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On the stabilizing effect of cannibalism in stage-structured population models
Bruno Buonomo1, Deborah Lacitignola
1Department of Mathematics and Applications, University of Naples Federico II, via Cintia, I-80126 Naples, Italy. buonomo@unina.it.
Mathematical Biosciences and Engineering : MBE
|April 6, 2010
Summary
Cannibalism in predator-prey models can suppress population cycles. Increasing cannibalism attack rates stabilizes coexistence, contrasting earlier models and aligning with copepod growth simulations.
Area of Science:
- Ecology
- Mathematical Biology
- Population Dynamics
Background:
- Predator-prey models are crucial for understanding ecological interactions.
- Cannibalism's role in population dynamics has been debated since 1995.
- Previous models suggested cannibalism could destabilize populations.
Purpose of the Study:
- To systematically investigate cannibalism's effect in stage-structured predator-prey models.
- To analyze the conditions under which cannibalism stabilizes or destabilizes population dynamics.
- To compare model predictions with empirical data from cannibalistic organisms.
Main Methods:
- Developed a stage-structured predator-prey model incorporating cannibalism.
- Employed Hopf bifurcation analysis to identify stability transitions.
- Conducted numerical simulations to validate mathematical findings.
- Utilized balance arguments for model construction and comparison.
Main Results:
- Demonstrated that population cycles are possible in the model.
- Proved that cannibalism acts as a stabilizing factor, suppressing these cycles.
- Showed that increasing cannibalism attack rate can shift coexistence from unstable to stable.
- Model results align with simulations of cannibalistic copepod growth.
Conclusions:
- Cannibalism can stabilize predator-prey systems by suppressing population cycles.
- The stage-structured model provides a new perspective on cannibalism's ecological impact.
- Findings contribute to the ongoing systematic investigation of cannibalism in ecological modeling.
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