Optimal design of biological sampling programs using the analysis of variance

An approach for optimizing environmental monitoring programs designed for the detection of biological or ecological change is developed. The monitoring designs use a factorial treatment structure that allows for seasonality, pre/post event status (where the event is typically an external perturbation), paired treatment-control stations, and auxiliary effects such as water depth variation. The sampling cost is assumed to be the sum of a fixed initial cost plus components for replication, number of stations visited, and number of sampling occasions. The optimization takes two forms: minimization of sampling cost for a given detectability of change (power), and maximization of power for a fixed cost. Both are solved using a Lagrange multiplier formulation. The resulting system of constrained nonlinear equations is solved using a modified Newton-Raphson method. Sensitivity analyses show that the monitoring design is relatively robust with respect to the decision variables as long as the power associated with the optimal design is modest.