Dynamics of a plant-herbivore-predator system with plant-toxicity

Mathematical Biosciences
By: , and 

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Abstract

A system of ordinary differential equations is considered that models the interactions of two plant species populations, an herbivore population, and a predator population. We use a toxin-determined functional response to describe the interactions between plant species and herbivores and use a Holling Type II functional response to model the interactions between herbivores and predators. In order to study how the predators impact the succession of vegetation, we derive invasion conditions under which a plant species can invade into an environment in which another plant species is co-existing with a herbivore population with or without a predator population. These conditions provide threshold quantities for several parameters that may play a key role in the dynamics of the system. Numerical simulations are conducted to reinforce the analytical results. This model can be applied to a boreal ecosystem trophic chain to examine the possible cascading effects of predator-control actions when plant species differ in their levels of toxic defense.

Additional publication details

Publication type Article
Publication Subtype Journal Article
Title Dynamics of a plant-herbivore-predator system with plant-toxicity
Series title Mathematical Biosciences
Volume 229
Issue 2
Year Published 2011
Language English
Publisher Elsevier
Publisher location Amsterdam, Netherlands
Contributing office(s) Southeast Ecological Science Center
Description 15 p.
Larger Work Type Article
Larger Work Subtype Journal Article
Larger Work Title Mathematical Biosciences
First page 190
Last page 204