. Nei, 1987, Molecular evolutionary genetics, Columbia University Press, New York.
31. Olsen G. J. The earliest phylogenetic branchings: Comparing rRNA-based evolutionary trees inferred with various techniques. Cold Spring Harbor Symp. Quant. Biol. 52:1987;825-837.
32. Penny D. Towards a basis for classification: The incompleteness of distance measures, incompatibility analysis and phenetic classification. J. Theor. Biol. 96:1982;129-142.
33. Reeves J. H. Heterogeneity in the substitution process of amino acid sites of proteins coded for by Mitochondrial DNA. J. Mol. Evol. 35:1992;17-31.
34. Rényi A. Probability Theory. 1970;North-Holland, Amsterdam.
35. Shoemaker J. S., Fitch W. M. Evidence from nuclear sequences that invariable sites should be considered when sequence divergence is calculated. Mol. Biol. Evol. 6:1989;270-289.
36. Steel M. A., Hendy M. D., Penny D. Loss of information in genetic distances. Nature. 336:1988;118.
37. Steel M. A., Hendy M. D., Penny D. Parsimony can be consistent! Syst. Biol. 42:1993;581-587.
38. Steel M. A., Hendy M. D., Székely L. A., Erdös P. L. Spectral analysis and a closest tree method for genetic sequences. Appl. Math. Lett. 5:1992;63-67.
39. Steel M. A., Székely L., Erdös P. L., Waddell P. J. A complete family of phylogenetic invariants for any number of taxa under Kimura's 3ST model. New Zealand Journal of Botany (Conference Issue). 31:1993;289-296.
40. Stuart A., Ord J. K. Kendall's Advanced Theory of Statistics. 1987;Edward Arnold, London.
41. Swofford D. L., Olsen G. J., Waddell P. J., Hillis D. M. Phylogenetic inference. Molecular Systematics. 1996;Sinauer, Sunderland. p. 407-514.
42. Székely L. A., Steel M. A., Erdös P. L. Fourier calculus on evolutionary trees. Adv. Appl. Math. 14:1993;200-216.
43. Tolimieri R., An M., Lu C. Algorithms for Discrete Fourier Transform and Convolution. 1989;Springer-Verlag, New York.
44. Uzzel T., Corbin K. W. Fitting discrete probability distributions to evolutionary events. Science. 172:1971;1089-1096.
45. P. J. Waddell, 1995, Statistical methods of Phylogenetic Analysis, Including Hadamard Conjugations, LogDet Transforms, and Maximum Likelihood, Massey University, New Zealand.
46. P. J. Waddell, 1996, Extended Materials and Methods Section to 'Hadamard Conjugations with Unequal Rates across Sites'.
47. Waddell P. J., Penny D. Evolutionary trees of apes and humans from DNA sequences. Lock A. J., Peters C. R. Handbook of Human Symbolic Evolution. 1996;53-73 Oxford Univ. Press, Oxford.
48. Waddell P. J., Penny D., Hendy M. D., Arnold G. The sampling distributions and covariance matrix of phylogenetic spectra. Mol. Biol. Evol. 11:1994;630-642.
49. P. J. Waddell, M. A. Steel, 1996, Time Reversible Distances Allowing a Distribution of Rates across Sites, University of Canterbury, New Zealand.
50. Yang Z. Maximum-likelihood estimation of phylogeny from DNA sequences when substitution rates differ over sites. Mol. Biol. Evol. 10:1993;1396-1401.
51. Yang Z. Maximum Likelihood phylogenetic estimation from DNA sequences with variable rates over sites: Approximate methods. J. Mol. Evol. 39:1994;306-314.