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1Centre for Mathematical Biology and Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada. jungmin@math.ualberta.ca
Bulletin of Mathematical Biology
|February 7, 2008
Summary
Introducing prey-taxis into predator-prey models reveals a surprising outcome. Active predator movement towards high prey density can hinder biological control of invasive species by drawing predators away from the invasion front.
Area of Science:
- Ecology
- Mathematical Biology
- Invasive Species Management
Background:
- Biological control strategies often involve introducing spatially moving predators to manage invasive species.
- Previous models demonstrated that prey invasions are halted only when prey exhibit an Allee effect, a phenomenon where population growth rate decreases at low densities.
Purpose of the Study:
- To investigate the impact of prey-taxis, the directed movement of predators towards higher prey concentrations, on the efficacy of biological control.
- To determine if prey-taxis influences the ability of predators to suppress advancing invasive populations.
Main Methods:
- Development and analysis of a reaction-diffusion model incorporating prey-taxis.
- Mathematical modeling to simulate predator-prey dynamics with spatially dependent predator movement.
- Analysis of invasion dynamics and the conditions for successful eradication.
Main Results:
- Prey-taxis causes predators to move away from the low-density leading edge of an invasion.
- This redistribution of predators can paradoxically reduce the effectiveness of biological control, even when prey exhibit an Allee effect.
- The likelihood of halting prey invasion is decreased by the inclusion of prey-taxis.
Conclusions:
- Prey-taxis, while seemingly beneficial for predator localization, can undermine biological control efforts.
- The spatial behavior of predators, specifically their attraction to high prey densities, is a critical factor in invasion dynamics.
- Future biocontrol strategies should carefully consider predator movement behaviors to ensure effective invasive species management.
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