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On the changing concept of evolutionary population stability as a reflection of a changing point of view in the quantitative theory of evolution

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Abstract

Eighteen different terms, currently employed to define various concepts of evolutionary stability in population dynamics are mentioned in this paper. Most of these terms are used in different connotations and even different meanings by different authors. On the other hand, different terms are often employed by different authors to define quite the same concept. Twenty-five years ago there was only one, well-defined, concept of stability, universally recognized in the field. In this paper I will try to relate the recent confusion, concerning concepts of population stability, with a more serious, though not that well-recognized, confusion in the modern analytic approach to population dynamics and quantitative evolution. Concepts of population stability will be examined in relation to each other on the one hand and, on the other hand, in relation to two dichotomies regarding the dynamic processes to which they correspond: Short-term versus long-term processes and processes concerning phenotypic changes versus process concerning genotypic changes. A hopefully more consistent use of the current terminology is suggested.

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References

  • Bishop, D. T. and C. Cannings. 1976. Models of animal conflict. Adv. Appl. Prob.8: 616–691

    Article  MATH  Google Scholar 

  • Christiansen, F. B. 1991. Conditions for evolutionary stability for a continuously varying character. Am. Nat.138(1): 37–50

    Article  Google Scholar 

  • Christiansen, F. B. and T. M. Fenchel, 1977. Theories of Populations in Biological Communities. Springer, New York

    MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  • Eshel, I. 1983. Evolutionary and continuous stability. J. Theor. Biol.108: 99–111.

    Article  MathSciNet  Google Scholar 

  • Eshel, I. 1985. Evolutionary genetic stability of Mendelian segregation and the role of free recombination in the chromosomal system. Am. Nat.125: 412–420.

    Article  Google Scholar 

  • 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 R. Selten (ed.), Game Equilibrium models. Vol. I: Evolution and Game Dynamics. pp. 6–28. Springer-Verlag. Berlin

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Eshel, I. and M. W. Feldman, 1982b. On the evolution of sex determination and sex ratio in haplodiploid populations. Theor. Pop. Biol.21: 440–450

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  • Eshel, I. and M. W. Feldman, 1991. The handicap principle in parent-offspring conflict: Comparison of optimality and population-genetic analysis. Am. Nat.137: 167–181

    Article  Google Scholar 

  • Eshel, I. and U. Motro, 1980. Kin selection and strong evolutionary stability of mutual help. Theor. Pop. Biol,19: 420–433

    Article  MathSciNet  Google Scholar 

  • Eshel, I. and E. Sansone, 1991. Parent-offspring conflict over the sex-ratio in a diploid population with different investiment in male and in female offspring. Am. Nat.138(4): 954–972

    Article  Google Scholar 

  • Eshel, I. and E. Sansone, 1993. Parent-offspring conflict over the sex-ratio II: Offspring's response to parents' manipulation. Am. Nat. (in press)

  • Eshel, I. and D. Weinshall, 1987. Sexual reproduction and viability selection of future offspring. Am. Nat.130(5): 775–787

    Article  Google Scholar 

  • Ewens, W. J. 1969. With additive fitness, the mean fitness increases. Nature (London)221. 1076

    Google Scholar 

  • Feldman, M. W. and L. L. Cavalli-Sforza, 1981. Further remarks on Darwinian selection and “altruism”. Theor. Pop. Bio.19: 251–260.

    Article  MathSciNet  MATH  Google Scholar 

  • Feldman, M. W., F. B. Christiansen and S. P. Otto, 1991. Lewontin and Kojima meet Fisher: Linkage in a symmetric model of sex determination. — Genetics129: 297–312

    Google Scholar 

  • Fenchel, T. M. and F. B. Christiansen, 1977. Selection and interspecific competition. Pages 477–498 in F. B. Christiansen and T. M. Fenchel, eds. Measuring selection in natural populations. Springer. New York

    Google Scholar 

  • Fisher, R. A. 1930. The Genetical Theory of Natural Selection. 2nd e. 1958. Dover, New York

    MATH  Google Scholar 

  • Hamilton, W. D. 1964. The genetical evolution of social behavior. I–II. J. Theor. Biol.7: 1–16, 17–52.

    Article  Google Scholar 

  • Hamilton, W. D. 1967. Extraordinary sex-ratio. Science.156: 477–488

    Google Scholar 

  • Hamilton, W. D. 1972. Altruism and related fenomena, mainly in social insects. Annu. Rev. Ecol. Syst.3: 193–232.

    Article  Google Scholar 

  • Hamilton, W. D. 1980. Sex versus non-sex versus parasite. Oikos35: 282–290

    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 “Natural Selection and Social Behavior”, R. D. Alexander and D. W. Tinkle (eds.) Chiron Press, New York

    Google Scholar 

  • Hammerstein, P. 1994. Darwinian adaptation, population genetics and the streetcar theory of evolution. This volume

  • Hammerstein, P. and R. Selten, 1993. Evolutionary Game Theory. In Handbook of Game Theory with Economic Applications, Vol. 2, eds. R. J. Aumann and S. Hart, North-Holland: Elsevier Science Publishers (in press)

    Google Scholar 

  • Hofbauer, J., P. Schuster and K. Sigmund, 1979. A note on evolutionary stable strategies and game dynamics. J. Theor. Biol.81: 609–612

    Article  MathSciNet  Google Scholar 

  • Hofbauer, J. and K. Sigmund, 1988. The Theory of Evolution and Dynamical Systems. Cambridge University Press. Cambridge

    MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  • Karlin, S. and Lessard, 1983. On the optimal sex ratio. Proc. Nat. Acad. Sc. USA.80: 5931–5935

    MathSciNet  MATH  Google Scholar 

  • Kingman, J. F. C., 1961. A mathematical problem in population genetics. Proc. Cambridge Phil. Soc.57: 574–582

    Article  MATH  MathSciNet  Google Scholar 

  • Kojima, K. and R. C. Lewontin, 1970. Evolutionary significance of linkage and epistatasis. In “Topics in Mathematical Genetics” (K. Kojima, Ed.). Springer-Verlag. New York

    Google Scholar 

  • Lessard, S. 1990. Evolutionary stability: one concept, several meanings. Theor. Pop. Biol.37: 159–170.

    Article  MATH  MathSciNet  Google Scholar 

  • Lewontin, R. C. 1972. Testing the theory of natural selection. Nature236: 181–82

    Article  Google Scholar 

  • Lewontin, R. C., 1974. The Genetic Basis of Evolutionary Change. Columbia University Press. New York

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  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  MathSciNet  MATH  Google Scholar 

  • Liberman, U., M. W. Feldman, I. Eshel and S. Otto. 1990. Two locus autosomal sex determination. I. On the evolution of genetic stability of the sex ratio. Proc. Nat. Ac. of Sc. (USA)87: 2013–2017

    MathSciNet  MATH  Google Scholar 

  • Luria, S. and M. Delbrück 1943. Mutations of bacteria from virus sensitivity to virus resistance. Genetics28: 491–444

    Google Scholar 

  • Matessi, C. and C. Di Pasquale. 1994. Long term evolution of multilocus traits. This volume

  • Matessi, C. and I. Eshel, 1992. Sex ratio in social hymenoptera: A population genetic study of long-term evolution. Am. Nat.139: 276–312

    Article  Google Scholar 

  • Maynard-Smith, J. 1974. The theory of games and the volution of animal conflict. J. Theor. Biol.47: 209–221

    Article  MathSciNet  Google Scholar 

  • Maynard-Smith, J. 1978. The Evolution of sex. Cambridge University Press. Cambridge

    Google Scholar 

  • Maynard-Smith, J. 1980. Models of the evolution of altruism. TPB18: 151–159

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

  • Moran, P. A. P., 1964. On the nonexistance of adaptive topographies. Ann. Hum. Genet.27: 283–293

    Google Scholar 

  • Motro, U. 1991. Avoiding inbreeding and sibling competitions: Evolution of sexual dimorphism for dispersal. Am. Nat.137: 108–115

    Article  Google Scholar 

  • Motro, U. 1993. Evolutionary and continuous stability in asymetric games with continuous strategy sets: The parental investment conflict as an example. Am. Nat. (in press)

  • Motro, U. 1993. Helpers at parents'nest: A game theoretic approach. Journal of Theoretical Biology163: 127–134

    Article  Google Scholar 

  • Popper, K. R. 1972. The Logic of Scientific Discovery. Hutchinson. London

    Google Scholar 

  • Taylor, P. D. 1988. Inclusive fitness models with two sexes. Theor. Pop. Biol.34: 145–168

    Article  MATH  Google Scholar 

  • Taylor, P. D. 1989. Evolutionary stability in one-parameter models under week selection. Theor. Pop. Biol.36, 125–143

    Article  MATH  Google Scholar 

  • Taylor, P. D. 1996. Inclusive fitness arguments in genetic models of behaviour. J. Math. Biol.34: 654–674

    Article  MATH  Google Scholar 

  • Weinshall, D. and I. Eshel, 1987. On the evolution of an optimal rate of sexual reproduction. Am. Nat.130: 758–770.

    Article  Google Scholar 

  • Williams, G. C. 1975. Sex and Evolution. Monographs in Population Biology. Princeton University Press

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  1. Department of Statistics and/or School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel

    Ilan Eshel

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  1. Ilan Eshel
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Eshel, I. On the changing concept of evolutionary population stability as a reflection of a changing point of view in the quantitative theory of evolution. J. Math. Biology 34, 485–510 (1996). https://doi.org/10.1007/BF02409747

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  • DOI: https://doi.org/10.1007/BF02409747

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