Skip to main content
SpringerLink
Log in

Diffusion Models of Population Genetics in the Age of Molecular Biology

  • Chapter
The Craft of Probabilistic Modelling

Part of the book series: Applied Probability ((APPLIEDPROB,volume 1))

Abstract

When I was a small boy, I was fascinated by the flowers my father loved and raised, and imitating him I grew various plants in the garden at home. The main reason why I was attracted by the flowers was their beauty. In addition, I was fascinated by the mystery of development; I wondered how a beautiful tulip, for instance, could emerge from a mere bulb. My interest in plants continued through elementary school. Then, in the second year of middle school, I met an interesting teacher who was a devoted naturalist. He encouraged my interest in plants, and gradually I became absorbed in botany; as a result, I made up my mind to become a botanist.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
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

  1. Calder, N. (1973) The Life Game. BBC Publications, London.

    Google Scholar 

  2. Calder, N. (1985) The lottery of life: changing views of evolution and human progress. In Population Genetics and Molecular Evolution, ed. T. Ohta and K. Aoki, Japan Scientific Societies Press, Tokyo; Springer-Verlag, Berlin.

    Google Scholar 

  3. Crow, J. F. (1972) The dilemma of nearly neutral mutations: How important are they for evolution and human welfare? J. Heredity 63, 306–316.

    Google Scholar 

  4. Crow, J. F. (1981) The neutralist-selectionist controversy: an overview. In Population and Biological Aspects of Human Mutation, ed. E. B. Hook, Academic Press, New York, 3–14.

    Google Scholar 

  5. Crow, J. F. and Kimura, M. (1956) Some genetic problems in natural populations. Proc. 3rd Berkeley Symp. Math. Statist. Prob. 4, 1–22.

    MathSciNet  Google Scholar 

  6. Crow, J. F. and Kimura, M. (1970) An Introduction to Population Genetics Theory. Harper and Row, New York.

    MATH  Google Scholar 

  7. Dawson, D. A. and Hochberg, K. J. (1983) Qualitative behavior of a selectively neutral allelic model. Theoret. Popn Biol. 23, 1–18.

    Article  MATH  Google Scholar 

  8. Dobzhansky, Th. (1937) Genetics and the Origin of Species. Columbia University Press, New York.

    Google Scholar 

  9. Feller, W. (1951) Diffusion processes in genetics. Proc. 2nd Berkeley Symp. Math. Statist. Prob., 227–246.

    Google Scholar 

  10. Fisher, R. A. and Ford, E. B. (1950) The ‘Sewall Wright effect’. Heredity 4, 117–119.

    Article  Google Scholar 

  11. Haldane, J. B. S. (1957) Karl Pearson, 1857–1957. Biometrika 44, 303–313.

    MathSciNet  MATH  Google Scholar 

  12. Kimura, M. (1950) The theory of the chromosome substitution between two different species. Cytologia 15, 281–294.

    Article  Google Scholar 

  13. Kimura, M. (1953) `Stepping-stone’ model of population. Ann. Rep. Nat. Inst. Genetics 3, 62–63.

    Google Scholar 

  14. Kimura, M. (1954) Process leading to Quasi-fixation of genes in natural populations due to random fluctuation of selection intensities. Genetics 39, 280–295.

    Google Scholar 

  15. Kimura, M. (1955) Solution of a process of random genetic drift with a continuous model. Proc. Nat. Acad. Sci. USA 41, 144–150.

    Article  MATH  Google Scholar 

  16. Kimura, M. (1955) Stochastic processes and distribution of gene frequencies under natural selection. Cold Spring Harbor Symp. Quant. Biol. 20, 33–53.

    Google Scholar 

  17. Kimura, M. (1957) Some problems of stochastic processes in genetics. Ann. Math. Statist.. 28, 882–901.

    Article  MathSciNet  MATH  Google Scholar 

  18. Kimura, M. (1964) Diffusion models in population genetics. J. Appl. Prob. 1, 177–232.

    Article  MATH  Google Scholar 

  19. Kimura, M. (1968) Evolutionary rate at the molecular level. Nature 217, 624–626.

    Article  Google Scholar 

  20. Kimura, M. (1971) Theoretical foundation of population genetics at the molecular level. Theoret. Popn Biol. 2, 174–208.

    Article  Google Scholar 

  21. Kimura, M. (1983) The Neutral Theory of Molecular Evolution. Cambridge University Press, Cambridge.

    Google Scholar 

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

    Google Scholar 

  23. Kimura, M. and Ohta, T. (1971) Theoretical Aspects of Population Genetics. Princeton University Press, Princeton, NJ.

    Google Scholar 

  24. Kimura, M. and Weiss, G. H. (1964) The stepping stone model of population structure and the decrease of genetic correlation with distance. Genetics 49, 561–576.

    Google Scholar 

  25. Kunisawa, K. (1951) Kindai-Kakuritsuron ( Modern Probability Theory ). Iwanami Shoten, Tokyo.

    Google Scholar 

  26. Li, Wen-Hsiung (Ed.) (1977) Stochastic Models in Population Genetics. Benchmark Papers in Genetics 7, Dowden, Hutchinson and Ross, Stroudsburg, Pa.

    Google Scholar 

  27. Maruyama, T. (1977) Stochastic Models in Population Genetics. Lecture Notes in Biomathematics 17, Springer-Verlag, Berlin.

    Google Scholar 

  28. Morse, P. M. and Feshbach, H. (1953) Methods of Theoretical Physics, Part I. McGraw-Hill, New York.

    Google Scholar 

  29. Ohta, T. (1973) Slightly deleterious mutant substitutions in evolution. Nature 246, 96–98.

    Article  Google Scholar 

  30. Ohta, T. (1974) Mutational pressure as the main cause of molecular evolution and polymorphism. Nature 252, 351–354.

    Article  Google Scholar 

  31. Ohta, T. (1980) Evolution and Variation of Multigene Families. Lecture Notes in Biomathematics 37, Springer-Verlag, Berlin.

    Google Scholar 

  32. Ohta, T. and Kimura, M. (1973) A model of mutation appropriate to estimate the number of electrophoretically detectable alleles in a finite population. Genet. Res., Cambridge 22, 201–204.

    Article  MathSciNet  Google Scholar 

  33. Provine, W. B. (1971) The Origin of Theoretical Population Genetics. The University of Chicago Press, Chicago, I I.

    Google Scholar 

  34. Robertson, A. (1960) A theory of limits in artificial selection. Proc. R. Soc. London B 153, 234–249.

    Google Scholar 

  35. Waddington, C. H. (1939) An Introduction to Modern Genetics. Allen and Unwin, London.

    Google Scholar 

  36. Weiss, G. H. and Kimura, M. (1965) A mathematical analysis of the stepping stone model of genetic correlation. J. Appl. Prob. 2, 129–149.

    Article  MathSciNet  MATH  Google Scholar 

  37. Wright, S. (1931) Evolution in Mendelian populations. Genetics 16, 97–159.

    Google Scholar 

  38. Wright, S. (1932) The roles of mutation, inbreeding, crossbreeding and selection in evolution. Proc. VI Internat. Congr. Genet. 1, 356–366.

    Google Scholar 

  39. Wright, S. (1945) The differential equation of the distribution of gene frequencies. Proc. Nat. Acad. Sci. USA 31, 382–389.

    Article  MATH  Google Scholar 

  40. Wright, S. (1949) Adaptation and selection. In Genetics, Paleontology, and Evolution, ed. G. L. Jepsen, E. Mayr and G. G. Simpson, Princeton University Press, Princeton, NJ, 365–389.

    Google Scholar 

  41. Wright, S. (1951) Fisher and Ford on ‘the Sewall Wright effect’. Amer. Scientist 39, 452–459.

    Google Scholar 

Download references

Authors
  1. Motoo Kimura
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Statistics Program Department of Mathematics, University of California, 93106, Santa Barbara, CA, USA

    J. Gani

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Applied Probability Trust

About this chapter

Cite this chapter

Kimura, M. (1986). Diffusion Models of Population Genetics in the Age of Molecular Biology. In: Gani, J. (eds) The Craft of Probabilistic Modelling. Applied Probability, vol 1. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8631-5_10

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-8631-5_10

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8633-9

  • Online ISBN: 978-1-4613-8631-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation