Variation in risk in single-species discrete-time models
Simple, discrete-time, population models typically exhibit complex dynamics, like cyclicoscillations and chaos, when the net reproductive rate, $R$, is large. These traditionalmodels generally do not incorporate variability in juvenile 'risk,'' defined to be ameasure of a juvenile...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2008-09-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.859 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Simple, discrete-time, population models typically exhibit complex dynamics, like cyclicoscillations and chaos, when the net reproductive rate, $R$, is large. These traditionalmodels generally do not incorporate variability in juvenile 'risk,'' defined to be ameasure of a juvenile's vulnerability to density-dependent mortality. For a broad class of discrete-time models we show that variability in risk across juveniles tends to stabilize the equilibrium. We consider both density-independent and density-dependent risk, and for each, we identify appropriate shapes of the distribution of risk that will stabilize the equilibrium for all values of $R$. In both cases, it is the shape of the distribution of risk and not the amount of variation in risk that is crucial for stability. |
|---|---|
| ISSN: | 1551-0018 |