Production models for nonlinear stochastic age-structured fisheries

The overriding feature of stock-recruitment data for most fisheries is the amount of variability involved. Previous production models have assumed either an underlying linear stock-recruitment relationship [11] or an equilibrium condition [23]. Here a production model is derived for an age-structured fishery exhibiting nonlinear stochastic recruitment under nonequilibrium conditions. In the first section deterministic age-structured production models are reviewed, and in the next section corresponding random variable models are presented. Equations for the first and second order moments for each age class, for the stock, and for the yield are then derived using two approaches. The first approach assumes that third and order higher moments associated with the noise can be neglected (thus extending the “small noise” approach in [23]). The second approach assumes that the distributions associated with the random variables can be characterized by a particular two parameter distribution. This latter approximation can be applied to systems with “large noise,” and precision will not be lost for situations where the exact form of the distribution, associated with the stock-recruitment data, is unknown. Equations are derived for the solution under equilibrium recruitment and constant harvesting conditions. Detailed expressions are also obtained for the case where the random variables are assumed to satisfy a gamma distribution.