Sharpness of saturation in harvesting and predation
Harvesting and predation occur through contact processes in which the rateat which the managed (prey) population can be found depends on thepopulation size, usually saturating at high densities. Many modelsincorporate saturation in this process without considering the effectsof the particular funct...
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| Format: | Article |
| Language: | English |
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AIMS Press
2009-08-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.719 |
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| author | Christopher M. Kribs-Zaleta |
| author_facet | Christopher M. Kribs-Zaleta |
| author_sort | Christopher M. Kribs-Zaleta |
| collection | DOAJ |
| description | Harvesting and predation occur through contact processes in which the rateat which the managed (prey) population can be found depends on thepopulation size, usually saturating at high densities. Many modelsincorporate saturation in this process without considering the effectsof the particular function used to describe it. We show that the sharpnesswith which this saturation occurs has an important effect upon the resultingpopulation dynamics, with bistability (sometimes involving a stableequilibrium and a stable limit cycle) occurring for saturation that isany sharper than the commonly used Michaelis-Menten (Holling type II)functional response. This sharpness threshold occurs across a wide rangeof model types, from simple harvesting to density-dependent andratio-dependent predation. |
| format | Article |
| id | doaj-art-d5ef9a8f0fac46ccb9483cea01b8ea02 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2009-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-d5ef9a8f0fac46ccb9483cea01b8ea022025-01-24T02:00:01ZengAIMS PressMathematical Biosciences and Engineering1551-00182009-08-016471974210.3934/mbe.2009.6.719Sharpness of saturation in harvesting and predationChristopher M. Kribs-Zaleta0University of Texas at Arlington, Box 19408, Arlington, TX 76019-0408Harvesting and predation occur through contact processes in which the rateat which the managed (prey) population can be found depends on thepopulation size, usually saturating at high densities. Many modelsincorporate saturation in this process without considering the effectsof the particular function used to describe it. We show that the sharpnesswith which this saturation occurs has an important effect upon the resultingpopulation dynamics, with bistability (sometimes involving a stableequilibrium and a stable limit cycle) occurring for saturation that isany sharper than the commonly used Michaelis-Menten (Holling type II)functional response. This sharpness threshold occurs across a wide rangeof model types, from simple harvesting to density-dependent andratio-dependent predation.https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.719population biologypredator-preysaturationbistability.harvesting |
| spellingShingle | Christopher M. Kribs-Zaleta Sharpness of saturation in harvesting and predation Mathematical Biosciences and Engineering population biology predator-prey saturation bistability. harvesting |
| title | Sharpness of saturation in harvesting and predation |
| title_full | Sharpness of saturation in harvesting and predation |
| title_fullStr | Sharpness of saturation in harvesting and predation |
| title_full_unstemmed | Sharpness of saturation in harvesting and predation |
| title_short | Sharpness of saturation in harvesting and predation |
| title_sort | sharpness of saturation in harvesting and predation |
| topic | population biology predator-prey saturation bistability. harvesting |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.719 |
| work_keys_str_mv | AT christophermkribszaleta sharpnessofsaturationinharvestingandpredation |