Doctoral Dissertations

Date of Award

12-1991

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Agricultural Economics

Major Professor

Luther Keller

Committee Members

Ray Huffaker, Bill Park

Abstract

The beaver population in the Southeastern United States has caused severe damage to valuable timber land through dam-building and flooding of bottom-land forest. Traditionally, beavers have been trapped by small group of people as a source of their livelihood. The low pelt price in the recent years has failed to stimulate adequate trapping pressure, and thus, resulted in increased beaver population and damage losses. The low trapping pressure has left the burden of nuisance control on property owners. Since the beaver population is mobile, extermination of beavers from affected parcels results in migration of beavers from neighboring less controlled parcels to less populated controlled parcels. This backward migration of beavers from uncontrolled habitat to controlled habitat imposes a negative diffusion externality on the owners of controlled parcels because they have to incur the future cost of trapping immigrating beavers. Unless all the land owners agree to control the beaver population simultaneously, the diffusion externality could result in a low incentive for control of beaver population on the part of individual land owners, causing a wedge between social and private needs for controlling beaver population.

This study attempts to develop a bioeconomic model that incorporates dispersive population dynamics of beavers into the design of a cost-minimizing trapping strategy. While recognizing the need for several management options, depending on the land owners attitude about beavers, this study focuses its attention on the situation where all the land owners in a given habitat share common interest of controlling beaver nuisance, and collectively agree to place the area-wide control decision in the hands of a public agency, on a cost sharing basis. The model is based on the notion that the public manager attempts to minimize the present value combined costs of beaver damage and trapping over a finite period of time subject to spatiotemporal dynamics of beaver population. The time and spatial dynamics of beaver population is summarized by the parabolic diffusive Volterra-Lotka partial differential equation. Thus, the current problem is a typical distributed parameter control problem.

The cost-minimizing area-wide trapping model is capable of characterizing the beaver control strategy that leaves enough beavers after taking into account the net migration at each location and time, so as to strike the optimal balance between timber damage and trapping cost. The marginality condition governing this tradeoff requires that the marginal damage savings from the beavers trapped at each location equal the marginal costs of trapping. The marginal savings from trapping activity, in turn, is measured as the imputed nuisance value (shadow price) of the beaver stock in a unit area.

The optimality system for this problem that characterizes the optimal control is solved numerically. The validity of the theoretical model is empirically examined using the bioeconomic data collected for the Wildlife Management Regions of the New York State Department of Environmental Conservation. The empirical simulation generated discrete values for the optimal beaver densities and trapping rates across all the individual operational units over time. The entire distribution of optimal beaver densities does gradually and smoothly decline over the period of time. The unevenness of the initial population distribution smoothes out eventually across the beaver habitat. At each geographical location, towards the end of the planning period optimal trapping rate will become zero, whereas the population density asymptotically approaches zero.

The sensitivity analysis where the cost and damage parameters of the model are alternated between high and low values indicates that an increase in the damage potential of beavers could substantially increase the net present value total cost. On the other hand, an increase in the cost of beaver trapping adds only marginally to the total cost, conserving more number of beavers. The geographical variation in the beaver damage potential has a noticeable reflection on the spatial distribution of trapping rates, with little impact on the optimal densities. The areas with higher beaver damage potentials require more intensive trapping operation.

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