Incorporating Uncertainty into Management Models for Marine Mammals

Abstract: Good management models and good models for understanding biology differ in basic philosophy. Management models must facilitate management decisions despite large amounts of uncertainty about the managed populations. Such models must be based on parameters that can be estimated readily, must explicitly account for uncertainty, and should be simple to understand and implement. In contrast, biological models are designed to elucidate the workings of biology and should not be constrained by management concerns. We illustrate the need to incorporate uncertainty in management models by reviewing the inadequacy of using standard biological models to manage marine mammals in the United States. Past management was based on a simple model that, although it may have represented population dynamics adequately, failed as a management tool because the parameter that triggered management action was extremely difficult to estimate for the majority of populations. Uncertainty in parameter estimation resulted in few conservation actions. We describe a recently adopted management scheme that incorporates uncertainty and its resulting implementation. The approach used in this simple management scheme, which was tested by using simulation models, incorporates uncertainty and mandates monitoring abundance and human-caused mortality. Although the entire scheme may be suitable for application to some terrestrial and marine problems, two features are broadly applicable: the incorporation of uncertainty through simulations of management and the use of quantitative management criteria to translate verbal objectives into levels of acceptable risk.     

Empirical likelihood confidence intervals for adaptive cluster sampling

Adaptive cluster sampling (ACS) is an efficient sampling design for estimating parameters of rare and clustered populations. It is widely used in ecological research. The modified Hansen-Hurwitz (HH) and Horvitz-Thompson (HT) estimators based on small samples under ACS have often highly skewed distributions. In such situations, confidence intervals based on traditional normal approximation can lead to unsatisfactory results, with poor coverage properties. Christman and Pontius (Biometrics 56:503–510, 2000) showed that bootstrap percentile methods are appropriate for constructing confidence intervals from the HH estimator. But Perez and Pontius (J Stat Comput Simul 76:755–764, 2006) showed that bootstrap confidence intervals from the HT estimator are even worse than the normal approximation confidence intervals. In this article, we consider two pseudo empirical likelihood functions under the ACS design. One leads to the HH estimator and the other leads to a HT type estimator known as the Hájek estimator. Based on these two empirical likelihood functions, we derive confidence intervals for the population mean. Using a simulation study, we show that the confidence intervals obtained from the first EL function perform as good as the bootstrap confidence intervals from the HH estimator but the confidence intervals obtained from the second EL function perform much better than the bootstrap confidence intervals from the HT estimator, in terms of coverage rate.