The Role of Prey Taxis in Biological Control: A Spatial Theoretical Model

We study a reaction‐diffusion‐advection model for the dynamics of populations under biological control. A control agent is assumed to be a predator species that has the ability to perceive the heterogeneity of pest distribution. The advection term represents the predator density movement according t...

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Bibliographic Details
Published in:The American naturalist 2003-07, Vol.162 (1), p.61-76
Main Authors: Sapoukhina, Natalia, Tyutyunov, Yuri, Arditi, Roger
Format: Article
Language:English
Subjects:
Analysis of PDEs
Animal behavior
Animal populations
Animals
Biodiversity
Computer Science
Computer Simulation
Ecology
Economic models
Food chains
Mathematics
Modeling
Modeling and Simulation
Models, Theoretical
Natural enemies
Oscillation
Pest control
Pest Control, Biological
Pests
Population density
Population Dynamics
Predation
Predators
Predatory Behavior
Spatial models
Trophic relationships
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Summary:We study a reaction‐diffusion‐advection model for the dynamics of populations under biological control. A control agent is assumed to be a predator species that has the ability to perceive the heterogeneity of pest distribution. The advection term represents the predator density movement according to a basic prey taxis assumption: acceleration of predators is proportional to the prey density gradient. The prey population reproduces logistically, and the local population interactions follow the Holling Type II trophic function. On the scale of the population, our spatially explicit approach subdivides the predation process into random movement represented by diffusion, directed movement described by prey taxis, local prey encounters, and consumption modeled by the trophic function. Thus, our model allows studying the effects of large‐scale predator spatial activity on population dynamics. We show under which conditions spatial patterns are generated by prey taxis and how this affects the predator ability to maintain the pest population below some economic threshold. In particular, intermediate taxis activity can stabilize predator‐pest populations at a very low level of pest density, ensuring successful biological control. However, very intensive prey taxis destroys the stability, leading to chaotic dynamics with pronounced outbreaks of pest density.
ISSN:0003-0147
1537-5323
DOI:10.1086/375297