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In this manuscript we investigate the long-term behavior of a single-speciesfishery, which is harvested by several fleets. The time evolution of thispopulation is modeled by a discrete time stochastic age-structured model. Weassume that incertitude only affects the recruitment. First, for thedeterministic version of this model, we characterize the equilibrium yields interms of the fishing mortality. Then, for the stochastic version, we introducethe concepts of maximum expected, log expected and harmonic expectedsustainable yield, and we analyze how the incertitude affects the behavior ofthese yields and their stationary distribution. All the numerical simulationsare performed with data obtained from Patagonian Tooth-fish fishery, which isharvested by four different type of fleets: Chilean Industrial fleet, ChileanArtisanal fleet, Argentinean longline fleet, and Argentinean Artisanal fleet.

Dynamics and biological reference points in a stochastic age-structured  fish population model with an illustration of the Patagonian toothfish  population