Scaling up predator-prey dynamics using spatial moment equations
Authored by Frederic Barraquand, David J Murrell
Date Published: 2013
DOI: 10.1111/2041-210x.12014
Sponsors:
French Ministry of Research
United Kingdom Natural Environment Research Council (NERC)
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Model Documentation:
Other Narrative
Mathematical description
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Abstract
Classical models of predatorprey dynamics, commonly used in community
and evolutionary ecology to explain population cycles, species
coexistence, the effects of enrichment, or predict the evolution of
behavioural traits, are often based on the mass-action assumption. This
means encounter rates between predators and prey are expressed as a
product of predator and prey landscape densities; as if the system was
well-mixed. While mass-action may occur at small spatial scales, spatial
variances and covariances in prey and predator densities affect
encounter rates at large spatial scales. In the context of
hostparasitoid interactions, this has been incorporated into theory for
some time, but for predators, well-mixed or other ad hoc models are
often used despite empirical evidence for intricate spatial variation in
predator and prey numbers. We review the classical models and concepts, their strengths and weaknesses, and we present two recent spatial moment
approaches that scale up predatorprey population dynamics from the
individual or patch level to large spatial scales. Both methods include
descriptors of spatial structure as corrections to encounter rates, but
differ in whether or not these descriptors have dynamics that are
explicit functions of movements, births and deaths. We describe how
these spatial moment techniques work, what new results they have so far
produced, and provide some suggestions to improve the connection of
predatorprey theoretical models to empirical studies.
Tags
individual-based models
Animal movement
Population-dynamics
Ecological-systems
Pattern-formation
Functional-responses
Exploitation ecosystems
Reaction-diffusion models
Encounter rate
Search rate