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Stabilizing effect of cannibalism in a two stages population model
Jonathan Rault1, Eric Benoît, Jean-Luc Gouzé
1INRIA BIOCORE, 2004 Route des Lucioles B.P. 93, 06902 Sophia Antipolis Cedex, France. jonathan.rault@inria.fr
Acta Biotheoretica
|February 6, 2013
Summary
This study introduces a predator-prey model with discrete weight classes and cannibalism. Cannibalism can stabilize the ecosystem by making unstable equilibria stable, as shown through mathematical analysis and simulations.
Area of Science:
- Ecology
- Mathematical Biology
- Population Dynamics
Background:
- Predator-prey models are crucial for understanding ecosystem stability.
- Incorporating discrete structures and cannibalism offers a more realistic representation of ecological interactions.
Purpose of the Study:
- To develop and analyze a prey-predator model with a discrete weight structure for the predator.
- To investigate the impact of cannibalism on ecosystem stability.
Main Methods:
- Development of a mathematical model conserving individuals and biomass.
- Analysis of predator growth and reproduction dependent on ingested food.
- Inclusion of cannibalism (predator consuming prey and other predators).
- Focus on a two-stage (larval, adult) model and mathematical derivations.
- Assumption of fast prey dynamics relative to predator dynamics.
Main Results:
- The model conserves both the number of individuals and biomass.
- Predator growth and reproduction are linked to food intake.
- Cannibalism, including intraspecific predation, is incorporated.
- Mathematical analysis reveals conditions under which cannibalism stabilizes the system.
- Numerical simulations demonstrate the stabilization effect of cannibalism on unstable equilibria.
Conclusions:
- Cannibalism can significantly enhance ecosystem stability in predator-prey dynamics.
- A previously unstable equilibrium can become almost globally stable with the introduction of cannibalism.
- The discrete weight structure and cannibalism provide a more nuanced understanding of population dynamics.
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