Skip to main content

Game Theory and Population Dynamics in Complex Genetical Systems: The Role of Sex in Short Term and in Long Term Evolution

  • Chapter
Game Equilibrium Models I

Abstract

The article maintains three major points:

  1. (1)

    In sexual populations with recombination, there is a qualitative difference between one process of natural selection which manifests itself in terms of changes of frequencies of genotypes already present in the population (say, short term selection) and another process which manifests itself in terms of selective gene substitutions (say, long term selection).

  2. (2)

    It is only the process of long term selection (due to gene substitutions) and not the process of short term selection (due to changes in genotype frequencies) that, quite generally, leads to the individual optimization of certain evolutionarily relevant payment functions and thus guarantees the stabilization of ESS population strategies.

  3. (3)

    These findings, based on theoretical analysis of the well studied genetic structure of sexual reproduction, fit into the main bulk of current theories about the evolution of the sexual system of reproduction in a changing environment. They can, in turn, throw some new light on the role of sex in preventing fast adaptation to short—term, notersisting environmental changes and, at the same time, allow (and, as I claim, even facilitate)) slow adaptation to long—term, persisting environmental changes.

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

Access this chapter

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
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover 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

  • Bell, G. (1982): The Masterpiece of Nature: The Evolution and Genetics of Sexuality. Berkeley: University of California Press.

    Google Scholar 

  • Bell, G. and J. Maynard Smith (1987): Short-term selection for recombination among mutually antagonistic species. Nature 328: 66–68.

    Article  Google Scholar 

  • Bernstein, H. (1983): Recombinational repair may be an important function of sexual reproduction. BioScience 33: 326–331.

    Article  Google Scholar 

  • Bernstein, H., H.C. Byerly, F.A. Hopf and R.E. Michod (1984): Origin of sex. J. theor. Biol. 110: 323–351.

    Article  Google Scholar 

  • Bernstein, H., H.C. Byerly, F.A. Hopf and R.E. Michod (1985): Genetic damage, mutation and the evolution of sex. Science 229: 1277–1281.

    Article  Google Scholar 

  • Bremermann, H.J. (1980): Sex and polymorphism as strategies in host-pathogen interaction. J. theor. Biol. 87: 671–702.

    Article  Google Scholar 

  • Bremermann, H.J. (1985): The adaptive significance of sexuality. Experientia 41: 1245–1254.

    Article  Google Scholar 

  • Bulmer, M.G. (1981): Worker-queen conflict in annual social hymenoptera. J. theor. Biol. 72: 701–727.

    Google Scholar 

  • Bulmer, M.G. and P.D. Taylor (1981): Worker-queen conflict and sex ratio in social hymenoptera. Heredity 47: 197–207.

    Article  Google Scholar 

  • Cavalli-Sforza, L.L. and M.W. Feldman (1978): Darwinian selection and altruism. Theor. Pop. Biol. 14: 268–280.

    Article  Google Scholar 

  • Charlesworth, B. (1976): Recombination modification in a fluctuating environment. Genetics 83: 181–195.

    Google Scholar 

  • Crow, J.F. (1988): The importance of recombination. In: R.E. Michod and B.R. Levin (Eds.): The Evolution of Sex: An Examination of Current Ideas. Sunderland, MS: Sinauer Ass., pp. 56–73.

    Google Scholar 

  • Crow, J.F. and M. Kimura (1965): Evolution in sexual and asexual populations. Amer. Natur. 99: 439–450.

    Article  Google Scholar 

  • Crow, J.F. and M. Kimura (1969): Evolution in sexual and asexual populations: A reply. Amer. Natur. 103: 89–91.

    Article  Google Scholar 

  • Eshel, I. (1970): On the evolution in a population with an infinite number of types. Theor. Pop. Biol. 2: 209–236.

    Article  Google Scholar 

  • Eshel, I. (1971): Evolution processes with continuity of types. Adv. Appl. Prob. 4: 475–507.

    Article  Google Scholar 

  • Eshel, I. (1972): Evolution in diploid populations with continuity of gametic types. Adv. Appl. Prob. 5: 55–65.

    Article  Google Scholar 

  • Eshel, I. (1974): Selection on the sex ratio and the evolution of sex-determination. Heredity 34: 351–361.

    Article  Google Scholar 

  • Eshel, I. (1982): Evolutionarily stable strategies and viability selection in Mendelian populations. Theor. Pop. Biol. 22: 204–217.

    Article  Google Scholar 

  • Eshel, I. (1984): On the evolution of an inner conflict. J. theor. Biol. 108: 65–76.

    Article  Google Scholar 

  • Eshel, I. (1985): On the evolutionary genetic stability of Mendelian segregation and the role of free recombination. Amer. Natur. 125: 412–420.

    Article  Google Scholar 

  • Eshel, I. and E. Akin (1983): Coevolutionary instability of mixed Nash solutions. J. Math. Biol. 18: 123–133.

    Article  Google Scholar 

  • Eshel, I. and M.W. Feldman (1970): On the evolutionary effect of recombination. Theor. Pop. Biol. 1: 88–100.

    Article  Google Scholar 

  • Eshel, I. and M.W. Feldman (1982): On the evolutionary genetic stability of the sex ratio. Theor. Pop. Biol. 21: 430–439.

    Article  Google Scholar 

  • Eshel, I. and M.W. Feldman (1984): Initial increase of new mutants and some continuity properties of ESS in two locus systems. Amer. Natur. 124: 631–640.

    Article  Google Scholar 

  • Eshel, I. and W.D. Hamilton (1984): Parent-offspring correlation in fitness under fluctuating selection. Proc. Roy. Soc. Lond. B 222: 1–14.

    Article  Google Scholar 

  • Eshel, I. and E. Sansone (1989): Parent offspring conflict over the sex ratio in a diploid population with different investment in male and in female offspring. Theor. Pop. Biol. (in press).

    Google Scholar 

  • Eshel, I. and D. Weinshall (1987): Sexual reproduction and viability of future offspring. Amer. Natur. 130: 775–787.

    Article  Google Scholar 

  • Ettinger, L. (1986): Meiosis: A selection stage preserving the genome’s pattern of organization. Evol. Theor. 8: 17–26.

    Google Scholar 

  • Ewens, W.J. (1968): A genetic model having complex linkage behavior. Theor. Appl. Genet. 38: 140–143.

    Article  Google Scholar 

  • Feldman, M.W. (1972): Selection for linkage modifications. I. Random mating populations. Theor. Pop. Biol. 3: 324–346.

    Article  Google Scholar 

  • Feldman, M.W. and B. Balkan (1972): Some results in the theory of three gene loci. In: T.N.E. Greville (Ed.): Population Dynamics. New York: Academic Press.

    Google Scholar 

  • Feldman, M.W. and F.B. Christiansen (1984): Population genetic theory of the cost of inbreeding. Amer. Natur. 123: 642–653.

    Article  Google Scholar 

  • Feldman, M.W., F.B. Christiansen and L.D. Brooks (1980): Evolution of recombination in a constant environment. Proc. Natl. Acad. Sci. USA 77: 4838–4841.

    Article  Google Scholar 

  • Feldman, M.W. and U. Liberman (1986): An evolutionary reduction principle for genetic modifiers. Proc. Natl. Acad. Sci. USA 83: 4824–4827.

    Article  Google Scholar 

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

    Google Scholar 

  • Fisher, R.A. (1935): The sheltering of lethals. Amer. Natur. 69: 445–446.

    Google Scholar 

  • Glesener, R. and D. Tilman (1978): Sexuality and the components of environmental uncertainty: Clues from geographic parthenogenesis in terrestrial animals. Amer. Natur. 112: 659–673.

    Article  Google Scholar 

  • Gould, S.J. and R.C. Lewontin (1979): The spandrels of San Marco and the Panglossian paradigm: A critique of the adaptationist programme. Proc. Roy. Soc. Lond. B 205: 581–598.

    Article  Google Scholar 

  • Hadeler, K. and U. Liberman (1975): Selection models with fertility differences. J. Math. Biol. 2: 19–32.

    Article  Google Scholar 

  • Hamilton, W.D. (1964): The genetical evolution of social behavior. J. theor. Biol. 7: 1–52.

    Article  Google Scholar 

  • Hamilton, W.D. (1967): Extraordinary sex ratios. Science 156: 477–488.

    Article  Google Scholar 

  • Hamilton, W.D. (1980): Sex versus non-sex versus parasite. Oikos 35: 282–290.

    Article  Google Scholar 

  • Hamilton, W.D. (1982): Pathogens as causes of genetic diversity in their host populations. In: R.M. Anderson and R.M. May (Eds.): Population Biology of Infectious Diseases. New York: Springer-Verlag.

    Google Scholar 

  • Hamilton, W.D., P.A. Henderson and N.A. Moran (1981): Fluctuation of environment and coevolved antagonist polymorphism as factors in the maintenance of sex. In: R.D. Alexander and D.W. Tinkle (Eds.): Natural Selection and Social Behavior. New York: Chiron Press.

    Google Scholar 

  • Hamilton, W.D. and M. Zuk (1982): Heritable true fitness and bright birds: A role for parasites? Science 218: 384–387.

    Article  Google Scholar 

  • Jaenike, J. (1978): An hypothesis to account for the maintenance of sex within populations. Evol. Theor. 3: 191–194.

    Google Scholar 

  • Karlin, S. (1968): Equilibrium behavior of population genetic models with nonrandom mating. J. App. Prob. 5: 487–566.

    Article  Google Scholar 

  • Karlin, S. (1973): Sex and infinity: A mathematical analysis of the advantages and disadvantages of genetic recombination. In: M. Bartlett and R. Hioms (Eds.): The Mathematical Theory of the Dynamics of Biological Populations. New York: Academic Press.

    Google Scholar 

  • Karlin, S. (1975): General two-locus selection models: Some objectives, results and interpretations. Theor. Pop. Biol. 7: 364–398.

    Article  Google Scholar 

  • Karlin, S. and S. Lessard (1983): On the optimal sex ratio. Proc. Natl. Acad. Sci. USA 80: 5931–5935.

    Article  Google Scholar 

  • Karlin, S. and S. Lessard (1986): Theoretical Studies on Sex Ratio Evolution. Princeton NJ: Princeton University Press.

    Google Scholar 

  • Kingman, J.F.C. (1961): A mathematical problem in population genetics. Proc. Camb. Philos. Soc. 57: 574–582.

    Article  Google Scholar 

  • Lessard, S. (1984): Evolutionary dynamics in frequency dependent two phenotype models. Theor. Pop. Biol. 25: 210–234.

    Article  Google Scholar 

  • Levin, B.R. (1988): The evolution of sex in bacteria. In: R.E. Michod and B.R. Levin (Eds.): The Evolution of Sex: An Examination of Current Ideas. Sunderland, MS: Sinauer Ass., pp. 194–211.

    Google Scholar 

  • Levin, D.A. (1975): Pest pressure and recombination systems in plants. Amer. Natur. 109: 437–451.

    Article  Google Scholar 

  • Lewontin, R.C. (1971): The effect of genetic linkage on the mean fitness of a population. Proc. Natl. Acad. Sci. USA 68: 984–986.

    Article  Google Scholar 

  • Liberman, U. (1976): Theory of meiotic drive: Is Mendelian segregation stable? Theor. Pop. Biol. 10: 127–132.

    Article  Google Scholar 

  • Liberman, U. (1988): External stability and ESS: Criteria for initial increase of a new mutant allele. J. Math. Biol. 26: 477–485.

    Article  Google Scholar 

  • Liberman, U. and M.W. Feldman (1986): A general reduction principle for genetic modifiers of recombination. Theor. Pop. Biol. 30: 341–371.

    Article  Google Scholar 

  • Liberman, U., M.W. Feldman, I. Eshel and S.P. Otto (1989): Two locus autosomal sex determination. I. On the evolutionary genetic stability of the even sex ratio. Manuscript.

    Google Scholar 

  • Maynard Smith, J. (1971): The origin and maintenance of sex. In: G.C. Williams (Ed.): Group Selection. Chicago: Aldine Atherton, pp. 165–175.

    Google Scholar 

  • Maynard Smith, J. (1974): The theory of games and the evolution of animal conflict. J. theor. Biol. 47: 209–221.

    Article  Google Scholar 

  • Maynard Smith, J. (1975): Evolution of sex. Nature 254.

    Google Scholar 

  • Maynard Smith, J. (1978): The Evolution of Sex. Cambridge: Cambridge University Press.

    Google Scholar 

  • Maynard Smith, J. (1982): Evolution and the Theory of Games. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Maynard Smith, J. (1988): Selection for recombination in a polygenic model — The mechanism. Genet. Res. Cam. 51: 59–63.

    Article  Google Scholar 

  • Maynard Smith, J. and G.A. Parker (1976): The logic of asymmetric contests. Anim. Behay. 24: 159–175.

    Article  Google Scholar 

  • Maynard Smith, J. and G.R. Price (1973): The logic of animal conflict. Nature 246: 15–18.

    Article  Google Scholar 

  • Moran, P.A.P. (1964): On the nonexistence of adaptive topographies. Ann. Hum. Genet. 27: 338–343.

    Google Scholar 

  • Muller, H.J. (1932): Some genetic aspects of sex. Amer. Natur. 66: 118–138.

    Article  Google Scholar 

  • Muller, H.J. (1958): Evolution by mutation. Bull. Amer. Math. Soc. 64: 137–160.

    Article  Google Scholar 

  • Oster, G., I. Eshel and D. Cohen (1977): Evolution of social insects. Theor. Pop. Biol. 12: 49–68.

    Article  Google Scholar 

  • Rice, W.R. (1983): Parent-offspring pathogen transmission: A selective agent promoting sexual reproduction. Amer. Natur. 121: 187–203.

    Article  Google Scholar 

  • Seger, J. and W.D. Hamilton (1988): Parasites and sex. In: R.E. Michod and B.R. Levin (Eds.): The Evolution of Sex: An Examination of Current Ideas. Sunderland, MS: Sinauer Ass., pp. 176–193.

    Google Scholar 

  • Selten, R. (1980): A note on evolutionarily stable strategies in asymmetric animal conflicts. J. theor. Biol. 84: 93–101.

    Article  Google Scholar 

  • Selten, R. (1983): Evolutionary stability in extensive two-person games. Math. Soc. Sci. 5: 269–363.

    Article  Google Scholar 

  • Sturtevant, A.H. and K. Mather (1938): The interrelations of inversions, heterosis and recombination. Amer. Natur. 72: 447–452.

    Article  Google Scholar 

  • Taylor, P.D. (1985): A general mathematical model for sex allocation. J. theor. Biol. 112: 799–818.

    Article  Google Scholar 

  • Thompson, V. (1976): Does sex accelerate evolution? Evol. Theory 1: 131–156.

    Google Scholar 

  • Tooby, J. (1982): Pathogens, polymorphism, and the evolution of sex. J. theor. Biol. 97: 557–576.

    Article  Google Scholar 

  • Trivers, R.L. and H. Hare (1976): Haplodiploidy and the evolution of social insects. Science 191: 249–263.

    Article  Google Scholar 

  • Uyenoyama, M.K. (1984): On the evolution of parthenogenesis: A genetic representation of the ‘cost of meiosis’. Evolution 38: 87–102.

    Article  Google Scholar 

  • Uyenoyama, M.K. and B.O. Bengtsson (1981): Towards a genetic theory for the evolution of the sex ratio. II. Haplodiploid and diploid models with sibling and parent control of the brood sex ratio and brood size. Theor. Pop. Biol. 20: 57–79.

    Article  Google Scholar 

  • Uyenoyama, M.K. and B.O. Bengtsson (1982): Towards a genetic theory for the evolution of the sex ratio. III. Parental and sibling control of brood investment ratio under partial sib-mating. Theor. Pop. Biol. 22: 43–668.

    Article  Google Scholar 

  • Uyenoyama, M.K. and M.W. Feldman (1981): On relatedness and adaptive topography in kin selection. Theor. Pop. Biol. 19: 87–123.

    Article  Google Scholar 

  • Weinshall, D. (1986): Why is a two-environment system not rich enough to explain the evolution of sex? Amer. Natur. 128: 736–750.

    Google Scholar 

  • Weinshall, D. and I. Eshel (1987): On the evolution of an optimal rate of sexuality. Amer. Natur. 130: 578–770.

    Google Scholar 

  • Williams, G.C. (1966): Adaptation and Natural Selection. Princeton: Princeton Univ. Press.

    Google Scholar 

  • Williams, G.C. (1975): Sex and Evolution. Princeton: Princeton Univ. Press.

    Google Scholar 

  • Williams, G.C. (1988): Retrospect on sex and kindred topics. In: R.E. Michod and B.R. Levin (Eds.): The Evolution of Sex: An Examination of Current Ideas. Sunderland, MS: Sinauer Ass., pp. 287–298.

    Google Scholar 

  • Williams, G.C. and J.B. Mitton (1973): Why reproduce sexually ? J. theor. Biol. 39: 545–554.

    Article  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Eshel, I. (1991). Game Theory and Population Dynamics in Complex Genetical Systems: The Role of Sex in Short Term and in Long Term Evolution. In: Selten, R. (eds) Game Equilibrium Models I. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02674-8_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-02674-8_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08108-8

  • Online ISBN: 978-3-662-02674-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics