OPTIMAL RESOURCE-ALLOCATION AND THE MARGINAL VALUE OF ORGANS

Using Pontryagin's maximum principle from optimal control theory, I investigate patterns of optimal allocation of energy toward the several state variables constituting an organism's body (e.g., locomotor system, acquisition or protective structures, etc.) and affecting its production rate (P) and/or mortality probability (mu). The trade-offs between state variables are assumed to be linear, the environment is constant, and the time horizon is infinite (i.e., no maximal longevity is assumed). The following rules are shown to be necessary conditions for the allocation strategy to result in the maximum feasible rate of increase (r*): all allocation must go to the organ(s) that provide(s) the highest return, in terms of increasing P/(r* + mu), provided that this return exceeds investment; if several organs provide the same return, then allocation must be simultaneous and must be such that the returns decrease at the same rate; and as soon as the highest return is equal to investment, all production must be channeled into reproduction. These results extend previous analyses and are discussed in the several contexts of ontogenetic changes and phenotypic plasticity in resource allocation, patterns of growth and survival, density dependence and r/K theory, complex life cycles, and colony expansion paths of insect societies.