Skip to main content
SpringerLink
Log in

Pattern of synonymous and nonsynonymous substitutions: An indicator of mechanisms of molecular evolution

  • Published:
Journal of Genetics Aims and scope Submit manuscript

Abstract

Comparison of numbers of synonymous and nonsynonymous substitutions is useful for understanding mechanisms of molecular evolution. In this paper, I examine the statistical properties of six methods of estimating numbers of synonymous and nonsynonymous substitutions. The six methods are Miyata and Yasunaga’s (MY) method; Nei and Gojobori’s (NG) method; Li, Wu and Luo’s (LWL) method; Pamilo, Bianchi and Li’s (PBL) method; and Ina’s (Ina) two methods. When the transition/transversion bias at the mutation level is strong, the numbers of synonymous and nonsynonymous substitutions are estimated more accurately by the PBL and Ina methods than by the NG, MY and LWL methods. When the nucleotide-frequency bias is strong and distantly related sequences are compared, all the six methods give underestimates of the number of synonymous substitutions. The concept of synonymous and nonsynonymous categories is also useful for analysis of DNA polymorphism data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Berg O. G. and Martelius M. 1995 Synonymous substitution-rate constraints inEscherichia coli andSalmonella typhimurium and their relationship to gene expression and selection pressure.J. Mol. Evol. 41:449–456

    Article  PubMed  CAS  Google Scholar 

  • Bulmer M. 1987 Coevolution of codon usage and transfer RNA abundance.Nature 325: 728–730

    Article  PubMed  CAS  Google Scholar 

  • Clark G. A. and Kao T.-H. 1991 Excess nonsynonymous substitution of shared polymorphic sites among self-incompatibility alleles of Solanaceae.Proc. Natl. Acad. Sci USA 88: 9823–9827

    Article  PubMed  CAS  Google Scholar 

  • Comeron J. M. 1995 A method for estimating the numbers of synonymous and nonsynonymous substitutions per site.J. Mol. Evol. 41: 1152–1159

    Article  PubMed  CAS  Google Scholar 

  • Crow J. F. and Kimura M. 1970An introduction to population genetics theory (New York: Harper and Row)

    Google Scholar 

  • Dayhoff M. O., Schwartz R. M. and Orcutt B. C. 1978 A model of evolutionary change in proteins. InAtlas of protein sequence and structure (ed.) M. O. Dayhoff (Washington, DC: National Biomedical Research Foundation) vol. 5, suppl. 3, pp. 345–352

    Google Scholar 

  • Easteal S. 1990 The pattern of mammalian evolution and the relative rate of molecular evolution.Genetics 124: 165–173

    PubMed  CAS  Google Scholar 

  • Easteal S. and Collet C. 1994 Consistent variation in amino-acid substitution rate, despite uniformity of mutation rate: Protein evolution in mammals is not neutral.Mol. Biol. Evol. 11: 643–647

    PubMed  CAS  Google Scholar 

  • Easteal S., Collet C. and Betty D. 1995The mammalian molecular clock (New York: Springer) pp. 135–145

    Google Scholar 

  • Efron B. 1979 Bootstrap methods: Another look at the jackknife.Ann. Statist. 7: 1–26

    Article  Google Scholar 

  • Felsenstein J. 1981 Evolutionary trees from DNA sequences: A maximum likelihood method approach.J. Mol. Evol. 17: 368–376

    Article  PubMed  CAS  Google Scholar 

  • Figueroa F., Gunther E. and Klein J. 1988 MHC polymorphism pre-dating speciation.Nature 335: 265–267

    Article  PubMed  CAS  Google Scholar 

  • Fu Y.-X. 1996 New statistical tests of neutrality for DNA samples from a population.Genetics 143: 557–570

    PubMed  CAS  Google Scholar 

  • Fu Y.-X. and Li W.-H. 1993 Statistical tests of neutrality of mutations.Genetics 133: 693–709

    PubMed  CAS  Google Scholar 

  • Gillespie J. H. 1995 On Ohta’s hypothesis: Most amino acid substitutions are deleterious.J. Mol Evol. 40: 64–69

    Article  CAS  Google Scholar 

  • Gojobori T. 1983 Codon substitution in evolution and the “saturation” of synonymous changes.Genetics 105:1011–1027

    PubMed  CAS  Google Scholar 

  • Gojobori T., Li W.-H. and Graur D. 1982a Patterns of nucleotide substitution in pseudogenes and functional genes.J. Mol. Evol. 18: 360–369

    Article  PubMed  CAS  Google Scholar 

  • Gojobori T., Ishii K. and Nei M. 1982b Estimation of average number of nucleotide substitutions when the rate of substitution varies with nucleotide.J. Mol. Evol. 18: 414–423

    Article  PubMed  CAS  Google Scholar 

  • Goldman N. and Yang Z. 1994 A codon-based model of nucleotide substitution for protein-coding DNA sequences.Mol. Biol. Evol. 11: 725–736

    PubMed  CAS  Google Scholar 

  • Grantham R. 1974 Amino acid difference formula to help explain protein evolution.Science 185: 862–864

    Article  PubMed  CAS  Google Scholar 

  • Grishin N. V. 1995 Estimation of the number of amino acid substitutions per site when the substitution rate varies among sites.J. Mol. Evol. 41: 675–679

    Article  PubMed  CAS  Google Scholar 

  • Hayashida H. and Miyata T. 1983 Unusual evolutionary conservation and frequent DNA segment exchange in class I genes of the major histocompatibility complex.Proc. Natl. Acad. Sci. USA 80: 2671–2675

    Article  PubMed  CAS  Google Scholar 

  • Hayashida H. and Miyata T. 1985 On the direction of gene conversion.Proc. Jpn. Acad. B61: 204–207

    Article  Google Scholar 

  • Hayashida H., Kuma K. and Miyata T. 1992 Interchromosomal gene conversion as a possible mechanism for explaining divergence patterns of ZFY-related genes.J. Mol. Evol. 35: 181–183

    Article  PubMed  CAS  Google Scholar 

  • Hein J. 1995 A maximum-likelihood approach to analyzing nonoverlapping and overlapping reading frames.J. Mol. Evol. 40: 181–189

    Article  PubMed  CAS  Google Scholar 

  • Hudson R. R. 1990 Gene genealogy and the coalescent process.Oxford Surv. Evol. Biol. 7: 1–44

    Google Scholar 

  • Hudson R. R., Kreitman M. and Aguade M. 1987 A test of neutral molecular evolution based on nucleotide data.Genetics 116: 153–159

    PubMed  CAS  Google Scholar 

  • Hughes A. L. 1991 Testing for interlocus genetic exchange in the MHC: A reply to Andersson and co-workers.Immunogenetics 33: 243–246

    PubMed  CAS  Google Scholar 

  • Hughes A. L. and Nei M. 1988 Pattern of nucleotide substitution at major histocompatibility complex loci reveals overdominant selection.Nature 335: 167–170

    Article  PubMed  CAS  Google Scholar 

  • Hughes A. L. and Nei M. 1989 Nucleotide substitution at major histocompatibility complex class II loci: Evidence for overdominant selection.Proc. Natl. Acad. Sci. USA 86: 958–962

    Article  PubMed  CAS  Google Scholar 

  • Ikemura T. 1985 Codon usage and tRNA content in unicellular and multicellular organisms.Mol. Biol Evol. 2: 13–34

    PubMed  CAS  Google Scholar 

  • Ina Y. 1993Estimation of the numbers of synonymous and nonsynonymous substitutions with special reference to viral evolution. Ph.D. thesis, Department of Genetics, School of Life Science, The Graduate University for Advanced Studies, Hayama, Japan

  • Ina Y. 1995 New methods for estimating the numbers of synonymous and nonsynonymous substitutions.J. Mol Evol. 40: 190–226

    Article  PubMed  CAS  Google Scholar 

  • Ina Y. 1996a Variance and covariance of the number of amino acid substitutions estimated by Kimura’s method.Genes Genet. Syst. 71: 43–46

    Article  CAS  Google Scholar 

  • Ina Y. 1996b Correlation between synonymous and nonsynonymous substitutions and variation in synonymous substitution numbers. InCurrent topics on molecular evolution (eds) M. Nei and T. Takahata (Pennsylvania: Institute of Molecular Evolutionary Genetics, The Pennsylvania State University, and Hayama: The Graduate University for Advanced Studies) pp. 105–113

    Google Scholar 

  • Ina Y. and Gojobori T. 1994 Statistical analysis of nucleotide sequences of the hemagglutinin gene of human influenza A viruses.Proc. Natl. Acad. Sci. USA 91: 8388–8392

    Article  PubMed  CAS  Google Scholar 

  • Ina Y., Mizokami M., Ohba K. and Gojobori T. 1994 Reduction of synonymous substitutions in the core protein gene of hepatitis C virus.J. Mol. Evol. 38: 50–56

    Article  PubMed  CAS  Google Scholar 

  • Jin L. and Nei M. 1990 Limitations of the evolutionary parsimony method of phylogenetic analysis.Mol. Biol. Evol. 7: 82–102

    PubMed  CAS  Google Scholar 

  • Johnson N. L. and Kotz S. 1973Distribution in statistics: Discrete distributions (Boston: Houghton-Mifflin)

    Google Scholar 

  • Jukes T. H. and Cantor C. R. 1969 Evolution of protein molecules. InMammalian protein metabolism (ed.) H. N. Munro (New York: Academic Press) pp. 21–132

    Google Scholar 

  • Kimura M. 1964 Diffusion models in population genetics,J. Appl. Prob. 1:177–232

    Article  Google Scholar 

  • Kimura M. 1968a Evolutionary rate at the molecular level.Nature 217: 624–626

    Article  PubMed  CAS  Google Scholar 

  • Kimura M. 1968b Genetic variability maintained in a finite population due to mutational production of neutral and nearly neutral isoalleles.Genet. Res. 11: 247–269

    Article  PubMed  CAS  Google Scholar 

  • Kimura M. 1969 The number of heterozygous nucleotide sites maintained in a finite population due to steady flux of mutations.Genetics 61: 893–903

    PubMed  CAS  Google Scholar 

  • Kimura M. 1977 Preponderance of synonymous changes as evidence for the neutral theory of molecular evolution.Nature 267: 275–276

    Article  PubMed  CAS  Google Scholar 

  • Kimura M. 1979 Model of effectively neutral mutations in which selective constraint is incorporated.Proc. Natl. Acad. Sci. USA 76: 3440–3444

    Article  PubMed  Google Scholar 

  • 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

    Article  PubMed  CAS  Google Scholar 

  • Kimura M. 1981a Estimation of evolutionary distances between homologous nucleotide sequences,Proc. Natl. Acad. Sci. USA 78: 454–458

    Article  PubMed  CAS  Google Scholar 

  • Kimura M. 1981b Possibility of extensive neutral evolution under stabilizing selection with special reference to nonrandom usage of synonymous codons.Proc. Natl. Acad. Sci. USA 78: 5773–5777

    Article  PubMed  CAS  Google Scholar 

  • Kimura M. 1983The neutral theory of molecular evolution (Cambridge: Cambridge University Press)

    Google Scholar 

  • Kimura M. and Ohta T. 1969 The average number of generations until fixation of a mutant gene in a finite population.Geneticsi 61: 763–771

    Google Scholar 

  • Kimura M. and Ohta T. 1971 Protein polymorphism as a phase of molecular evolution.Nature 229:467–469

    Article  PubMed  CAS  Google Scholar 

  • Kimura M. and Ohta T. 1972 On the stochastic model for estimation of mutational distance between homologous proteins.J. Mol Evol. 2: 87–90

    Article  PubMed  CAS  Google Scholar 

  • Kondo R., Horai S., Satta Y. and Takahata N. 1993 Evolution of hominoid mitochondrial DNA with special reference to the silent substitution rate over the genome.J. Mol. Evol. 36: 517–531

    Article  PubMed  CAS  Google Scholar 

  • Krushkal J. and Li W.-H. 1995 Substitution rates in hepatitis delta virus.J. Mol. Evol. 41: 721–726

    Article  PubMed  CAS  Google Scholar 

  • Kumar S., Tamura K. and Nei M. 1993MEGA: Molecular evolutionary genetics analysis (version 1.0). The Pennsylvania State University, University Park, USA

    Google Scholar 

  • Lawlor D. A., Ward F. E., Ennis P. D., Jackson A. P. and Parham P. 1988HLA-A andB polymorphisms predate the divergence of humans and chimpanzees.Nature 335: 268–271

    Article  PubMed  CAS  Google Scholar 

  • Li W.-H. 1987 Models of nearly neutral mutations with particular implications for nonrandom usage of synonymous codons.J. Mol. Evol. 24: 337–345

    Article  PubMed  CAS  Google Scholar 

  • Li W.-H. 1993 Unbiased estimation of the rates of synonymous and nonsynonymous substitution.J. Mol. Evol. 36: 96–99

    Article  PubMed  CAS  Google Scholar 

  • Li W.-H., Gojobori T. and Nei M. 1981 Pseudogenes as a paradigm of neutral evolution.Nature 292: 237–239

    Article  PubMed  CAS  Google Scholar 

  • Li W.-H., Wu C.-I. and Luo C.-C. 1984 Nonrandomness of point mutation as reflected in nucleotide substitutions in pseudogenes and its evolutionary implications.J. Mol. Evol. 21: 58–71

    Article  PubMed  CAS  Google Scholar 

  • Li W.-H., Wu C.-I. and Luo C.-C. 1985a A new method for estimating synonymous and nonsynonymous rates of nucleotide substitution considering the relative likelihood of nucleotide and codon changes,Mol. Biol. Evol 2: 150–174

    PubMed  Google Scholar 

  • Li W.-H., Luo C.-C. and Wu C.-I. 1985b Evolution of DNA sequences. InMolecular evolutionary genetics (ed.) R. J. MacIntyre (New York: Plenum Press) pp. 1–94

    Google Scholar 

  • Li W.-H., Ellsworth D, L., Krushkal J., Chang B. H.-J. and Hewett-Emmett D. 1996 Rates of nucleotide substitution in primates and rodents and the generation-time effect hypothesis.Mol Phylogenet. Evol. 5: 182–187

    Article  PubMed  CAS  Google Scholar 

  • McDonald J. H. and Kreitman M. 1991 Adaptive protein evolution at theAdh locus inDrosophila.Nature 351: 652–654

    Article  PubMed  CAS  Google Scholar 

  • Miyata T. and Yasunaga T. 1978 Evolution of overlapping genes.Nature 272: 532–535

    Article  PubMed  CAS  Google Scholar 

  • Miyata T. and Yasunaga T. 1980 Molecular evolution of mRN A: A method for estimating evolutionary rates of synonymous and amino acid substitutions from homologous nucleotide sequences and its application.J.Mol Evol. 16:23–36

    Article  PubMed  CAS  Google Scholar 

  • Miyata T. and Yasunaga T. 1981 Rapidly evolving mouse α-globin-related pseudo gene and its evolutionary history.Proc. Natl. Acad. Sci. USA 78: 450–453

    Article  PubMed  CAS  Google Scholar 

  • Miyata T., Miyazawa S. and Yasunaga T. 1979 Two types of amino acid substitutions in protein evolution.J. Mol. Evol. 12: 219–236

    Article  PubMed  CAS  Google Scholar 

  • Miyata T., Yasunaga T. and Nishida T. 1980 Nucleotide sequence divergence and functional constraint in mRNA evolution.Proc. Natl. Acad. Sci. USA 77: 7328–7332

    Article  PubMed  CAS  Google Scholar 

  • Miyata T., Hayashida H., Kuma K., Mitsuyasu K. and Yasunaga T. 1987 Male-driven molecular evolution: A model and nucleotide sequence analysis.Cold Spring Harbor Symp. Quant. Biol. 52: 863–867

    PubMed  CAS  Google Scholar 

  • Mouchiroud D., Gautier C. and Bernardi G. 1995 Frequencies of synonymous substitutions in mammals are gene-specific and correlated with frequencies of nonsynonymous substitutions.J. Mol. Evol. 40:107–113

    Article  PubMed  CAS  Google Scholar 

  • Muse S. V. 1995 Evolutionary analyses of DNA sequence subject to constraints on secondary structure.Genetics 139: 1429–1439

    PubMed  CAS  Google Scholar 

  • Muse S. V. 1996a Estimating synonymous and nonsynonymous substitution rates.Mol Biol Evol. 13: 105–114

    PubMed  CAS  Google Scholar 

  • Muse S. V. 1996b Evolutionary analysis when nucleotides do not evolve independently. InCurrent topics on molecular evolution (eds) M. Nei and N. Takahata (Pennsylvania: Institute of Molecular Evolutionary Genetics, The Pennsylvania State University, and Hayama: The Graduate University for Advanced Studies) pp. 115–124

    Google Scholar 

  • Muse S. V. and Gaut B. S. 1994 A likelihood approach for comparing synonymous and nonsynonymous nucleotide substitution rates, with application to the chloroplast genome.Mol Biol. Evol. 11: 715–724

    PubMed  CAS  Google Scholar 

  • Nei M. 1987Molecular evolutionary genetics (New York: Columbia University Press)

    Google Scholar 

  • Nei M. and Gojobori T. 1986 Simple methods for estimating the numbers of synonymous and nonsynonymous substitutions.Mol. Biol Evol 3: 418–426

    PubMed  CAS  Google Scholar 

  • Ohta T. 1973 Slightly deleterious mutant substitutions in evolution.Nature 246: 96–98

    Article  PubMed  CAS  Google Scholar 

  • Ohta T. 1977 Extension to the neutral mutation random drift hypothesis. InMolecular evolution and polymorphism (ed.) M. Kimura (Mishima: National Institute of Genetics) pp. 148–167

    Google Scholar 

  • Ohta T. 1992 The nearly neutral theory of molecular evolution.Annu. Rev. Ecol. Syst. 23: 263–286

    Article  Google Scholar 

  • Ohta T. 1993 An examination of generation-time effect on molecular evolution.Proc. Natl. Acad. Sci. USA 90: 10676–10680

    Article  PubMed  CAS  Google Scholar 

  • Ohta T. 1995a Gene conversion vs point mutation in generating variability at the antigen recognition site of major histocompatibility complex loci.J. Mol Evol 41: 115–119

    PubMed  CAS  Google Scholar 

  • Ohta T. 1995b Synonymous and nonsynonymous substitutions in mammalian genes and the nearly neutral theory.J. Mol. Evol. 40: 56–63

    Article  PubMed  CAS  Google Scholar 

  • Ohta T. and Ina Y. 1995 Variation in synonymous rates among mammalian genes and the correlation between synonymous and nonsynonymous divergences.J. Mol Evol. 41: 717–720

    PubMed  CAS  Google Scholar 

  • Ota T. and Nei M. 1994a Estimation of the number of amino acid substitutions per site when the substitution rate varies among sites.J. Mol. Evol. 38: 642–643

    Article  CAS  Google Scholar 

  • Ota T. and Nei M. 1994b Variance and covariances of the numbers of synonymous and nonsynonymous substitutions per site.Mol. Biol. Evol. 11: 613–619

    PubMed  CAS  Google Scholar 

  • Pamilo P. and Bianchi O. N. 1993 Evolution of theZfx andZfy genes: Rates and interdependence between the genes.Mol. Biol. Evol 10: 271–281

    PubMed  CAS  Google Scholar 

  • Parham P. and Ohta T. 1996 Population biology of antigen presentation by MHC class I molecules.Science 272: 67–74

    Article  PubMed  CAS  Google Scholar 

  • Perler F., Efstratiadis A., Lomedico P., Gilbert W., Kolodner R. and Dodgeson J. 1980 The evolution of genes: The chicken preproinsulin gene.Cell 20: 555–566

    Article  PubMed  CAS  Google Scholar 

  • Rzhetsky A. 1995 Estimating substitution rates in ribosomal RNA genes.Genetics 141: 771–783

    PubMed  CAS  Google Scholar 

  • Sawyer S. 1989 Statistical tests for detecting gene conversion.Mol. Biol. Evol. 6: 526–538

    PubMed  CAS  Google Scholar 

  • Schöniger M. and von Haeseler A. 1994 A stochastic model for the evolution of auto correlated DNA sequences.Mol Phylogenet. Evol. 3: 240–247

    Article  PubMed  Google Scholar 

  • Sharp P. M. and Li W.-H. 1987 The rate of synonymous substitution in enterobacterial genes is inversely related to codon usage bias.Mol Biol Evol. 4: 222–230

    PubMed  CAS  Google Scholar 

  • Shields D. C., Sharp P. M., Higgins D. G. and Wright F. 1988 “Silent” sites inDrosophila genes are not neutral: Evidence of selection among synonymous codons.Mol. Biol. Evol. 5: 704–716

    PubMed  CAS  Google Scholar 

  • Shimmin L. C., Chang B. H.-J. and Li W.-H. 1993 Male-driven evolution of DNA sequences.Nature 362:745–747

    Article  PubMed  CAS  Google Scholar 

  • Stephens J. C. 1985 Statistical methods of DNA sequence analysis: Detection of intragenic recombination or gene conversion.Mol Biol. Evol. 2: 539–556

    PubMed  CAS  Google Scholar 

  • Tajima F. 1989 Statistical method for testing the neutral mutation hypothesis by DNA polymorphism.Genetics 23: 585–595

    Google Scholar 

  • Tajima F. 1991 Determination of window size for analyzing DNA sequences.J. Mol Evol 33: 470–473

    Article  PubMed  CAS  Google Scholar 

  • Tajima F. 1993 Statistical analysis of DNA polymorphism.Jpn. J. Genet. 68: 567–595

    Article  PubMed  CAS  Google Scholar 

  • Tajima F. and Nei M. 1982 Biases of the estimates of DNA divergence obtained by the restriction enzyme technique.J. Mol. Evol. 18: 115–120

    Article  PubMed  CAS  Google Scholar 

  • Tajima F. and Nei M. 1984 Estimation of evolutionary distance between nucleotide sequences.Mol. Biol. Evol. 1:269–285

    PubMed  CAS  Google Scholar 

  • Takahata N. 1990 A simple genealogical structure of strongly balanced allelic lines and trans-species evolution of polymorphism.Proc. Natl. Acad. Sci. USA 87: 2419–2423

    Article  PubMed  CAS  Google Scholar 

  • Takahata N. 1991 A trend in population genetics theory. InNew aspects of the genetics of molecular evolution (eds) M. Kimura and N. Takahata (Tokyo: Japan Scientific Societies Press) pp. 27–47

    Google Scholar 

  • Takahata N. 1994 Comments on the detection of reciprocal recombination or gene conversion.Immunogenetics 39: 146–149

    Article  PubMed  CAS  Google Scholar 

  • Takahata N. and Kimura M. 1981 A model of evolutionary base substitutions and its application with special reference to rapid change of pseudogenes.Genetics 98: 641–657

    PubMed  CAS  Google Scholar 

  • Takahata N. and Nei M. 1990 Allelic genealogy under overdominant and frequency-dependent selection and polymorphism of major histocompatibility complex loci.Genetics 124: 967–978

    PubMed  CAS  Google Scholar 

  • Tamura K. 1992 Estimation of the number of nucleotide substitutions when there are strong transition-transversion and G+C-content biases.Mol. Biol. Evol. 9: 678–687

    PubMed  CAS  Google Scholar 

  • Tamura K. and Nei M. 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

    PubMed  CAS  Google Scholar 

  • Tillier E. R. M. 1994 Maximum likelihood with multiparameter models of substitution.J. Mol Evol. 39: 409–417

    Article  CAS  Google Scholar 

  • Tillier E. R. M. and Collins R. A. 1995 Neighbor joining and maximum likelihood with RNA sequences: Addressing the interdependence of sites.Mol Biol Evol. 12: 7–15

    CAS  Google Scholar 

  • Uzzell T. and Corbin K. W. 1971 Fitting discrete probability distributions to evolutionary events.Science 172: 1089–1096

    Article  PubMed  CAS  Google Scholar 

  • Wakeley J. 1996 The excess of transition among nucleotide substitutions: New methods of estimating transition bias underscore its significance.Trends Ecol. Evol. 11: 158–163

    Article  Google Scholar 

  • Wolfe K. H. and Sharp P. M. 1993 Mammalian gene evolution: Nucleotide sequence divergence between mouse and rat.J. Mol Evol. 37: 441–456

    Article  PubMed  CAS  Google Scholar 

  • Wolfe K. H., Sharp P. M. and Li W.-H. 1989 Mutation rates differ among regions of the mammalian genome.Nature 337: 283–285

    Article  PubMed  CAS  Google Scholar 

  • Wu C.-I. and Li W.-H. 1985 Evidence for higher rates of nucleotide substitution in rodents than in man.Proc. Natl. Acacl. Sci. USA 82: 1741–1745

    Article  CAS  Google Scholar 

  • Yang Z. 1993 Maximum-likelihood estimation of phylogeny from DNA sequences when substitution rates differ over sites.Mol. Biol. Evol 10: 1396–1401

    PubMed  CAS  Google Scholar 

  • Yang Z. 1995Phylogenetic analysis by maximum likelihood (PAML)version 1.1. Institute of Molecular Evolutionary Genetics, The Pennsylvania State University, University Park, USA

    Google Scholar 

  • Yang Z. and Kumar S. 1996 Approximate methods for estimating the pattern of nucleotide substitutions and the variation of substitution rates among sites.Mol Biol. Evol. 13: 650–659

    PubMed  CAS  Google Scholar 

  • Zharkikh A. 1994 Estimation of evolutionary distances between nucleotide sequences.J. Mol. Evol. 39: 315–329

    Article  PubMed  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Population Genetics, National Institute of Genetics, 411, Mishima, Japan

    Yasuo Ina

Authors
  1. Yasuo Ina
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ina, Y. Pattern of synonymous and nonsynonymous substitutions: An indicator of mechanisms of molecular evolution. J. Genet. 75, 91–115 (1996). https://doi.org/10.1007/BF02931754

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02931754

Keywords

Search

Navigation