Skip to main content
Log in

Mutation-selection models in population genetics and evolutionary game theory

  • II. Selection and Evolutionary Games
  • Published:
Acta Applicandae Mathematica Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

References

  • Akin E. 1979. The Geometry of Population Genetics. Lect. Notes Biomath. 31. Berlin-Heidelberg-New York. Springer Verlag.

    Google Scholar 

  • Akin E., Hofbauer J. 1982. Recurrence of the unfit. Math. Biosci. 61, 51–63.

    Google Scholar 

  • Barton N. 1986. The maintenance of polygenic variation through a balance between mutation and stabilizing selection. Genet. Res. 47, 209–216.

    Google Scholar 

  • Bulmer M.G. 1971. Protein polymocphism. Nature 234, 410–411.

    Google Scholar 

  • Bürger R. 1983. Dynamics of the classical genetic model for the evolution of dominance. Math. Biosci. 67, 269–280.

    Google Scholar 

  • Bürger R. 1986. On the maintenance of genetic variation: Global analysis of Kimura's continuum-of-alleles model. J. Math. Biol. 24, 341–351.

    Google Scholar 

  • Bürger R. 1988a. Perturbations of positive semigroups and applications to population genetics. Math. Z. 197, 259–272.

    Google Scholar 

  • Bürger, R. 1988b. Mutation-selection balance and continuum-of-alleles models. Math. Biosci. To appear.

  • Bürger, R. 1988c. Linkage and the maintenance of heritable variation by mutation-selection balance. Submitted.

  • Bürger, R., Wagner, G., Stettinger, F. 1988. How much heritable variation can be maintained in finite populations by a mutation-selection balance? Submitted.

  • Crow J.F., Kimura M. 1964. The theory of genetic loads. Proc. XI Int. Congr. Genet. pp. 495–505. Oxford: Pergamon Press.

    Google Scholar 

  • Crow J.F., Kimura M. 1970. An Introduction to Population Genetics. New York: Harper and Row.

    Google Scholar 

  • Eigen M. 1971. Selforganization of matter and the evolution of biological macromolecules. Die Naturwissenschaften 58, 465–523.

    Google Scholar 

  • Fleming W.H. 1979. Equilibrium distributions of continuous polygenic traits. SIAM J. Appl. Math. 36, 148–168.

    Google Scholar 

  • Hadeler K.P. 1981. Stable polymorphisms in a selection model with mutation, SIAM J. Appl. Math. 41, 1–7.

    Google Scholar 

  • Hofbauer J. 1985. The selection mutation equation. J. Math. Biol. 23, 41–53.

    Google Scholar 

  • Hofbauer, J., Sigmund, K. (1988). Dynamical Systems and the Theory of Evolution. Cambridge Univ. Press. In press.

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

    Google Scholar 

  • Kingman J.F.C. 1961a. On an inequality in partial averages. Quart. J. Math. 12, 78–80.

    Google Scholar 

  • Kingman J.F.C. 1961b. A convexity property of positive matrices. Quart. J. Math. 12, 283–284.

    Google Scholar 

  • Kingman J.F.C. 1977. On the properties of bilinear models for the balance between genetic mutation and selection. Math. Proc. Camb. Phil. Soc. 81, 443–453.

    Google Scholar 

  • Kingman J.F.C. 1978. A simple model for the balance between selection and mutation. J. Appl. Prob. 15, 1–12.

    Google Scholar 

  • Losert V., Akin E. 1983. Dynamics of games and genes: discrete versus continuous time. J. Math. Biol. 17, 241–251.

    Google Scholar 

  • Lyubich Yu.I., Maistrovskii G.D., Ol'klovski Yu.G. 1980. Selection-induced convergence to equilibrium in a single-locus autosomal population. Problemy Peredachi Informatsii 16, 93–104 (engl. transl.).

    Google Scholar 

  • Moran P.A.P. 1976. Global stability of genetic systems governed by mutation and selection. Math. Proc. Camb. Phil. Soc. 80, 331–336.

    Google Scholar 

  • Moran P.A.P. 1977. Global stability of genetic systems governed by mutation and selection. II. Math. Proc. Camb. Phil. Soc. 81, 435–441.

    Google Scholar 

  • Mulholland H.P., Smith C.A.B. 1959. An inequality arising in genetic theory. Amer. Math. Monthly 66, 673–683.

    Google Scholar 

  • Nagylaki T. 1984. Selection on a quantitative character. In: Human Population Genetics: The Pittsburgh Symposium. (A. Chakravarti, Ed.) New York: Van Nostrand.

    Google Scholar 

  • Nagylaki T., Crow J.F. 1974. Continuous selective models. Theor. Pop. Biol. 5, 257–283.

    Google Scholar 

  • Newburgh J.D. 1951. The variation of spectra. Duke Math. J. 18, 165–176.

    Google Scholar 

  • O'Brien P. 1985. A genetic model with mutation and selection. Math. Biosci. 73, 239–251.

    Google Scholar 

  • Ohta T., Kimura M. 1973. A model of mutation appropriate to estimate the number of electrophoretically detectable alleles in a finite population. Gen. Res. 22, 201–204.

    Google Scholar 

  • Ohta T., Kimura M. 1975. Theoretical analysis of electrophoretically detectable polymorphisms: Models of very slightly deleterious mutations. Amer. Natur. 109, 137–145.

    Google Scholar 

  • Scheuer P., Mandel S. 1959. An inequality in population genetics. Heredity 13, 519–524.

    Google Scholar 

  • Sigmund K. 1987. Game dynamics, mixed strategies, and gradient systems. Theor. Pop. Biol. 32, 114–126.

    Google Scholar 

  • Taylor P., Jonker L. 1978. Evolutionarily stable strategies and game dynamics. Math. Biosci. 40, 145–156.

    Google Scholar 

  • Thomas, B. Evolutionarily stable sets and mixed strategist models. Theor. Pop. Biol. 28, 332–341.

  • Thompson C.J., McBride J.L. 1974. On Eigen's theory of self-organization of matter and the evolution of biological macromolecules. Math. Biosci. 21, 127–142.

    Google Scholar 

  • Turelli M. 1984. Heritable genetic variation via mutation-selection balance: Lerch's zeta meets the abdominal bristle. Theor. Pop. Biol. 25, 138–193.

    Google Scholar 

  • Turelli M. 1986. Gaussian versus non-Gaussian genetic analyses of polygenic mutation-selection balance. pp. 607–628. In: Evolutionary Processes and Theory (edt. by S. Karlin and E. Nevo). New York: Academic Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bürger, R. Mutation-selection models in population genetics and evolutionary game theory. Acta Appl Math 14, 75–89 (1989). https://doi.org/10.1007/BF00046675

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00046675

AMS Subject Classification (1980)

Key words

Navigation