  In this manuscript we investigate the long-term behavior of a single-species
fishery, which is harvested by several fleets. The time evolution of this
population is modeled by a discrete time stochastic age-structured model. We
assume that incertitude only affects the recruitment. First, for the
deterministic version of this model, we characterize the equilibrium yields in
terms of the fishing mortality. Then, for the stochastic version, we introduce
the concepts of maximum expected, log expected and harmonic expected
sustainable yield, and we analyze how the incertitude affects the behavior of
these yields and their stationary distribution. All the numerical simulations
are performed with data obtained from Patagonian Tooth-fish fishery, which is
harvested by four different type of fleets: Chilean Industrial fleet, Chilean
Artisanal fleet, Argentinean longline fleet, and Argentinean Artisanal fleet.
