Mathematical theory for plant-herbivore systems
type: Item
instance of: scholarly article
title: Mathematical theory for plant-herbivore systems
zbMATH Open document ID: 0596.92020
DOI: 10.1007/BF00275719
author: Leah Edelstein-Keshet
published in: Journal of Mathematical Biology
publication date: 1986-01-01T00:00:00Z
review text: The model incorporates effects of the feature of vegetation loosely termed ''plant quality'', which conveys how a given part of the vegetation might be ''rated'' by a herbivore. After having shown that the frequency distribution of plant quality satisfies a conservation equation, qualitative aspects of the system are discussed in the following three situations: (1) mobile herbivores interacting with all plants; (2) sessile herbivores feeding exclusively on single plants; (3) intermediate situations in which mobility is moderate to low. It is shown that depending on the plant quality response and the herbivore response, it is possible to obtain stable equilibria and stable periodic oscillations. In the former case, the populations tend to lose their heterogeneity; in the latter case, oscillations are accompanied by alternate narrowing and broadening of the distribution. A discussion is given on the model compared with other theoretical work. Empirical approaches are also outlined.
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 92F05
zbMATH DE Number: 3961409
zbMATH Keywords: plant-herbivore systems
zbMATH Keywords: structured populations
zbMATH Keywords: mathematical
zbMATH Keywords: models
zbMATH Keywords: plant quality
zbMATH Keywords: conservation equation
zbMATH Keywords: mobile herbivores
zbMATH Keywords: sessile herbivores
zbMATH Keywords: stable equilibria
zbMATH Keywords: stable periodic oscillations
MaRDI profile type: Publication
Wikidata QID: Q113909297
cites work: Q3923307
cites work: Q3707286
cites work: Q3856484
cites work: Random walk with persistence and external bias
full work available at URL: https://doi.org/10.1007/bf00275719
OpenAlex ID: W2040185381
description: scientific article; zbMATH DE number 3961409