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Combining perturbations and parameter variation to influence mean first passage times
Kevin L S Drury1, David M Lodge
1Department of Mathematics, Bethel College, Mishawaka, IN 46545, USA. kevin.drury@bethelcollege.edu
Bulletin of Mathematical Biology
|April 28, 2012
Summary
Parameter drift significantly alters the time to shift between population states, impacting ecological resilience. Understanding these dynamics is crucial for pest control and sustainable harvest strategies.
Area of Science:
- Ecology
- Mathematical Biology
- Population Dynamics
Background:
- Ecological models feature stable states, influenced by perturbations and parameter drift.
- Parameter drift can lead to equilibrium bifurcation, potentially causing population collapse.
- Intraguild predation (IGP) models illustrate complex species interactions.
Purpose of the Study:
- To investigate the combined effects of perturbations and parameter drift in ecological models.
- To analyze how parameter drift influences equilibrium number and stability in a two-species IGP model.
- To quantify the impact of these factors on transitions between stable states.
Main Methods:
- Bifurcation analysis was used to identify parameters affecting equilibrium.
- A stochastic process modeled population perturbations.
- Mean first passage time calculated transitions between stable states.
Main Results:
- Parameter drift affects equilibrium number, with competition and predation rates acting as bifurcating parameters.
- Parameter drift minimally impacts expected time within a basin of attraction.
- Parameter drift dramatically alters expected time to shift between basins of attraction by affecting equilibrium resilience.
Conclusions:
- The interplay of perturbations and parameter drift is critical for understanding ecological dynamics.
- Parameter drift's influence on inter-basin transitions has significant implications for population management.
- Methods are generalizable to pest control and sustainable harvest applications.
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