A stochastic Pella Tomlinson model and its maximum sustainable yield

This paper investigates the biological reference points, such as the maximum sustainable yield (MSY), for the Pella Tomlinson and the Fox surplus production models (SPM) in the presence of a multiplicative environmental noise. These models are used in fisheries stock assessment as a firsthand tool for the elaboration of harvesting strategies. We derive conditions on the environmental noise distribution that insure that the biomass process for an SPM has a stationary distribution, so that extinction is avoided. Explicit results about the stationary behavior of the biomass distribution are provided for a particular specification of the noise. The consideration of random noise in the MSY calculations leads to more conservative harvesting target than deterministic models. The derivations account for a possible noise autocorrelation that represents the occurrence of spells of good and bad years. The impact of the noise is found to be more severe on Pella Tomlinson model for which the asymmetry parameter p is large while it is less important for Fox model.