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A comparative analysis of host-parasitoid models with density dependence preceding parasitism
1Department of Applied Mathematics, University of Washington, Seattle, WA, USA.
Journal of Biological Dynamics
|July 1, 2020
Summary
This study compares four host-parasitoid models, revealing how density dependence and parasitism type influence population cycles. Overcompensation can cause bifurcations, while Poisson parasitism destabilizes equilibria, leading to population dynamics.
Area of Science:
- Ecology
- Mathematical Biology
- Population Dynamics
Background:
- Host-parasitoid interactions are crucial in ecological systems.
- Discrete-time models are widely used to study population dynamics.
- Understanding density dependence and parasitism is key to predicting population stability.
Purpose of the Study:
- To systematically compare four discrete-time host-parasitoid models.
- To analyze the impact of density-dependent growth and parasitism distributions on population dynamics.
- To identify previously undetected dynamics in existing models.
Main Methods:
- Comparison of Beverton-Holt and Ricker maps for density-dependent growth.
- Analysis of Poisson and negative binomial distributions for parasitoid attack functions.
- Application of bifurcation theory (period-doubling, Neimark-Sacker) to discrete-time models.
Main Results:
- Overcompensatory density dependence can lead to supercritical or subcritical period-doubling bifurcations.
- Poisson parasitism can destabilize coexistence equilibria via Neimark-Sacker bifurcations, inducing population cycles.
- Analytic methods uncovered novel dynamics in one model not found through prior numerical investigation.
Conclusions:
- The structure of discrete-time host-parasitoid models significantly impacts predicted population dynamics.
- Clear articulation of biological assumptions in models is essential for accurate ecological predictions and communication.
- Bifurcation analysis provides deeper insights into the stability and cyclical behavior of host-parasitoid systems.
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