Excessive predation pressure from the waterfowl Phalacrocorax carbo(Great Cormorant)on Plecoglossus altivelis(Ayu)has recently been a severe problem of river environment in Japan.Local fishery cooperatives are current...Excessive predation pressure from the waterfowl Phalacrocorax carbo(Great Cormorant)on Plecoglossus altivelis(Ayu)has recently been a severe problem of river environment in Japan.Local fishery cooperatives are currently suffering from economic difficulties due to decrease of the fish catch of P.altivelis.Local fishery cooperatives and municipalities have been enthusiastically trying to develop countermeasures that can effectively reduce the predation pressure;however,their effectiveness and efficiency have not been systematically quantified well.This aim can be achieved with the help of an appropriate mathematical model.In this paper,based on a pure death process,a practical stochastic control model for population dynamics of released P.altivelis in river environment under predation pressure from P.carbo,harvesting by human,and environmental fluctuations is proposed.Finding an optimal management strategy ultimately reduces to solving a 2D Hamilton–Jacobi–Bellman equation,which is performed with a finite element scheme.Its application to a Japanese river environment successfully computes the optimal management strategy that is consistent with the reality.Numerical sensitivity analysis of the presented mathematical model is also performed for comprehension of dependence of the optimal strategy on the model parameters.展开更多
基金the helpful comments and advice by officers in Hii-River Fishery Cooperatives and Dr.Kayoko Kameda of Lake Biwa Museum.The River Found No.27-1263-020 and No.28-5311-020JSPS Research Grants No.15H06417 and No.16KT0018WEC Research Grant No.2016-02,and The Kyoto University Foundation support this research.
文摘Excessive predation pressure from the waterfowl Phalacrocorax carbo(Great Cormorant)on Plecoglossus altivelis(Ayu)has recently been a severe problem of river environment in Japan.Local fishery cooperatives are currently suffering from economic difficulties due to decrease of the fish catch of P.altivelis.Local fishery cooperatives and municipalities have been enthusiastically trying to develop countermeasures that can effectively reduce the predation pressure;however,their effectiveness and efficiency have not been systematically quantified well.This aim can be achieved with the help of an appropriate mathematical model.In this paper,based on a pure death process,a practical stochastic control model for population dynamics of released P.altivelis in river environment under predation pressure from P.carbo,harvesting by human,and environmental fluctuations is proposed.Finding an optimal management strategy ultimately reduces to solving a 2D Hamilton–Jacobi–Bellman equation,which is performed with a finite element scheme.Its application to a Japanese river environment successfully computes the optimal management strategy that is consistent with the reality.Numerical sensitivity analysis of the presented mathematical model is also performed for comprehension of dependence of the optimal strategy on the model parameters.
