  We analyze the harvesting and stocking of a population that is affected by
random and seasonal environmental fluctuations. The main novelty comes from
having three layers of environmental fluctuations. The first layer is due to
the environment switching at random times between different environmental
states. This is similar to having sudden environmental changes or catastrophes.
The second layer is due to seasonal variation, where there is a significant
change in the dynamics between seasons. Finally, the third layer is due to the
constant presence of environmental stochasticity -- between the seasonal or
random regime switches, the species is affected by fluctuations which can be
modelled by white noise. This framework is more realistic because it can
capture both significant random and deterministic environmental shifts as well
as small and frequent fluctuations in abiotic factors. Our framework also
allows for the price or cost of harvesting to change deterministically and
stochastically, something that is more realistic from an economic point of
view.
  The combined effects of seasonal and random fluctuations make it impossible
to find the optimal harvesting-stocking strategy analytically. We get around
this roadblock by developing rigorous numerical approximations and proving that
they converge to the optimal harvesting-stocking strategy. We apply our methods
to multiple population models and explore how prices, or costs, and
environmental fluctuations influence the optimal harvesting-stocking strategy.
We show that in many situations the optimal way of harvesting and stocking is
not of threshold type.
