Optimal Genetic Augmentation Strategies for a Threatened Species using a Continent-Island Model

Abstract

One conservation method of reducing species loss is to augment a declining/threatened wild population with individuals from a captive-bred or stable, wild population. This method is known as species augmentation. We have modeled the change in the frequency of a detrimental allele in a threatened population using the continent-island genetic population model. We use optimal control theory to determine augmentation strategies which minimize the presence of the detrimental allele in an endangered population in minimum time while minimizing the cost of augmenting the endangered population. We present the construction of the optimal control formulation, the necessary conditions for an optimal control, the characterization of an optimal control, the algorithm for computing numerical solutions, and some numerical simulations. Additionally, we discuss some of the challenges of systematically exploring the effects of uncertain parameters in time minimizing optimal control problems and demonstrate one method for quantifying the sensitivity of the optimal control strategy with respect to uncertain parameter values.