Summary
A formal mathematical analysis of Kimura's (1981) six-parameter model of nucleotide substitution for the case of unequal substitution rates among different pairs of nucleotides is conducted, and new formulae for estimating the number of nucleotide substitutions and its standard error are obtained. By using computer simulation, the validities and utilities of Jukes and Cantor's (1969) one-parameter formula, Takahata and Kimura's (1981) four-parameter formula, and our sixparameter formula for estimating the number of nucleotide substitutions are examined under three different schemes of nucleotide substitution. It is shown that the one-parameter and four-parameter formulae often give underestimates when the number of nucleotide substitutions is large, whereas the six-parameter formula generally gives a good estimate for all the three substitution schemes examined. However, when the number of nucleotide substitutions is large, the six-parameter and four-parameter formulae are often inapplicable unless the number of nucleotides compared is extremely large. It is also shown that as long as the mean number of nucleotide substitutions is smaller than one per nucleotide site the three formulae give more or less the same estimate regardless of the substitution scheme used.
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References
Gojobori T, Nei M, Ishii K (1981) Mathematical model of nucleotide substitutions with unequal substitution rates. Genetics 97:s43
Hardison RC, Butler III ET, Lacy E, Maniatis T, Rosenthal N, Efstratiadis A (1979) The structure and transcription of four Iinked rabbitβ-like globin genes. Cell 18:1285–1297
Jukes TH, Cantor CR (1969) Evolution of protein molecules. In: Munro HN (ed) Mammalian protein metabolism. Academic Press, New York, pp 21–123
Kimura M (1980) A simple method for estimating evolutionary rates of base substitutions through comparative studies of nucleotide sequences. J Mol Evol 16:111–120
Kimura M (1981) Estimation of evolutionary distances between homologous nucleotide sequences. Proc Natl Acad Sci USA 78:454–458
Konkel DA, Maizel Jr JV, Leder P (1979) The evolution and sequence comparison of two recently diverged mouse chromosomalβ-globin genes. Cell 18:865–873
Nei M, Tateno Y (1978) Nonrandom amino acid substitution and estimation of the number of nucleotide substitutions in evolution. J Mol Evol 11:333–347
Perler R, Efstratiadis A, Lomedico P, Gilbert W, Klodner R, Dodgson J (1980) The evolution of genes: the chicken preproinsulin gene. Cell 20:555–566
Takahata N, Kimura M (1981) A model of evolutionary base substitutions and its application with special reference to rapid change of pseudogenes. Genetics 98:641–657
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On leave of absence from the Department of Biology, Faculty of Science, Kyushu University 33, Fukuoka 812, Japan
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Gojobori, T., Ishii, K. & Nei, M. Estimation of average number of nucleotide substitutions when the rate of substitution varies with nucleotide. J Mol Evol 18, 414–422 (1982). https://doi.org/10.1007/BF01840889
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DOI: https://doi.org/10.1007/BF01840889