Genetic versus phenotypic models of selection: Can genetics be neglected in a long-term perspective?

Game theoretical concepts in evolutionary biology have been criticized by populations geneticists, because they neglect such crucial aspects as the mating system-or the mode of inheritance. In fact, the dynamics of natural selection does not necessarily lead to a fitness maximum or an ESS if genetic constraints are taken into account. Yet, it may be premature to conclude that game theoretical concepts do not have a dynamical justification. The new paradigm of long-term evolution postulates that genetic constraints, which may be dominant in a short-term perspective, will in the long run disappear in the face of the ongoing influx of mutations. Two basic results (see Hammerstein; this issue) seem to reconcile the dynamical approach of long-term population genetics with the static approach of evolutionary game theory: (1) only populations at local fitness optima (Nash strategies) can be long-term stable; and (2) in monomorphic populations, evolutionary stability is necessary and sufficient to ensure long-term dynamic stability. The present paper has a double purpose. On the one hand, it is demonstrated by fairly general arguments that the scope of the results mentioned above extends to non-linear frequency dependent selection, to multiple loci, and to quite general mating systems. On the other hand, some limitations of the theory of long-term evolution will also be stressed: (1) there is little hope for a game theoretical characterization of stability in polymorphic populations; (2) many interesting systems do not admit long-term stable equilibria; and (3) even if a long-term stable equilibrium exists, it is not at all clear whether and how it is attainable by a series of gene substitution events