Journal of Mathematical Biology

, Volume 34, Issue 5–6, pp 511–532 | Cite as

Darwinian adaptation, population genetics and the streetcar theory of evolution

  • Peter Hammerstein


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 ofn-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 inn-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 


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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Peter Hammerstein
    • 1
  1. 1.Abteilung WicklerMax-Planck-Institut für VerhaltensphysiologieSeewiesenGermany

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