Plant-herbivore interactions mediated by plant toxicity

Zhilan Feng, Rongsong Liu, Donald L. DeAngelis

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

We explore the impact of plant toxicity on the dynamics of a plant-herbivore interaction, such as that of a mammalian browser and its plant forage species, by studying a mathematical model that includes a toxin-determined functional response. In this functional response, the traditional Holling Type 2 response is modified to include the negative effect of toxin on herbivore growth, which can overwhelm the positive effect of biomass ingestion at sufficiently high plant toxicant concentrations. Two types of consumption decisions of the herbivore are considered. One of these (Case 1) incorporates the adaptation of the herbivore to control its rate of consumption of plant items when that is likely to lead to levels of toxicity that more than offset the marginal gain to the herbivore of consuming more plant biomass, while the other (Case 2) simply assumes that, although the herbivore's rate of ingestion of plant biomass is negatively affected by increasing ingestion of toxicant relative to the load it can safely deal with, the herbivore is not able to prevent detrimental or even lethal levels of toxicant intake. A primary result of this work is that these differences in behavior lead to dramatically different outcomes, summarized in bifurcation diagrams. In Case 2, a wide variety of dynamics may occur due to the interplay of Holling Type 2 dynamics and the effect of the plant toxicant. These dynamics include the occurrence of bistability, in which both a periodic solution and the herbivore-extinction equilibrium are attractors, as well the possibility of a homoclinic bifurcation. Whether the herbivore goes to extinction in the bistable case depends on initial conditions of herbivore and plant biomasses. For relatively low herbivore resource acquisition rates, the toxicant effect increases the likelihood of 'paradox of enrichment' type limit cycle oscillations, but at higher resource acquisition rates, the toxicant may decrease the likelihood of these cycles.

Original languageEnglish
Pages (from-to)449-459
Number of pages11
JournalTheoretical Population Biology
Volume73
Issue number3
DOIs
StatePublished - May 1 2008

Fingerprint

plant-herbivore interaction
Herbivory
herbivore
herbivores
toxicity
toxic substances
Biomass
functional response
biomass
Eating
bifurcation
ingestion
toxin
extinction
toxins
resource
forage
oscillation
diagram
Theoretical Models

Keywords

  • Bifurcation diagram
  • Chemical defense
  • Extinction
  • Limit cycle
  • Plant toxicity
  • Plant-herbivore

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Ecology, Evolution, Behavior and Systematics

Cite this

Plant-herbivore interactions mediated by plant toxicity. / Feng, Zhilan; Liu, Rongsong; DeAngelis, Donald L.

In: Theoretical Population Biology, Vol. 73, No. 3, 01.05.2008, p. 449-459.

Research output: Contribution to journalArticle

Feng, Zhilan ; Liu, Rongsong ; DeAngelis, Donald L. / Plant-herbivore interactions mediated by plant toxicity. In: Theoretical Population Biology. 2008 ; Vol. 73, No. 3. pp. 449-459.
@article{e3f2693bfc614774b7925fdda779c543,
title = "Plant-herbivore interactions mediated by plant toxicity",
abstract = "We explore the impact of plant toxicity on the dynamics of a plant-herbivore interaction, such as that of a mammalian browser and its plant forage species, by studying a mathematical model that includes a toxin-determined functional response. In this functional response, the traditional Holling Type 2 response is modified to include the negative effect of toxin on herbivore growth, which can overwhelm the positive effect of biomass ingestion at sufficiently high plant toxicant concentrations. Two types of consumption decisions of the herbivore are considered. One of these (Case 1) incorporates the adaptation of the herbivore to control its rate of consumption of plant items when that is likely to lead to levels of toxicity that more than offset the marginal gain to the herbivore of consuming more plant biomass, while the other (Case 2) simply assumes that, although the herbivore's rate of ingestion of plant biomass is negatively affected by increasing ingestion of toxicant relative to the load it can safely deal with, the herbivore is not able to prevent detrimental or even lethal levels of toxicant intake. A primary result of this work is that these differences in behavior lead to dramatically different outcomes, summarized in bifurcation diagrams. In Case 2, a wide variety of dynamics may occur due to the interplay of Holling Type 2 dynamics and the effect of the plant toxicant. These dynamics include the occurrence of bistability, in which both a periodic solution and the herbivore-extinction equilibrium are attractors, as well the possibility of a homoclinic bifurcation. Whether the herbivore goes to extinction in the bistable case depends on initial conditions of herbivore and plant biomasses. For relatively low herbivore resource acquisition rates, the toxicant effect increases the likelihood of 'paradox of enrichment' type limit cycle oscillations, but at higher resource acquisition rates, the toxicant may decrease the likelihood of these cycles.",
keywords = "Bifurcation diagram, Chemical defense, Extinction, Limit cycle, Plant toxicity, Plant-herbivore",
author = "Zhilan Feng and Rongsong Liu and DeAngelis, {Donald L.}",
year = "2008",
month = "5",
day = "1",
doi = "10.1016/j.tpb.2007.12.004",
language = "English",
volume = "73",
pages = "449--459",
journal = "Theoretical Population Biology",
issn = "0040-5809",
publisher = "Academic Press Inc.",
number = "3",

}

TY - JOUR

T1 - Plant-herbivore interactions mediated by plant toxicity

AU - Feng, Zhilan

AU - Liu, Rongsong

AU - DeAngelis, Donald L.

PY - 2008/5/1

Y1 - 2008/5/1

N2 - We explore the impact of plant toxicity on the dynamics of a plant-herbivore interaction, such as that of a mammalian browser and its plant forage species, by studying a mathematical model that includes a toxin-determined functional response. In this functional response, the traditional Holling Type 2 response is modified to include the negative effect of toxin on herbivore growth, which can overwhelm the positive effect of biomass ingestion at sufficiently high plant toxicant concentrations. Two types of consumption decisions of the herbivore are considered. One of these (Case 1) incorporates the adaptation of the herbivore to control its rate of consumption of plant items when that is likely to lead to levels of toxicity that more than offset the marginal gain to the herbivore of consuming more plant biomass, while the other (Case 2) simply assumes that, although the herbivore's rate of ingestion of plant biomass is negatively affected by increasing ingestion of toxicant relative to the load it can safely deal with, the herbivore is not able to prevent detrimental or even lethal levels of toxicant intake. A primary result of this work is that these differences in behavior lead to dramatically different outcomes, summarized in bifurcation diagrams. In Case 2, a wide variety of dynamics may occur due to the interplay of Holling Type 2 dynamics and the effect of the plant toxicant. These dynamics include the occurrence of bistability, in which both a periodic solution and the herbivore-extinction equilibrium are attractors, as well the possibility of a homoclinic bifurcation. Whether the herbivore goes to extinction in the bistable case depends on initial conditions of herbivore and plant biomasses. For relatively low herbivore resource acquisition rates, the toxicant effect increases the likelihood of 'paradox of enrichment' type limit cycle oscillations, but at higher resource acquisition rates, the toxicant may decrease the likelihood of these cycles.

AB - We explore the impact of plant toxicity on the dynamics of a plant-herbivore interaction, such as that of a mammalian browser and its plant forage species, by studying a mathematical model that includes a toxin-determined functional response. In this functional response, the traditional Holling Type 2 response is modified to include the negative effect of toxin on herbivore growth, which can overwhelm the positive effect of biomass ingestion at sufficiently high plant toxicant concentrations. Two types of consumption decisions of the herbivore are considered. One of these (Case 1) incorporates the adaptation of the herbivore to control its rate of consumption of plant items when that is likely to lead to levels of toxicity that more than offset the marginal gain to the herbivore of consuming more plant biomass, while the other (Case 2) simply assumes that, although the herbivore's rate of ingestion of plant biomass is negatively affected by increasing ingestion of toxicant relative to the load it can safely deal with, the herbivore is not able to prevent detrimental or even lethal levels of toxicant intake. A primary result of this work is that these differences in behavior lead to dramatically different outcomes, summarized in bifurcation diagrams. In Case 2, a wide variety of dynamics may occur due to the interplay of Holling Type 2 dynamics and the effect of the plant toxicant. These dynamics include the occurrence of bistability, in which both a periodic solution and the herbivore-extinction equilibrium are attractors, as well the possibility of a homoclinic bifurcation. Whether the herbivore goes to extinction in the bistable case depends on initial conditions of herbivore and plant biomasses. For relatively low herbivore resource acquisition rates, the toxicant effect increases the likelihood of 'paradox of enrichment' type limit cycle oscillations, but at higher resource acquisition rates, the toxicant may decrease the likelihood of these cycles.

KW - Bifurcation diagram

KW - Chemical defense

KW - Extinction

KW - Limit cycle

KW - Plant toxicity

KW - Plant-herbivore

UR - http://www.scopus.com/inward/record.url?scp=41149111294&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=41149111294&partnerID=8YFLogxK

U2 - 10.1016/j.tpb.2007.12.004

DO - 10.1016/j.tpb.2007.12.004

M3 - Article

C2 - 18262578

AN - SCOPUS:41149111294

VL - 73

SP - 449

EP - 459

JO - Theoretical Population Biology

JF - Theoretical Population Biology

SN - 0040-5809

IS - 3

ER -