Predator-prey systems with group defence: The paradox of enrichment revisited
type: Item
instance of: scholarly article
title: Predator-prey systems with group defence: The paradox of enrichment revisited
zbMATH Open document ID: 0612.92017
DOI: 10.1007/BF02462320
published in: Bulletin of Mathematical Biology
publication date: 1986-01-01T00:00:00Z
review text: The authors discuss survival and extinction of predators in models of predator-prey systems exhibiting group defence of the prey. Such phenomena were less studied before. They show that if there is no mutual interference among predators, enrichment of the prey can lead to extinction in a closed ecosystem and thereby provide more support for Rosenzweig's warning that is well-known and controverted. But if there is mutual interference among predators, the model is uniformly persistent just as in previus work. Numerical examples are also indicated. The models of this paper can be carefully studied with a specific response function. Recently, Zhang Faqin obtained conditions on existence and uniqueness of limit cycles and persistence and extinction for this model with generally chosen parameters (to appear in J. Biomath., Vol. 3).
Mathematics Subject Classification ID: 92D40
zbMATH DE Number: 3991324
zbMATH Keywords: paradox of enrichment
zbMATH Keywords: survival
zbMATH Keywords: extinction
zbMATH Keywords: predator-prey systems
zbMATH Keywords: group defence
zbMATH Keywords: mutual interference among predators
Wikidata QID: Q52653401
author: H. I. Freedman
author: Gail S. K. Wolkowicz
MaRDI profile type: Publication
cites work: Uniformly Persistent Systems
cites work: Modeling persistence and mutual interference among subpopulations of ecological communities
cites work: Graphical stability, enrichment, and pest control by a natural enemy
cites work: Stability analysis of a predator-prey system with mutual interference and density-dependent death rates
cites work: Q3895297
cites work: The trade-off between mutual interference and time lags in predator-prey systems
cites work: Homage to the red queen. II. Coevolutionary response to enrichment of exploitation ecosystems
cites work: Homage to the red queen. I. Coevolution of predators and their victims
full work available at URL: https://doi.org/10.1007/bf02462320
OpenAlex ID: W4234127854
description: scientific article; zbMATH DE number 3991324