Wildlife Conservation Planning Using Stochastic Optimization and Importance Sampling

Formulations for determining conservation plans for sensitive wildlife species must account for economic costs of habitat protection and uncertainties about how wildlife populations will respond. This paper describes such a formulation and addresses the computational challenge of solving it. The problem is to determine the cost-efficient level of habitat protection that satisfies a viability constraint for a sensitive wildlife population. The viability constraint requires a high probability of attaining a population size target. Because of the complexity of wildlife prediction models, population survival probabilities under alternative protection plans must be estimated using Monte Carlo simulation. The computational challenge arises from the conflicting effects of sample size: fewer replications used to estimate survival probability increases the speed of the search algorithm but reduces the precision of the estimator of the optimal protection plan. Importance sampling is demonstrated as a simulation technique for reducing estimator variance for a given sample size, particularly when the tail of the population distribution is of critical importance. The method is demonstrated on a hypothetical problem involving gray wolf management in the Great Lakes region of the United States. In comparison to random sampling, importance sampling produces a 21-fold reduction in the variance of the estimator of the minimum-cost protection plan. Results from the optimization model demonstrate the extreme sensitivity of the minimum-cost protection plan to the structure of the growth model and the magnitude of environmental variation. This sensitivity is not widely recognized in the literature on wildlife habitat planning and is a strong reason for using optimization methods that can handle stochastic population models with a wide range of structures.