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!
|
| _version_ | 1832590176153501696 |
|---|---|
| author | Abhyudai Singh Roger M. Nisbet |
| author_facet | Abhyudai Singh Roger M. Nisbet |
| author_sort | Abhyudai Singh |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2e2d1054b36d4221b508d584252a3c67 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2008-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-2e2d1054b36d4221b508d584252a3c672025-01-24T01:58:42ZengAIMS PressMathematical Biosciences and Engineering1551-00182008-09-015485987510.3934/mbe.2008.5.859Variation in risk in single-species discrete-time modelsAbhyudai Singh0Roger M. Nisbet1Department of Ecology, Evolution and Marine Biology, University of California at Santa Barbara, CA 93106-9610Department of Ecology, Evolution and Marine Biology, University of California at Santa Barbara, CA 93106-9610Simple, 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.https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.859ricker modelpopulation dynamicsvariation in risksingle-species modelsdiscrete-time modelssensitivity of the equilibrium to reproduction rate |
| spellingShingle | Abhyudai Singh Roger M. Nisbet Variation in risk in single-species discrete-time models Mathematical Biosciences and Engineering ricker model population dynamics variation in risk single-species models discrete-time models sensitivity of the equilibrium to reproduction rate |
| title | Variation in risk in single-species discrete-time models |
| title_full | Variation in risk in single-species discrete-time models |
| title_fullStr | Variation in risk in single-species discrete-time models |
| title_full_unstemmed | Variation in risk in single-species discrete-time models |
| title_short | Variation in risk in single-species discrete-time models |
| title_sort | variation in risk in single species discrete time models |
| topic | ricker model population dynamics variation in risk single-species models discrete-time models sensitivity of the equilibrium to reproduction rate |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.859 |
| work_keys_str_mv | AT abhyudaisingh variationinriskinsinglespeciesdiscretetimemodels AT rogermnisbet variationinriskinsinglespeciesdiscretetimemodels |