Dynamics of a plant-herbivore-predator system with plant-toxicity
Mathematical Biosciences
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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.
Suggested Citation
Feng, Z., Qiu, Z., Liu, R., DeAngelis, D.L., 2011, Dynamics of a plant-herbivore-predator system with plant-toxicity: Mathematical Biosciences, v. 229, no. 2, p. 190-204, https://doi.org/10.1016/j.mbs.2010.12.005.
| Publication type | Article |
|---|---|
| Publication Subtype | Journal Article |
| Title | Dynamics of a plant-herbivore-predator system with plant-toxicity |
| Series title | Mathematical Biosciences |
| DOI | 10.1016/j.mbs.2010.12.005 |
| 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. |
| First page | 190 |
| Last page | 204 |