Stabilizing effects in spatial parasitoid-host and predator-prey models: a review.

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Spatial models are crucial for understanding ecological interactions.
• Dispersal is a key factor influencing population dynamics and stability.
• Previous models often show dispersal destabilizing local equilibria.

Purpose of the Study:

• To review literature on spatial host-parasitoid and predator-prey models.
• To identify mechanisms by which limited dispersal promotes persistence and stability.
• To explore the role of spatial heterogeneity and non-linear responses.

Main Methods:

• Literature review of spatial ecological models.
• Analysis of host-parasitoid and predator-prey dynamics.
• Examination of dispersal effects in spatially explicit models.

Main Results:

• Dispersal alone does not stabilize populations and can destabilize local equilibria.
• Limited dispersal, combined with heterogeneity, promotes persistence via three mechanisms: statistical stabilization, immigration decoupling, and altered average parameters.
• Spatially explicit models with local dispersal often exhibit self-organized spatial patterning.

Conclusions:

• Limited dispersal is not inherently stabilizing but can enhance population persistence and stability under specific conditions.
• Spatial heterogeneity and non-linear density responses are critical for stabilization with limited dispersal.
• Self-organized patterning is a common outcome in spatially explicit models with local dispersal.