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Stability of a perturbed Leslie model
J P Quinn1, R J Nash, A Georgallas
1Department of Mathematics and Computing Sciences, St. Francis Xavier University, Antigonish, Nova Scotia, Canada.
Theoretical Population Biology
|February 1, 1997
Summary
A small change in the stochastic Leslie model can create a stable population where extinction was predicted. This surprising finding is explained by a related model incorporating a density-dependent sex ratio.
Area of Science:
- Population dynamics
- Mathematical biology
- Ecology
Background:
- The stochastic Leslie model is a standard tool for population viability analysis.
- Stochastic models often predict population extinction under certain conditions.
Purpose of the Study:
- To investigate the effect of small perturbations on population dynamics predicted by the stochastic Leslie model.
- To understand the mechanisms behind unexpected population persistence.
Main Methods:
- Analysis of the stochastic Leslie model with a small perturbation.
- Comparison with a modified model featuring a density-dependent sex ratio.
Main Results:
- A small perturbation can lead to a long-lived, stable population in parameter regions where the unperturbed model predicts extinction.
- The modified model with a density-dependent sex ratio demonstrates similar stabilizing features.
Conclusions:
- Population persistence can occur even when stochastic models predict demise, highlighting the importance of considering model sensitivities.
- Density-dependent mechanisms, such as a variable sex ratio, can significantly alter population persistence outcomes.