  In inland fisheries, transporting fishery resource individuals from a habitat
to spatially apart habitat(s) has recently been considered for fisheries stock
management 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 control
framework to tackle this issue based on a simple but new stochastic growth
model of individual fishes. The novel growth model governing individuals' body
weights uses a Wright-Fisher model as a latent driver to reproduce plausible
growth dynamics. The optimization problem is formulated as an impulse control
problem of a cost-benefit functional constrained by a degenerate parabolic
Fokker-Planck equation of the stochastic growth dynamics. Because the growth
dynamics have an observable variable and an unobservable variable (a variable
difficult or impossible to observe), we consider both full-information and
partial-information cases. The latter is more involved but more realistic
because of not explicitly using the unobservable variable in designing the
controls. In both cases, resolving an optimization problem reduces to solving
the associated Fokker-Planck and its adjoint equations, the latter being
non-trivial. We present a derivation procedure of the adjoint equation and its
internal boundary conditions in time to efficiently derive the optimal
transporting strategy. We finally provide a demonstrative computational example
of a transporting problem of Ayu sweetfish (Plecoglossus altivelis altivelis)
based on the latest real data set.
