Determining optimal policies for management of an aquatic ecosystem

A methodology was developed by which a state fish and game agency can determine Optimal Ecosystem Policies (OEP). This methodology consisted of: (1) an ecosystem simulation model which depicted a variety of interactions among and between species; (2) an objective function consisting of several criteria; and (3) a computer implemented optimization procedure designed to find the time sequence of decision activities which maximized the objective function. OEP was applied to a specific case study area, a stream fishery in Rich Creek, Monroe County, West Virginia.

The simulation model consisted of a system of difference equations calculated for discrete time stages (one year time horizon). Interaction was modeled using a special queueing framework, where an animal's actions were governed by a preemptive priority sequence. Using the queueing framework, all interactions become density-dependent, and probability parameters may be estimated subjectively. Ration size, mortality, and reproduction were calculated and were inputs to population abundance, growth, and metabolism calculating routines.

The criteria considered in the objective function in the Rich Creek study were: (1) catch per unit effort by the commercial operators summed over all time stages (a measure of benefits to the commercial fishermen); (2) the environmental stability measured by a diversity index; (3) the number of fishermen visiting the stream during the year (angler-days); and (4) the sum over the year of a measure of angler satisfaction (utility). The utility function was a function of the attributes: size of fish caught, species of fish caught, number of fish caught, and crowding by other anglers. The utility model was empirically determined and it was found to be multiplicative over the attributes. Terminal (year end) constraints in OEP were a budgetary constraint, a diversity constraint, and a commercial catch constraint. Thus, the objective was maximization of a linear combination of the four criteria subject to the three terminal constraints.

The approximate optimal solution was found by search by Regression and Application of the Maximum Principle (RAMP search). Quadratic transition functions were fit to simulated data and the optimal policy was found for these transitions using the discrete maximum principle. This policy was returned to the simulation to generate new data and the procedure was iterated until a convergence criterion was met.

Optimization and sensitivity analysis of the Rich Creek model showed that an adequate budget was needed to maintain levels of stocked trout (the preferred species) to produce relatively high levels of angler utility. At low budgets other species became more important and diversity became an active constraint. Diversity and commercial catch criteria conflicted, therefore optimal catch occurred early in the year so that diversity could recover later. Solutions were most sensitive to three system components: (1) human aspects such as population size, preferences, and angler abundance; (2) the temperature prediction function (it served as a driver for many other variables); and (3) trout biomass variables.Future research on Rich Creek should be directed toward these three components.