How Predation can Slow, Stop or Reverse a Prey Invasion

Owen, Markus R.; Lewis, Mark A.

doi:10.1006/bulm.2001.0239

Cited by 178 publications

(152 citation statements)

References 21 publications

Supporting

Mentioning

143

Contrasting

Unclassified

Order By: Relevance

“…In particular, we consider the foraging behavior of the predator toward high prey density and investigate the role of prey-taxis in spatial predator-prey interactions. For that, we extend the diffusion-reaction model in Owen and Lewis (2001) by incorporating the mechanism of prey-taxis into spatial predator-prey systems (Kareiva and Odell, 1987).…”

Section: Introductionmentioning

confidence: 99%

“…Predator-prey models have been studied by numerous people using different frameworks, such as discrete models (Hassell, 1978), ODE models (Wangersky, 1978;Auger et al, 2002), and diffusion-reaction models (Dunbar, 1983;Cantrell and Cosner, 1996;Owen and Lewis, 2001;Huang et al, 2003). Diffusion-reaction models describe spatial structures explicitly by means of diffusive motility of species in heterogeneous environments, and they describe temporal structures via reaction terms.…”

Section: Introductionmentioning

confidence: 99%

“…Diffusion-reaction models describe spatial structures explicitly by means of diffusive motility of species in heterogeneous environments, and they describe temporal structures via reaction terms. Owen and Lewis (2001) showed that when a prey species grows logistically, a predator population that catches up with an invading prey wave is in general not able to slow down the prey spread. To demonstrate this, they used diffusion-reaction systems and linearized about the leading edge of the wave (where the densities of the prey and the predator are close to zero).…”

Section: Introductionmentioning

confidence: 99%

“…Here we obtain the model by incorporating a prey-taxis term into the reactiondiffusion model of Owen and Lewis (2001) as follows…”

Section: Introductionmentioning

confidence: 99%

“…= 0 was considered by Dunbar (1983). Owen and Lewis (2001) considered the case where prey also moved, i.e. > 0.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Continuous Traveling Waves for Prey-Taxis

2008

View full text Add to dashboard Cite

Spatially moving predators are often considered for biological control of invasive species. The question arises as to whether introduced predators are able to stop an advancing pest or foreign population. In recent studies of reaction-diffusion models, it has been shown that the prey invasion can only be stopped if the prey dynamics observes an Allee effect.In this paper, we include prey-taxis into the model. Prey-taxis describe the active movement of predators to regions of high prey density. This effect leads to the observation that predators are drawn away from the leading edge of a prey invasion where its density is low. This leads to counterintuitive result that prey-taxis can actually reduce the likelihood of effective biocontrol.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Here we obtain the model by incorporating a prey-taxis term into the reactiondiffusion model of Owen and Lewis (2001) as follows…”

Section: Introductionmentioning

confidence: 99%

“…= 0 was considered by Dunbar (1983). Owen and Lewis (2001) considered the case where prey also moved, i.e. > 0.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Continuous Traveling Waves for Prey-Taxis

2008

View full text Add to dashboard Cite

show abstract

Global dynamics of a tritrophic food chain model subject to the Allee effects in the prey population with sexually reproductive generalized‐type top predator

Debnath

Ghosh

Sarkar

2019

Comp and Math Methods

View full text Add to dashboard Cite

In this article, we have considered a continuous tritrophic food chain model subject to the Allee effect on the prey growth function with prey‐dependent Holling type II functional response between the prey and intermediate predator; Crowley‐Martin senses functional response between intermediate predator and top predator, and the top predator is of sexually reproductive type. We have established the positivity and boundedness of the system and the condition of existence of different equilibrium points. The local and global stability of the solutions about the various equilibrium points has been investigated. The center manifold theorem has been used to find the nature of the solution in the neighborhood of the nonhyperbolic equilibrium points and the direction of Hopf bifurcations. Numerical simulation has been carried out to establish the theoretical findings and finally some concluding remarks are given.

show abstract

Take me for a ride: Herbivores can facilitate plant reinvasions

Sullivan

Shaw

2023

Ecology

View full text Add to dashboard Cite

Herbivores shape plant invasions through impacts on demography and dispersal, yet only demographic mechanisms are well understood. Although herbivores negatively impact demography by definition, they can affect dispersal either negatively (e.g., seed consumption), or positively (e.g., caching). Exploring the nuances of how herbivores influence spatial spread will improve the forecasting of plant movement on the landscape. Here, we aim to understand how herbivores impact how fast plant populations spread through varying impacts on plant demography and dispersal. We strive to determine whether, and under what conditions, we see net positive effects of herbivores, in order to find scenarios where herbivores can help to promote spread. We draw on classic invasion theory to develop a stage-structured integrodifference equation model that incorporates herbivore impacts on plant demography and dispersal. We simulate seven herbivore "syndromes" (combinations of demographic and/or dispersal effects) drawn from the literature to understand how increasing herbivore pressure alters plant spreading speed. We find that herbivores with solely negative effects on plant demography or dispersal always slow plant spreading speed, and that the speed slows monotonically as herbivore pressure increases. However, we also find that plant spreading speed can be hump shaped with respect to herbivore pressure: plants spread faster in the presence of herbivores (for low herbivore pressure) and then slower (for high herbivore pressure). This result is robust, occurring across all syndromes in which herbivores have a positive effect on plant dispersal, and is a sign that the positive effects of herbivores on dispersal can outweigh their negative effects on demography. For all syndromes we find that sufficiently high herbivore pressure results in population collapse. Thus, our findings show that herbivores can speed up or slow down plant spread. These insights allow for a greater understanding of how to slow invasions, facilitate native species recolonization, and shape range shifts with global change.

show abstract

How Predation can Slow, Stop or Reverse a Prey Invasion

Cited by 178 publications

References 21 publications

Continuous Traveling Waves for Prey-Taxis

Continuous Traveling Waves for Prey-Taxis

Global dynamics of a tritrophic food chain model subject to the Allee effects in the prey population with sexually reproductive generalized‐type top predator

Take me for a ride: Herbivores can facilitate plant reinvasions

Contact Info

Product

Resources

About