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An optimal strategy for energy allocation in a multiple resource environment.

D Brian Walton¹, Benjamin P Leard, Anthony Tongen

¹Department of Mathematics and Statistics, James Madison University, Harrisonburg, VA 22807, USA. waltondb@jmu.edu

Bulletin of Mathematical Biology

|January 22, 2010

Summary

This study models population growth based on acquiring two essential resources. The optimal strategy for population survival and resisting invasion is typically to equally divide energy between obtaining both resources.

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Area of Science:

Population dynamics
Ecological modeling
Evolutionary game theory

Background:

Fecundity is influenced by resource acquisition up to a saturation point.
Population strategies involve allocating energy to obtain essential resources.

Purpose of the Study:

To model population dynamics with two essential resources.
To identify optimal energy allocation strategies for population survival and stability.
To analyze the stability of different resource acquisition strategies.

Main Methods:

Developed a discrete-time, nonoverlapping generations population model.
Assumed resource acquisition functions are increasing and concave down.
Analyzed competing subpopulations with different energy allocation strategies.
Utilized pairwise invasibility plots to illustrate model behavior.

Main Results:

Identified a unique optimal strategy for population resilience.
This optimal strategy involves equal energy division between resources, except when one resource is easily saturated.
Characterized the stability of all possible equilibria.

Conclusions:

Equal energy allocation is often the most robust strategy for populations.
The model provides insights into evolutionary stability in resource-limited environments.
Pairwise invasibility plots effectively visualize subpopulation invasion dynamics.