A general principle for the allocation of limited resources

Abstract

A marginal fitness theorem is derived for the allocation of a limited resource among alternative activities that have effects on the fitness of an individual. The ‘marginal advantage theorem’ states that at the evolutionarily stable strategy (ESS), the marginal gains from increasing each of the allocations (expressed as partial derivatives of the fitness advantage of a rare mutant) are equal. The theorem is true for all proportional allocations (a + b + c + ...=j), regardless of the number of allocations, the nature of the response curves describing the direct effects of the allocations [f(a), etc.], or the way the effects of different allocations combine into fitness. The theorem is extended to size-number compromises and packaging strategies. The marginal advantage theorem is used to derive general theorems about the marginal effects of allocations [f′ (a), etc.] at the ESS and matching rules concerned with the total fitness to cost ratios of allocations at the ESS. The marginal advantage theorem is applicable to diverse allocation strategies, and provides a method for obtaining ESS allocations for any number of allocations and their components.