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

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... 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. 2(d) plot the computed 0,pr J , 0,cau J , 0,cos J and 0,tot J in the r V plane, respectively. Figure 2 shows that 0,pr J , 0,cau J , and 0,tot J monotonically increase as r increases. This is considered due to that in average t X increases as r increases, which consequently leads to the increase of 0,cau J , 0,pr J , and 0,tot J . Figure 2 also shows that they monotonically decrease as V increases. A heuristic consideration based on simplified models (Grigoriu, 2014) infers that increase of V increases stochastic fluctuations of the population dynamics, which in general results in higher probability of the population extinction. According to Figure 2(d), 0,tot J is maximized in the plane for low V and high r , and it becomes negative for large V . The index 0,tot J more sensitively responses to V than r for the range of the parameters. The computational results imply that to decrease V than r more effectively gain profit. Being different from the three indices that monotonically response to r and V , the index 0,cos J is not monotonic as shown in Figure 2(c); it is maximized at 2 J , (b) 0,cau J , (c) 0,cos J , and (d) 0,tot J on the -r V plane Figure 3: The indices (a) 0,pr J , (b) 0,cau J , (c) 0,cos J , and (d) 0,tot J on the 0 -X V plane Figure 4: The indices (a) 0,pr J , (b) 0,cau J , (c) 0,cos J , and (d) 0,tot J on the 0 -r X plane JOURNAL OF RAINWATER CATCHMENT SYSTEMS/VOL.22 NO.1 2016 11 computed 0,pr J , 0,cau J , 0,cos J , and 0,tot J in the 0 X V plane, respectively. Figure 3 shows that increase of 0 X in the plane increase 0,pr J , 0,cau J , and 0,tot J for small V . On the other hand, increase of 0 X doesn't significantly affect them for large V . Figure 3 also shows that all the indices monotonically decrease as V increases. The decrease of the 0,cos J is the most significant among them. Figure 3(d) shows that the total profit 0,tot J is negative for large V or small 0 X . 3.4.3 Sensitivity on the parameters r and 0 X Sensitivity of the strategy on the growth rate r and the release amount 0 X with the noise intensity 0.24 V (1/day 1/2 ) is examined. Figure 4 (a) through 4(d) plot computed 0,pr J , 0,cau J , 0,cos J , and 0,tot J in the 0 r X plane, respectively. Increase of r in the plane doesn't increase 0,pr J , 0,cau J and 0,tot J for small 0 X . On the other hand, for large 0 X , increase of r leads to their significant increase. For the index 0,cos J , increase of 0 X induces its rapid increase. Figure 4 (d) shows that the total profit 0,tot J is negative for small r or 0 X .