The beaver (Castor canadensis) population in the United States has caused severe damage to valuable timberland through dam-building and flooding of bottomland forest. This study attempts to develop a bioeconomic model that incorporates dispersive population dynamics of beavers into the design of a cost-minimizing trapping strategy. Attention is focused on the situation where all landowners in a given habitat share a common interest in controlling beaver damages, and thus collectively agree to place the area-wide control decision in the hands of a public agency on a cost-sharing basis. The public manager is assumed to minimize the present value of combined timber damage and trapping costs over a finite period of time, subject to spatiotemporal dynamics of beaver population. These dynamics are summarized by a parabolic diffusive Volterra-Lotka partial differential equation, and the population control problem is cast in the framework of a distributed-parameter-control model. The sensitivity analysis alternates trapping-cost and timber-damage parameters between high and low values. Increased trapping costs decrease the level of trapping in the initial years of the optimal program, thereby leaving more beavers in the habitat. This triggers more intensive trapping during the later years of the program, requires more beavers to be trapped over the entire time horizon, and results in a higher overall program cost. Alternatively, increased timber-damage potential calls for increased trapping in the initial years of the program. Fewer beavers are maintained in the habitat and less trapping is required in the later years. Perhaps surprisingly, this results in a smaller number of beavers trapped over the entire time horizon.
