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

Zhilan Feng, Zhipeng Qiu, Rongsong Liu, Donald L. DeAngelis

Research output: Contribution to journalArticle

21 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)190-204
Number of pages15
JournalMathematical Biosciences
Volume229
Issue number2
DOIs
StatePublished - Feb 1 2011

Fingerprint

Herbivory
Predator
Toxicity
herbivores
toxicity
predators
Functional Response
Population
Poisons
Ordinary differential equations
Ecosystems
Interaction
predator control
Invasion
functional response models
Vegetation
Ecosystem
System of Ordinary Differential Equations
Computer simulation
toxins

Keywords

  • Boreal ecosystem
  • Plant toxicity
  • Plant-herbivore interactions
  • Stability conditions
  • Tritrophic chain

ASJC Scopus subject areas

  • Medicine(all)
  • Immunology and Microbiology(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Agricultural and Biological Sciences(all)
  • Modeling and Simulation
  • Statistics and Probability
  • Applied Mathematics

Cite this

Dynamics of a plant-herbivore-predator system with plant-toxicity. / Feng, Zhilan; Qiu, Zhipeng; Liu, Rongsong; DeAngelis, Donald L.

In: Mathematical Biosciences, Vol. 229, No. 2, 01.02.2011, p. 190-204.

Research output: Contribution to journalArticle

Feng, Zhilan ; Qiu, Zhipeng ; Liu, Rongsong ; DeAngelis, Donald L. / Dynamics of a plant-herbivore-predator system with plant-toxicity. In: Mathematical Biosciences. 2011 ; Vol. 229, No. 2. pp. 190-204.
@article{fb0f2c46ddcf4f749bc94fa2148287b4,
title = "Dynamics of a plant-herbivore-predator system with plant-toxicity",
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.",
keywords = "Boreal ecosystem, Plant toxicity, Plant-herbivore interactions, Stability conditions, Tritrophic chain",
author = "Zhilan Feng and Zhipeng Qiu and Rongsong Liu and DeAngelis, {Donald L.}",
year = "2011",
month = "2",
day = "1",
doi = "10.1016/j.mbs.2010.12.005",
language = "English",
volume = "229",
pages = "190--204",
journal = "Mathematical Biosciences",
issn = "0025-5564",
publisher = "Elsevier Inc.",
number = "2",

}

TY - JOUR

T1 - Dynamics of a plant-herbivore-predator system with plant-toxicity

AU - Feng, Zhilan

AU - Qiu, Zhipeng

AU - Liu, Rongsong

AU - DeAngelis, Donald L.

PY - 2011/2/1

Y1 - 2011/2/1

N2 - 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.

AB - 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.

KW - Boreal ecosystem

KW - Plant toxicity

KW - Plant-herbivore interactions

KW - Stability conditions

KW - Tritrophic chain

UR - http://www.scopus.com/inward/record.url?scp=79551567009&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79551567009&partnerID=8YFLogxK

U2 - 10.1016/j.mbs.2010.12.005

DO - 10.1016/j.mbs.2010.12.005

M3 - Article

C2 - 21195093

AN - SCOPUS:79551567009

VL - 229

SP - 190

EP - 204

JO - Mathematical Biosciences

JF - Mathematical Biosciences

SN - 0025-5564

IS - 2

ER -