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In inland fisheries, transporting fishery resource individuals from a habitatto spatially apart habitat(s) has recently been considered for fisheries stockmanagement in the natural environment. However, its mathematical optimization,especially finding when and how much of the population should be transported,is still a fundamental unresolved issue. We propose a new impulse controlframework to tackle this issue based on a simple but new stochastic growthmodel of individual fishes. The novel growth model governing individuals' bodyweights uses a Wright-Fisher model as a latent driver to reproduce plausiblegrowth dynamics. The optimization problem is formulated as an impulse controlproblem of a cost-benefit functional constrained by a degenerate parabolicFokker-Planck equation of the stochastic growth dynamics. Because the growthdynamics have an observable variable and an unobservable variable (a variabledifficult or impossible to observe), we consider both full-information andpartial-information cases. The latter is more involved but more realisticbecause of not explicitly using the unobservable variable in designing thecontrols. In both cases, resolving an optimization problem reduces to solvingthe associated Fokker-Planck and its adjoint equations, the latter beingnon-trivial. We present a derivation procedure of the adjoint equation and itsinternal boundary conditions in time to efficiently derive the optimaltransporting strategy. We finally provide a demonstrative computational exampleof a transporting problem of Ayu sweetfish (Plecoglossus altivelis altivelis)based on the latest real data set.

Impulsive fishery resource transporting strategies based on an open-ended stochastic growth model having a latent variable