Does frequency-dependent selection optimize fitness?

In evolutionary biology, the axiom that natural selection tends ideally to maximize inclusive fitness of the individual or some other suitable quantity is often advanced (Cody, 1974; Maynard Smith, 1978; Krebs & McCleery, 1984; Houston et al., 1988). Moreover, the evolutionists generally distinguish two situations (Dawkins, 1980; Maynard Smith, 1982): one in which fitness is independent of the frequency of the phenotypes present in the population (frequency-independent selection), and one in which it does depend on this frequency (frequency-dependent selection). This led some authors such as Parker (1984), and more recently Parker & Maynard Smith (1990), to consider "a 2-speed optimization": frequency-independent selection should lead to a "simple optimum" at the end of the selective process, since all the individuals should have the same strategy and the mean fitness of the population should be maximized; frequency-dependent selection, formulated in terms of the theory of games, should lead to a "competitive optimum" even though the "evolutionary stable strategy" (or "ESS"; Maynard Smith & Price, 1973) characterizing the equilibrium "is not the strategy that maximizes fitness in a population sense" (Parker & Maynard Smith, 1990: 30). Our aim in this short communication is to criticize the concept of "competitive optimum" by Parker & Maynard Smith, as well as the general ability of natural selection to "maximize fitness", even in "phenotypic models" (Lloyd, 1977). These models, devoid of genetic constraints since each strategist is assumed to reproduce its own kind, are especially suitable for examining the ideal effect of natural selection.