Optimum foraging area in a three-trophic food chain
Abstract
Organisms' foraging strategies are shaped by a trade-off between search area and local capture efficiency. This trade-off leads individuals to adapt their foraging area to an optimal value, impacting population dynamics. Here we study the effect of multiple foraging areas in a predator-prey model composed of three trophic levels. The interactions between predators and prey occur only within a limited neighborhood of the predators, where adaptation can occur over generations. We assume a trade-off where local predation efficiency is inversely proportional to the foraging area. These dynamics were implemented computationally via cellular automata and analytically via Master Equations with mean-field and pair approximations. Unlike the mean-field approximation, the pair approximation reproduced the dependence of population density on foraging area observed in the simulations. However, the simulations showed that the optimal foraging area does not maximize population density. Moreover, we found that a polymorphic population emerged, where not a single optimal strategy but a range of optimal strategies can coexist. Using the framework of Adaptive Dynamics, we confirm that the range of optimal areas is not the one that maximizes population size, but the Evolutionary Stable Strategy that can invade a population and not be invaded.
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BibTeX
@misc{massoni2026optimum,
title = {{Optimum foraging area in a three-trophic food chain}},
author = {Lucas Massoni and Rafael Menezes and Marcus A. M. de Aguiar and Sabrina B. L. Araujo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18609},
eprint = {2609.18609},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18609},
}
RIS
TY - UNPB
TI - Optimum foraging area in a three-trophic food chain
AU - Lucas Massoni
AU - Rafael Menezes
AU - Marcus A. M. de Aguiar
AU - Sabrina B. L. Araujo
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18609
UR - https://arxiv.org/abs/2609.18609
AB - Organisms' foraging strategies are shaped by a trade-off between search area and local capture efficiency. This trade-off leads individuals to adapt their foraging area to an optimal value, impacting population dynamics. Here we study the effect of multiple foraging areas in a predator-prey model composed of three trophic levels. The interactions between predators and prey occur only within a limited neighborhood of the predators, where adaptation can occur over generations. We assume a trade-off where local predation efficiency is inversely proportional to the foraging area. These dynamics were implemented computationally via cellular automata and analytically via Master Equations with mean-field and pair approximations. Unlike the mean-field approximation, the pair approximation reproduced the dependence of population density on foraging area observed in the simulations. However, the simulations showed that the optimal foraging area does not maximize population density. Moreover, we found that a polymorphic population emerged, where not a single optimal strategy but a range of optimal strategies can coexist. Using the framework of Adaptive Dynamics, we confirm that the range of optimal areas is not the one that maximizes population size, but the Evolutionary Stable Strategy that can invade a population and not be invaded.
ER -