Optimal control applied to a model for species augmentation
Species augmentation is a method of reducing species loss via augmenting declining or threatened populations with individuals from captive-bred or stable, wild populations. In this paper, we develop a differential equations model and optimal control formulation for a continuous time augmentation of...
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| Format: | Article |
| Language: | English |
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AIMS Press
2008-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.669 |
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| _version_ | 1832590227126878208 |
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| author | Erin N. Bodine Louis J. Gross Suzanne Lenhart |
| author_facet | Erin N. Bodine Louis J. Gross Suzanne Lenhart |
| author_sort | Erin N. Bodine |
| collection | DOAJ |
| description | Species augmentation is a method of reducing species loss via augmenting declining or threatened populations with individuals from captive-bred or stable, wild populations. In this paper, we develop a differential equations model and optimal control formulation for a continuous time augmentation of a general declining population. We find a characterization for the optimal control and show numerical results for scenarios of different illustrative parameter sets. The numerical results provide considerably more detail about the exact dynamics of optimal augmentation than can be readily intuited. The work and results presented in this paper are a first step toward building a general theory of population augmentation, which accounts for the complexities inherent in many conservation biology applications. |
| format | Article |
| id | doaj-art-e9552b304a864c1b9f965a0a00120e14 |
| 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-e9552b304a864c1b9f965a0a00120e142025-01-24T01:58:42ZengAIMS PressMathematical Biosciences and Engineering1551-00182008-09-015466968010.3934/mbe.2008.5.669Optimal control applied to a model for species augmentationErin N. Bodine0Louis J. Gross1Suzanne Lenhart2Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300Species augmentation is a method of reducing species loss via augmenting declining or threatened populations with individuals from captive-bred or stable, wild populations. In this paper, we develop a differential equations model and optimal control formulation for a continuous time augmentation of a general declining population. We find a characterization for the optimal control and show numerical results for scenarios of different illustrative parameter sets. The numerical results provide considerably more detail about the exact dynamics of optimal augmentation than can be readily intuited. The work and results presented in this paper are a first step toward building a general theory of population augmentation, which accounts for the complexities inherent in many conservation biology applications.https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.669optimal controlpopulation dynamicsordinary differential equationsspeciesaugmentation |
| spellingShingle | Erin N. Bodine Louis J. Gross Suzanne Lenhart Optimal control applied to a model for species augmentation Mathematical Biosciences and Engineering optimal control population dynamics ordinary differential equations speciesaugmentation |
| title | Optimal control applied to a model for species augmentation |
| title_full | Optimal control applied to a model for species augmentation |
| title_fullStr | Optimal control applied to a model for species augmentation |
| title_full_unstemmed | Optimal control applied to a model for species augmentation |
| title_short | Optimal control applied to a model for species augmentation |
| title_sort | optimal control applied to a model for species augmentation |
| topic | optimal control population dynamics ordinary differential equations speciesaugmentation |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.669 |
| work_keys_str_mv | AT erinnbodine optimalcontrolappliedtoamodelforspeciesaugmentation AT louisjgross optimalcontrolappliedtoamodelforspeciesaugmentation AT suzannelenhart optimalcontrolappliedtoamodelforspeciesaugmentation |