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 language | English |
|---|---|
| Pages (from-to) | 449-459 |
| Number of pages | 11 |
| Journal | Theoretical Population Biology |
| Volume | 73 |
| Issue number | 3 |
| DOIs | |
| State | Published - May 1 2008 |
Fingerprint
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 journal › Article
}
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 -