Diet optimization with a nutrient or toxin constraint
type: Item
instance of: scholarly article
title: Diet optimization with a nutrient or toxin constraint
zbMATH Open document ID: 0843.92023
author: Hirofumi Hirakawa
published in: Theoretical Population Biology
publication date: 1995-09-04T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 92D40
zbMATH DE Number: 792757
zbMATH Keywords: prey-selection model
zbMATH Keywords: nutrient constraint
zbMATH Keywords: constraint inequality
zbMATH Keywords: contingency model
zbMATH Keywords: toxin constraint
zbMATH Keywords: diet optimization model
zbMATH Keywords: two-prey-type case
MaRDI profile type: Publication
full work available at URL: tpbi.1995.1015
OpenAlex ID: W1999118693
Wikidata QID: Q72041758
DOI: 10.1006/TPBI.1995.1015
description: scientific article; zbMATH DE number 792757