A simple method for estimating evolutionary rates of base substitutions through comparative studies of nucleotide sequences

  title={A simple method for estimating evolutionary rates of base substitutions through comparative studies of nucleotide sequences},
  author={Motoo Kimura},
  journal={Journal of Molecular Evolution},
  • M. Kimura
  • Published 1 December 1980
  • Biology
  • Journal of Molecular Evolution
SummarySome simple formulae were obtained which enable us to estimate evolutionary distances in terms of the number of nucleotide substitutions (and, also, the evolutionary rates when the divergence times are known). In comparing a pair of nucleotide sequences, we distinguish two types of differences; if homologous sites are occupied by different nucleotide bases but both are purines or both pyrimidines, the difference is called type I (or “transition” type), while, if one of the two is a… 
Evolutionary change of restriction sites under unequal rates of nucleotide substitution among the three positions of codons
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Rates of molecular evolution and the fraction of nucleotide positions free to vary
  • S. Palumbi
  • Biology
    Journal of Molecular Evolution
  • 2005
Differences in the fraction of nucleotide positions free to vary can serve as an important alternative hypothesis to explain differences in DNA divergence rates.
A method for estimating the numbers of synonymous and nonsynonymous substitutions per site
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Estimation of average number of nucleotide substitutions when the rate of substitution varies with nucleotide
SummaryA 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,
Computing Ka and Ks with a consideration of unequal transitional substitutions
The comparative results deriving from consistency analysis, computer simulations and authentic datasets, indicate that ignoring unequal transitional rates may lead to serious biases and that MYN performs well in most of the tested cases, and suggest that acquisitions of reliable synonymous and nonsynonymous substitution rates primarily depend on less biased estimates of transition/transversion rate ratio.
Nonuniformity of nucleotide substitution rates in molecular evolution: Computer simulation and analysis of 5S ribosomal RNA sequences
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Relative-Rate Test for Nucleotide Substitutions between Two Lineages
The relative-rate test of Wu and Li ( 1985) is extended to cases where more than one taxon are sampled for one nucleotide sequence in two lineages compared, and formulas for calculating both the weighted number of substitutions in each lineage as compared with a common reference taxon and the variance of the difference in the weightedNumber of nucleotide substitutions between the two lineage are presented.
Pattern of synonymous and nonsynonymous substitutions: An indicator of mechanisms of molecular evolution
  • Y. Ina
  • Biology
    Journal of Genetics
  • 2008
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.
Factors affecting the errors in the estimation of evolutionary distances between sequences.
The accuracy of likelihood-based distance estimates is much higher than those based on log transform formulae, particularly in cases where there is a large range of timescales involved in the rate matrix and when the ratio of transition to transversion rates is large.


Molecular evolution of mRNA: A method for estimating evolutionary rates of synonymous and amino acid substitutions from homologous nucleotide sequences and its application
It is suggested that, in the coding regions surrounding the splicing points of intervening sequences ofβ-globin genes, there exist rigid secondary structures that show the slowing down of evolutionary rates of both synonymous and amino acid substitutions in the primate line.
Two types of amino acid substitutions in protein evolution
SummaryThe frequency of amino acid substitutions, relative to the frequency expected by chance, decreases linearly with the increase in physico-chemical differences between amino acid pairs involved
Preponderance of synonymous changes as evidence for the neutral theory of molecular evolution
By comparative studies of messenger RNA (mRNA) sequences reliable estimates can be obtained of the evolutionary rates (in terms of mutant substitutions) at the third positions of the codon, and that the estimates conform remarkably well with the framework of the neutral theory.
On some principles governing molecular evolution.
  • M. Kimura, T. Ohta
  • Biology, Chemistry
    Proceedings of the National Academy of Sciences of the United States of America
  • 1974
Five Pillars of Evolution were culled from the accumulated evidence on molecular evolution and theoretical considerations of the population dynamics of mutant substitutions.
Comparison of total sequence of a cloned rabbit beta-globin gene and its flanking regions with a homologous mouse sequence.
The nucleotide sequence of a cloned rabbit chromosomal DNA segment which contains a beta-globin gene is presented and the homologous introns may be derived from common ancestral introns by large insertions and deletions rather than be multiple point mutations.
On the stochastic model for estimation of mutational distance between homologous proteins
SummaryA set of simple equations is derived which gives the relationship between the observed amino acid differences per 100 codons and the evolutionary distance per 100 codons using Holmquist's
Unusual alpha-globin-like gene that has cleanly lost both globin intervening sequences.
Cloned and determined the nucleotide sequence of a mouse alpha-globin-like gene that entirely lacks the two intervening sequences that interrupt all globin genes thus far examined, and proposes a mechanism that would permit the loss of either or both intervening sequences independently.