# Darwinian adaptation, population genetics and the streetcar theory of evolution

- 421 Downloads
- 101 Citations

## Abstract

This paper investigates the problem of how to conceive a robust theory of phenotypic adaptation in non-trivial models of evolutionary biology. A particular effort is made to develop a foundation of this theory in the context of*n*-locus population genetics. Therefore, the evolution of phenotypic traits is considered that are coded for by more than one gene. The potential for epistatic gene interactions is not a priori excluded. Furthermore, emphasis is laid on the intricacies of frequency-dependent selection. It is first discussed how strongly the scope for phenotypic adaptation is restricted by the complex nature of ‘reproduction mechanics’ in sexually reproducing diploid populations. This discussion shows that one can easily lose the traces of Darwinsm in*n*-locus models of population genetics. In order to retrieve these traces, the outline of a new theory is given that I call ‘streetcar theory of evolution’. This theory is based on the same models that geneticists have used in order to demonstrate substantial problems with the ‘adaptationist programme’. However, these models are now analyzed differently by including thoughts about the evolutionary removal of genetic constraints. This requires consideration of a sufficiently wide range of potential mutant alleles and careful examination of what to consider as a stable state of the evolutionary process. A particular notion of stability is introduced in order to describe population states that are phenotypically stable against the effects of all mutant alleles that are to be expected in the long-run. Surprisingly, a long-term stable state can be characterized at the phenotypic level as a fitness maximum, a Nash equilibrium or an ESS. The paper presents these mathematical results and discusses — at unusual length for a mathematical journal — their fundamental role in our current understanding of evolution.

## Key words

Adaptation Optimality Nash equilibrium ESS N-locus genetics Epistasis Long-term evolution Rationality paradox## Preview

Unable to display preview. Download preview PDF.

## References

- Dawkins, R. (1976). The selfish gene. Oxford: Oxford Unversity PressGoogle 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 (Eds), Game Equilibrium Models I: Evolution and Game Dynamics (pp. 6–28). Berlin: Springer-VerlagGoogle Scholar
- Eshel, I. (1983). Evolutionary and continuous stability. J. Theor. Biol.
**103**, 99–111CrossRefMathSciNetGoogle Scholar - Eshel, I. (1995). On the changing concept of population stability as a reflection of changing problematics in the quantitative theory of evolution. J. Math. Biol.
**34**, 485–510.CrossRefGoogle Scholar - Eshel, I. and Feldman, M. W. (1984). Initial increase of new mutants and some continuity properties of ESS in two locus systems. Am. Nat.
**124**, 631–640CrossRefGoogle Scholar - Ewens, W. J. (1968). A genetic model having complex linkage behavior. Theor. and Appl. Genet.,
**38**, 140–143CrossRefGoogle Scholar - Fudenberg, D. and Tirole, J. (1991). Game Theory. Cambridge, Massachusetts: The MIT PressGoogle Scholar
- Gould, S. J. and Lewontin, R. C. (1979). The spandrels of San Marco and the Panglossian paradigm: a critique of the adaptationist programme. Proc. R. Soc. Lond. B,
**205**, 581–598CrossRefGoogle Scholar - Hammerstein, P. and Selten, R. (1994). Game theory and evolutionary biology. In: R. J. Aumann and S. Hart (Eds), Handbook of Game Theory with Economic Applications. Volume 2, pp. 929–993. Amsterdam: ElsevierGoogle Scholar
- Harsanyi, J. C. and Selten, R. (1988). A general theory of equilibrium selection in games. Cambridge, Massachusetts: The MIT PresszbMATHGoogle Scholar
- Karlin, S. (1975). General two-locus selection models: some objectives, results and interpretations, Theor. Pop. Biol.,
**7**, 364–398CrossRefzbMATHMathSciNetGoogle Scholar - Lessard, S. (1984). Evolutionary dynamics in frequency-dependent two phenotype models. Theor. Pop. Biol.
**25**, 210–234CrossRefzbMATHGoogle Scholar - Liberman, U. (1988). External stability and ESS: criteria for initial increase of a new mutant allele. J. Math. Biol.,
**26**, 477–485.zbMATHMathSciNetGoogle Scholar - Maynard Smith, J. (1978). Optimisation theory in evolution. Am. Rev. Ecol. Syst.,
**9**, 31–56CrossRefGoogle Scholar - Maynard Smith, J. (1982). Evolution and the Theory of Games. Cambridge: Cambridge University PresszbMATHGoogle Scholar
- Maynard Smith, J. and Price, G. R. (1973). The logic of animal conflict. Nature,
**246**, 15–18CrossRefGoogle Scholar - Moran, P. A. P. (1964). On the nonexistence of adaptive topographies. Am. Human Genet.,
**27**, 338–343Google Scholar - Nash, J. F. (1951). Non-cooperative games. Ann. Math.
**54**, 286–295CrossRefzbMATHMathSciNetGoogle Scholar - Tyszka, T. (1983). Contextual multiattribute decision rules. In: L. Sjöberg, T. Tyszka and J. A. Wise (Eds), Human Decision Making (pp. 243–256)Google Scholar
- Weissing, F. J. (1995). Genetic versus phenotypic models of selection: can genetics be neglected in a long-term perspective? J. Math. Biol.
**34**, 533–555CrossRefGoogle Scholar - Wright, S. (1932). The roles of mutation, inbreeding, crossbreeding, and selection in evolution. Proc. XI. Internat. Congr. Genetics,
**1**, 356–366Google Scholar