Open AccessOptimal control applied to a model for species augmentation
Author(s) -
Erin N Bodine,
Louis J Gross,
Suzanne Lenhart
Publication year - 2008
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2008.5.669
Subject(s) - threatened species , optimal control , population , population model , mathematical optimization , control (management) , computer science , ecology , mathematical economics , mathematics , econometrics , biology , artificial intelligence , demography , sociology , habitat
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.