Skip to main content
SpringerLink
Log in

Stochastic Theory of Population Genetics and Evolution

  • Conference paper
Vito Volterra Symposium on Mathematical Models in Biology

Part of the book series: Lecture Notes in Biomathematics ((LNBM,volume 39))

Abstract

The stochastic theory in population genetics has a long history. In his 1922 paper Fisher first studied the effect of genetic drift on the genetic variability of a random mating population, introducing a new concept of stochastic change of gene frequencies. He reached the conclusion that the rate of change of genetic variability due to genetic drift is extremely small in a large population. This study affected his view as well as his followers on the role of genetic drift in evolution. Some of his followers (e.g. Ford 1975) still maintain the view that virtually all characters of an organism are the product of natural selection and genetic drift is unimportant except in an extremely small population. Fisher himself, however, was aware of the importance of the stochastic factor in evolution at least in the initial process of gene frequency increase. In fact, it was Fisher (1922, 1930) and Haldane (1927) who showed that genetic drift will eliminate a majority of advantageous mutations in a few generations after they occur and only a small proportion of them will be fixed in the population.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Ayala, F. J. 1972. Darwinian versus non-Darwinian evolution in natural populations of Drosophila. Proc. 6th Berkeley Symp. Math. Stat. Prob. V: 211–236.

    Google Scholar 

  • Bodmer, W. F. and A. W. F. Edwards. 1962. Linkage and recombination in evolution. Adv. Genet. 11: 1–100.

    Article  Google Scholar 

  • Chakraborty, R. and M. Nei. 1976. Hidden genetic variability within electromorphs in finite populations. Genetics 84: 385–393.

    Google Scholar 

  • Chakraborty, R. and M. Nei. 1977. Bottleneck effects on average heterozygosity and genetic distance with the stepwise mutation model. Evolution 31: 347–356.

    Article  Google Scholar 

  • Chakraborty, R., P. A. Fuerst, and M. Nei. 1978. Statistical studies on protein polymorphism in natural populations. II. Gene differentiation between populations. Genetics 88: 367–390.

    Google Scholar 

  • Chakraborty, R., P. A. Fuerst, and M. Nei. 1980. Statistical studies on protein polymorphism in natural populations. III. Distribution of allele frequencies and the number of alleles per locus. Genetics (in press)

    Google Scholar 

  • Clayton, G. A. and A. Robertson. 1957. Mutation and cumulative variation. Amer. Nat. 89: 151–155.

    Article  Google Scholar 

  • Dayhoff, M. O., ed. 1972. Atlas of Protein Sequence and Structure. Vol. 5. Natl. Biomed. Res. found., Washington, D.C.

    Google Scholar 

  • Darwin, C. 1872. The Origin of Species. 6th ed. D. Appleton, London.

    Google Scholar 

  • Dempster, E. R. 1955. Maintenance of genetic heterogeneity. Cold Spring Harbor Symp. Quant. Biol. 20: 25–32.

    Article  Google Scholar 

  • Ewens, W. J. 1964. The maintenance of alleles by mutation. Genetics 50: 891–898.

    Google Scholar 

  • Felsenstein, J. 1976. The theoretical population genetics of variable selection and migration. Ann. Rev. Genet. 10: 253–280.

    Google Scholar 

  • Fisher, R. A. 1922. On the dominance ratio. Proc. Roy. Soc. Edinburgh 42: 321–341.

    Google Scholar 

  • Fisher, R. A. 1930. The Genetical Theory of Natural Selection. Clarendon Press, Oxford.

    MATH  Google Scholar 

  • Fisher, R. A. and E. B. Ford. 1947. The spread of a gene in natural conditions in a colony of the moth Panaxia dominula L. Heredity 1: 143–174.

    Article  Google Scholar 

  • Fitch, W. M. and E. Margoliash. 1967. A method for estimating the number of invariant amino acid coding positions in a gene using cytochrome c as a model case. Biochem. Genet. 1: 65–71.

    Article  Google Scholar 

  • Ford, E. B. 1975. Ecological Genetics. 4th ed. Chapman and Hall Ltd., London.

    Google Scholar 

  • Frelinger, J. A. 1972. The maintenance of transferrin polymorphism in pigeons, Proc. Natl. Acad. Sci. US 69: 326–329

    Google Scholar 

  • Fuerst, P. A. and R. E. Ferrell. 1980. The stepwise mutation model: an experimental evaluation utilizing hemoglobin variants. Genetics (in press)

    Google Scholar 

  • Fuerst, P. A., R. Chakraborty, and M. Nei. 1977. Statistical studies on protein polymorphism in natural populations. I. Distribution of single-locus heterozygosity. Genetics 86: 455–483.

    Google Scholar 

  • Gillespie, J. H. 1977. Sampling theory for alleles in a random environment. Nature 266: 443–445.

    Article  Google Scholar 

  • Gillespie, J. H. 1978. A general model to account for enzyme variation in natural populations. V. The SAS-CFF model. Theoret. Popul. Biol. 14: 1–45.

    MATH  Google Scholar 

  • Gillespie, J. H. and C. H. Langley. 1974. A general model to account for enzyme variation in natural populations. Genetics 76: 837–848.

    Google Scholar 

  • Gulick, J. T. 1905. Evolutiony Racial and Eabitudinal. Publ. 25. Carnegie Institution of Washington.

    Google Scholar 

  • Haldane, J. B. S. 1927. The mathematical theory of natural and artificial selection. Part V. Proc. Comb. Philos. Soc. 23: 838–844.

    Article  MATH  Google Scholar 

  • Haldane, J. B. S. 1964. A defense of beanbag genetics. Perspectives in Biology and Medicine 7: 343–359.

    Google Scholar 

  • Haldane, J. B. S. and S. D. Jayakar. 1963. Polymorphism due to selection of varying direction. J. Genet. 58: 237–242.

    Article  Google Scholar 

  • Hedrick, P. W. 1974. Genetic variation in a heterogeneous environment. I. Temporal heterogeneity and the absolute dominance model. Genetics 78: 757–770.

    Google Scholar 

  • Hedrick, P. W., M. E. Ginevan, and E. P. Ewing. 1976. Genetic polymorphism in heterogeneous environments. Ann. Rev. Ecol. Syst. 7: 1–32.

    Article  Google Scholar 

  • Holt, S. B. 1961. Quantitative genetics of finger-print patterns. Brit. Med. Bull. 17: 247–250.

    Google Scholar 

  • Karlin, S. and U. Lieberman. 1974. Random temporal variation in selection intensities: Case of a large population size. Theoret. Popul. Biol. 6: 355–382.

    Article  MathSciNet  Google Scholar 

  • Kimura, M. 1965. A stochastic model concerning the maintenance of genetic variability in quantitative characters. Proc. Natl. Acad. Sci. US 54: 731–736.

    Google Scholar 

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

    Article  Google Scholar 

  • Kimura, M. 1979. The neutral theory of molecular evolution. Scientific American 241: 98–126.

    Article  Google Scholar 

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

    Google Scholar 

  • Kimura, M. and J. F. Crow. 1964. The number of alleles that can be maintained in a finite population. Genetics 49: 725–738.

    Google Scholar 

  • Kimura, M. and T. Maruyama. 1971. Pattern of neutral polymorphism in a geographically structured population. Genet. Res. 18: 125–131.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Kimura, M. and T. Ohta. 1973. Mutation and evolution at the molecular level. Genetics 73 (Suppl.): 19–35.

    Google Scholar 

  • Kimura, M. and T. Ohta. 1974. On some principles governing molecular evolution. Proc. Natl. Acad. Sci. US 71: 2848–2852.

    Article  Google Scholar 

  • Koehn, R. K. 1969. Esterase heterogeneity: Dynamics of a polymorphism. Science 163: 943–944.

    Article  Google Scholar 

  • Kojima, K., J. Gillespie, and Y. N. Tobari. 1970. A profile of Drosophila species’ enzymes assayed by electrophoresis. I. Number of alleles, heterozygosities, and linkage disequilibrium in glucose-metabolizing systems and some other enzymes. Biochem. Genet. 4: 627–637.

    Google Scholar 

  • Langley, C. H. and W. M. Fitch. 1974. An examination of the constancy of the rate of molecular evolution. J. Mol. Evol. 3: 161–177.

    Google Scholar 

  • Langley, C. H., Y. N. Tobari, and K. Kojima. 1974. Linkage disequilibrium in natural populations of drosophila melanogaster. Genetics 78: 921–936.

    Google Scholar 

  • Latter, B. D. H. 1975. Influence of selection pressures on enzyme polymorphisms in Drosophila. Nature 257: 590–592.

    Article  Google Scholar 

  • Lederberg, J. and E. M. Lederberg. 1952. of bacterial mutants. J. Bacteriology 63: 399–406.

    Google Scholar 

  • Levene, H. 1953. Genetic equilibrium when available. Amer. Nat. 87: 331–333.

    Article  Google Scholar 

  • Lewontin, R. C. 1964. The interaction of Genetics 50: 757–782.

    Google Scholar 

  • Lewontin, R. C., L. R. Ginzburg, and S. D. explanation for large amounts of genie Genetics 88: 149–170.

    Google Scholar 

  • Li, W.-H. 1976. A mixed model of mutation for electrophoretic identity of proteins within and between populations. Genetics 83: 423–432.

    Google Scholar 

  • Li, W.-H. 1977. Maintenance of genetic variability under mutation and selection pressures in a finite population. Proc. Natl. Acad. Sci. US 74: 2509–2513.

    Google Scholar 

  • Li, W.-H. 1978. Maintenance of genetic variability under the joint effect of mutation, selection and random drift. Genetias 90: 349–382.

    Google Scholar 

  • Li, W.-H. 1979. Maintenance of genetic variability under the pressure of neutral and deleterious mutations in a finite population. Genetias 92: 647–667.

    Google Scholar 

  • Li, W.-H. 1979. Variance of genetic distance and correlation of heterozygosity between populations under the pressure of stepwise mutation. Theoret. Popul. Biol. 15: 171–190.

    Google Scholar 

  • Li, W.-H. and M. Nei. 1975. Drift variances of heterozygosity and genetic distance in transient states. Genet. Res. 25: 229–248.

    Google Scholar 

  • Li, W.-H. and M. Nei. 1977. Persistence of common alleles in two related populations or species. Genetias 86: 901–914.

    MathSciNet  Google Scholar 

  • Maruyama, T. 1972. A note on the hypothesis: protein polymorphism as a phase of molecular evolution. J. Mol. Evol. 1: 201–219.

    Article  Google Scholar 

  • Mayr, E. 1959. Where are we? Cold Spring Harbor Symp. Quant. Biol. 24: 409–440.

    Article  Google Scholar 

  • Mayr, E. 1963. Animal Speaies or Evolution. Harvard Univ. Press, Cambridge, Mass.

    Google Scholar 

  • McDonald, J. F. and F. J. Ayala. 1974. Genetic response to environmental heterogeneity. Nature 250: 572–574.

    Article  Google Scholar 

  • Monod, J. 1971. Chanae and Neaessity. Translated by A. Wainhouse. Originally published in France as Le Hasard et la Neaessité by editions du Seuil, Paris, 1970. Alfred A. Knopf, Inc., New York.

    Google Scholar 

  • Mukai, T., L. E. Mettler, and S. I. Chigusa. 1971. Linkage disequilibrium in a local population of Drosophila melanogaster. Proa. Natl. Aaad. Sai. US 68: 1065–1069.

    Google Scholar 

  • Nei, M. 1975. Moleaular Population Genetias and Evolution. North Holland, Amsterdam.

    Google Scholar 

  • Nei, M. 1976. Mathematical models of speciation and genetic distance. In: Population Genetias and Eaology. S. Karlin and E. Nevo, eds. Academic Press, New York. 723–765.

    Google Scholar 

  • Nei, M. 1978. The theory of genetic distance and evolution of human races. Japan. J. Hum. Genet. 23: 341–369.

    Google Scholar 

  • Nei, M. and W.-H. Li. 1975. Probability of identical monomorphism in related species. Genet. Res. 26: 31–43.

    Article  Google Scholar 

  • Nei, M. and W.-H. Li. 1976. The transient distribution of allele frequencies under mutation pressure. Genet. Res. 28: 205–214.

    Article  Google Scholar 

  • Nei, M. and W.-H. Li. 1980. Non-random association between electromorphs and inversion chromosomes in finite populations. Genet. Res, (in press)

    Google Scholar 

  • Nei, M. and A. K. Roychoudhury. 1973. Probability of fixation and mean fixation time of an overdominant mutation. Genetics 74: 371–380.

    Google Scholar 

  • Nei, M. and A. K. Roychoudhury. 1974. Genie variation within and between the three major races of man, Caucasoids, Negroids, and Mongoloids. Amer. J. Hum. Genet. 26: 421–443.

    Google Scholar 

  • Nei, M. and A. K. Roychoudhury. 1980. Genetic relationship and evolution of human races, (submitted)

    Google Scholar 

  • Nei, M. and Y. Tateno. 1975. Interlocus variation of genetic distance and the neutral mutation theory. Proc. Natl. Acad. Sci. US 72: 2758–2760.

    Google Scholar 

  • Nei, M. and S. Yokoyama. 1976. Effects of random fluctuation of selection intensity on genetic variability in a finite population. Japan. J. Genet. 51: 355–369.

    Article  Google Scholar 

  • Nei, M., T. Maruyama, and R. Chakraborty. 1975. The bottleneck effect and genetic variability in populations. Evolution 29: 1–10.

    Article  Google Scholar 

  • Nei, M., R. Chakraborty, and P. A. Fuerst. 1976. Infinite allele model with varying mutation rate. Proc. Natl. Acad. Sci. US 73: 4164–4168.

    Google Scholar 

  • Nei, M., P. A. Fuerst, and R. Chakraborty. 1976. Testing the neutral mutation hypothesis by distribution of single-locus heterozygosity. Nature 262: 491–493.

    Article  Google Scholar 

  • Nei, M., P. A. Fuerst, and R. Chakraborty. 1978. Subunit molecular weight and genetic variability of proteins in natural populations. Proc. Natl. Acad. Sci. US 75: 3359–3362.

    Google Scholar 

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

    Article  Google Scholar 

  • Ohta, T. 1975. Statistical analyses of Drosophila and human protein polymorphisms. Proc. Natl. Acad. Sci. US 72: 3194–3196.

    Article  Google Scholar 

  • Ohta, T. 1977. Extension to the neutral mutation random drift hypothesis. Proc. 2nd Taniguchi Intl. Symp. Biophysics.

    Google Scholar 

  • Powell, J. R. 1971. Genetic polymorphisms in varied environments. Scienoe 174: 1035–1036.

    Article  Google Scholar 

  • Powell, J. R. and C. E. Taylor. 1979. Genetic variation in ecologically diverse environments. Amer. Scientist 67: 590–596.

    Google Scholar 

  • Ramshaw, J. A. M., J. A. Coyne, and R. C. Lewontin. 1980. The sensitivity of gel electrophoresis as a detector of genetic variation. Genetics (in press)

    Google Scholar 

  • Rigby, P. W. J., B. D. Burleigh, Jr., and B. S. Hartley. 1974. Gene duplication in experimental enzyme evolution. Nature 251: 200–204.

    Article  Google Scholar 

  • Robertson, A. 1967. The nature of quantitative genetic variation. In: Heritage from Mendel. R. A. Brink, ed. Univ. of Wisconsin Press, Madison, Wisconsin. 265–280.

    Google Scholar 

  • Soule, M. 1976. Allozyme variation: its determinants in space and time. In: Molecular Evolution. F. J. Ayala, ed. Sinauer Associates, Sunderland, Mass. 60–77.

    Google Scholar 

  • Takahata, N. and M. Kimura. 1979. Genetic variability maintained in a finite population under mutation and autocorrelated random fluctuation of selection intensity. Proc. Natl. Acad. Sci. US 76: 5813–5817.

    Google Scholar 

  • Waddington, C. H. 1957. The Strategy of the Genes. Allen and Unwin, London.

    Google Scholar 

  • Watterson, G. A. 1977. Heterosis or neutrality? Genetics 85: 789–814.

    MathSciNet  Google Scholar 

  • Wilson, A. C., S. S. Carlson, and T. J. White. 1977. Biochemical evolution. Ann. Rev. Biochem. 46: 573–639.

    Google Scholar 

  • Wright, S. 1931. Evolution in Mendelian populations. Genetics 16: 97–159.

    Google Scholar 

  • Wright, S. 1932. The roles of mutation, inbreeding, crossbreeding, and selection in evolution. Proc. 6th Intl. Cong. Genet. 1: 356–366.

    Google Scholar 

  • Wright, S. 1935. The analysis of variance and the correlation between relatives with respect to deviations from an optimum. J. Genet. 30: 243–256.

    Article  Google Scholar 

  • Wright, S. 1938. Size of population and breeding structure in relation to evolution. Science 87: 430–431.

    Google Scholar 

  • Wright, S. 1948. On the roles of directed and random changes in gene frequency in the genetics of populations. Evolution 2: 279–294.

    Article  Google Scholar 

  • Wright, S. 1949. Adaptation and selection. In: Genetics, Paleontology, and Evolution. G. L. Jepson, G. G. Simpson, and E. Mayr, eds. Princeton Univ. Press, Princeton, N.J. 365–389.

    Google Scholar 

  • Wright, S. 1971. Random drift and the shifting balance theory of evolution. In: Mathematical Topics in Population Genetics. K. Kojima, ed. Springer-Verlag, Berlin. 1–31.

    Google Scholar 

  • Wright, S. 1978. Variability Within and Among Natural Populations. Vol. 4 of: Evolution and the Genetics of Populations. Univ. of Chicago Press, Chicago.

    Google Scholar 

  • Yokoyama, S. and M. Nei. 1979. Population dynamics of sex-determining alleles in honey bees and self-incompatibility alleles in plants. Genetics 91: 609–626.

    MathSciNet  Google Scholar 

  • Zuckerkandl, E. and L. Pauling. 1965. Evolutionary divergence and convergence in proteins. In: Evolving Genes and Proteins. V. Bryson and H. J. Vogel, eds. Academic Press, New York. 97–166.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Demographic and Population Genetics, University of Texas at Houston, Houston, Texas, 77025, USA

    Masatoshi Nei

Authors
  1. Masatoshi Nei
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Via Celoria 10, Milan, Italy

    Claudio Barigozzi

Rights and permissions

Reprints and permissions

Copyright information

© 1980 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Nei, M. (1980). Stochastic Theory of Population Genetics and Evolution. In: Barigozzi, C. (eds) Vito Volterra Symposium on Mathematical Models in Biology. Lecture Notes in Biomathematics, vol 39. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93161-1_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-93161-1_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10279-3

  • Online ISBN: 978-3-642-93161-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation