Optimal Strategies for Harvesting and Predator Extermination to Sustain Plecoglossus altivelis (Ayu) Population in Stochastic River Environment

Abstract

  This paper presents a stochastic process model for optimal strategies of harvesting and predator extermination to sustain Plecoglossus altivelis (Ayu) population in stochastic river environment. Human activities, which are extermination of Phalacrocorax carbo (Great Cormorant) from the river and fishing activity to harvest P. altivelis in the river, are taken as control variables in the model. An optimal management problem to maximize the profit from harvesting P. altivelis and simultaneously to minimize the cost to exterminate P. carbo while to sustain P. altivelis, is then formulated on the basis of the dynamic programming principle. The problem to be solved mathematically reduces to approximating solutions to a Hamilton-Jacobi-Bellman equation. Sensitivity of the optimal management strategy to three critical components of the present model, which are the intrinsic growth rate, environmental noise that makes the dynamics in a river be inherently stochastic, and the two human activities, is numerically verified focusing on the case of Hii River, Japan where most of the population of P. altivelis is thought to be maintained by release of juveniles.