American Institute of Mathematical Sciences

Advanced
2008, 5(4): 669-680. doi: 10.3934/mbe.2008.5.669

Optimal control applied to a model for species augmentation

Erin N. Bodine 1, , Louis J. Gross 2, and  Suzanne Lenhart 1,

1. 

Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300, United States
2. 

Department of Mathematics & Department of Ecology and Evolutionary Biology, University of Tennessee, Knoxville, TN 37996-1300, United States

Received  December 2007 Revised  March 2008 Published  October 2008

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.
Keywords: Optimal Control, Population Dynamics, Ordinary Differential Equations, Species Augmentation.
Mathematics Subject Classification: 49N90, 92D25, 34A34.
Citation: Erin N. Bodine, Louis J. Gross, Suzanne Lenhart. Optimal control applied to a model for species augmentation. Mathematical Biosciences & Engineering, 2008, 5 (4) : 669-680. doi: 10.3934/mbe.2008.5.669
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