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Between discrete and continuous: consumer-resource dynamics with synchronized reproduction.

E Pachepsky¹, R M Nisbet, W W Murdoch

¹Department of Ecology, Evolution and Marine Biology, University of California, Santa Barbara, California 93106, USA. leeza@microsoft.com

|April 2, 2008

Summary

This study introduces a semi-discrete model for consumer-resource dynamics, bridging discrete and continuous population models. It reveals that consumer-driven cycles can emerge with shorter periods than previously thought.

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Area of Science:

Ecology
Mathematical Biology
Population Dynamics

Background:

Consumer-resource systems often feature synchronized consumer reproduction and continuous resource dynamics.
Existing models like Nicholson-Bailey and Lotka-Volterra address discrete or continuous systems, respectively.
A gap exists for models integrating both discrete and continuous population dynamics.

Purpose of the Study:

To define and analyze a canonical semi-discrete model for consumer-resource interactions.
To provide a foundation for more complex, realistic ecological models.
To explore the cyclical dynamics and stability of such semi-discrete systems.

Main Methods:

Development of a novel semi-discrete mathematical model.
Analysis of model behavior including equilibria and cycles.
Comparison with existing discrete and continuous population models.

Main Results:

The semi-discrete model can exhibit stable equilibria, consumer-resource cycles, and overcompensation cycles.
High consumer fecundity can induce cycles, potentially leading to consumer-only dynamics.
Cycles with periods as short as two years are possible, unlike in many discrete models.

Conclusions:

Semi-discrete models are essential for accurately representing ecological systems with mixed temporal dynamics.
The proposed model offers a more realistic framework for understanding population cycles.
Consumer traits, like high fecundity, play a critical role in shaping population dynamics and stability.