Optimal control applied to a model for species augmentation

Erin N. Bodine; Louis J. Gross; Suzanne Lenhart; Erin N. Bodine; Louis J. Gross; Suzanne Lenhart

doi:10.3934/mbe.2008.5.669

Mathematical Biosciences and Engineering

2008, Volume 5, Issue 4: 669-680. doi: 10.3934/mbe.2008.5.669

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Optimal control applied to a model for species augmentation

1.
Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300
2.
Department of Mathematics & Department of Ecology and Evolutionary Biology, University of Tennessee, Knoxville, TN 37996-1300

Received: 01 December 2007 Accepted: 29 June 2018 Published: 01 October 2008
MSC : 49N90, 92D25, 34A34

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.
- Optimal Control,
- Population Dynamics,
- Ordinary Differential Equations,
- Species Augmentation
Citation: Erin N. Bodine, Louis J. Gross, Suzanne Lenhart. Optimal control applied to a model for species augmentation[J]. Mathematical Biosciences and Engineering, 2008, 5(4): 669-680. doi: 10.3934/mbe.2008.5.669

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Abstract

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.
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