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Simplifying a physiologically structured population model to a stage-structured biomass model.

André M De Roos¹, Tim Schellekens, Tobias Van Kooten

¹Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, P.O.Box 94084, 1090 GB Amsterdam, The Netherlands. A.M.deRoos@uva.nl

Theoretical Population Biology

|November 17, 2007

Summary

This study introduces a consumer-resource model linking individual life history to population dynamics. The stage-structured model accurately approximates the size-structured model, especially when adults are better foragers.

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Area of Science:

Ecology
Mathematical Biology
Population Dynamics

Background:

Individual life history traits, such as size-dependent growth and stage-specific mortality, influence population dynamics.
Physiologically structured population models offer detailed insights but can be complex to analyze.

Purpose of the Study:

To formulate and analyze a stage-structured consumer-resource model as an approximation to a physiologically structured model.
To investigate how individual life history processes translate to population-level dynamics.
To compare the dynamics of stage-structured and size-structured models under various conditions.

Main Methods:

Formulation of an ordinary differential equation-based stage-structured consumer-resource model.
Derivation of the stage-structured model as an approximation to a physiologically structured population model.
Analysis of model dynamics under semi-chemostat and logistic resource growth scenarios.

Main Results:

The stage-structured and size-structured models yield identical predictions under equilibrium conditions.
The stage-structured model closely approximates size-structured dynamics when adults are superior foragers (higher mass-specific ingestion rate).
The size-structured model exhibits unique single-generation cycles when juveniles have higher mass-specific intake rates, a dynamic not captured by the stage-structured model due to its distributed time delay for maturation.

Conclusions:

Stage-structured models can effectively approximate physiologically structured models for population dynamics.
The foraging efficiency of different life stages (juveniles vs. adults) significantly impacts population dynamics and model behavior.
Differences in maturation representation (discrete vs. distributed delay) between models lead to distinct population dynamics under specific consumer-resource interactions.