Diet optimization with a nutrient or toxin constraint
The optimal foraging theory has been established as a major branch of ecology in the last two decades. The most basic model for prey selection is called the contingency model or the prey model as opposed to the patch model. The contingency model concerns only energy intake and predicts a zero-one type selection based on the ranking of prey types according to energy/handling-time ratio. The possible influences of nutrient or toxin constraints on prey selection have been suggested for generalist herbivores. These were developed into algebraic models as an extension of the contingency model or as a linear programming model. \textit{H. R. Pulliam} [Am Nat. 109, 765-768 (1975)]\ formulated a prey-selection model with a nutrient constraint by adding a constraint inequality to the contingency model and showed its solution for the two-prey-type case. \textit{P. W. Stephens} and \textit{J. R. Krebs} [Foraging theory. (1986); pp. 61-63]\ modified his model to represent the situation with a toxin constraint by reversing the direction of constraint inequality. However, I believe the constraint conditions of these models were not properly formulated and present the appropriate formulation of a diet optimization model with a toxin or nutrient constraint. Its general solutions for the optimal diet will be provided, and the solutions for the two-prey-type case will be compared with those of Pulliam and of Stephens and Krebs.
scientific article; zbMATH DE number 792757