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Numerical equilibrium analysis for structured consumer resource models
A M de Roos1, O Diekmann, P Getto
1Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, The Netherlands.
Bulletin of Mathematical Biology
|August 1, 2009
Summary
This study develops numerical methods for analyzing population dynamics, specifically how size-structured populations compete for resources. The findings help define stability and existence boundaries for ecological models.
Area of Science:
- Ecology
- Mathematical Biology
- Computational Science
Background:
- Ecological models often simplify population structures.
- Understanding resource competition is key to population dynamics.
- Numerical analysis is crucial for complex ecological models.
Purpose of the Study:
- To develop and present numerical methods for equilibrium and stability analysis.
- To analyze size-structured populations competing for unstructured resources.
- To define and trace existence and stability boundaries in a two-parameter plane.
Main Methods:
- Numerical tracing of implicitly defined curves using prediction-correction methods.
- Integration over individual size and survival probability as functions of age.
- Combining numerical ODE solutions with curve tracing for discontinuous functions.
- Implementation in C-code for "Daphnia consuming algae" models.
Main Results:
- Successfully traced existence and stability boundaries in a two-parameter plane.
- Demonstrated the application of the methods to Daphnia-algae competition models.
- Visualized results graphically, showing model behavior.
Conclusions:
- The developed numerical methods are effective for analyzing size-structured population models.
- The approach provides insights into ecological stability and equilibrium conditions.
- The study offers a framework for similar analyses in population ecology.
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