If an optimization principle -0 exists, each successful mutant increases -0(X), and hence any ESS attracts. Moreover, 0(Eattr(X)) increases with each increase in ^(X). Since fitness decreases with 0 where it counts, that is, around zero, 0 may be dubbed pessimization principle. When a pessimization principle exists, in the end the worst attainable world remains, together with the type(s) that can just cope with it.
The following example may give a more concrete feel for the issue. Consider a structured population in continuous time regulated through an additional h-state-independent death rate dE and with all other demographic parameters independent of E. Then the mean death rate (dE(E(t)))time associated with an environment provides a pessimization, and the asymptotic relative growth rate p0 calculated on the assumption that dE — 0 an optimization principle. A special case is where the environment is constant except for occasional decimating catastrophes, provided the latter kill totally indiscriminately (so that p0 may be identified with r for that constant environment). But for the (essential, but generally unmentioned) indiscriminateness, this is the condition touted in the textbooks as supporting r-maximization.
Optimization principles come closest to the textbook intuition for the meaning offitness, which generally fails to account for the fact that the fitnesses of all possible types are bound to change with any change in the character of the residents. The results above show that optimization principles, although frequently encountered in the literature, are exceptions rather than the rule.
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