Using production models to assess the stock of Paralomis spinosissima around South Georgia Island

Four production models were fit to a time series of daily catch per unit effort (CPUE) data from the 1991/92 fishery for Paralomis spinosissima around South Georgia Island. The four models considered recruitment in different ways. Model 1 contained a linear recruitment function; Model 2 had constant recruitment; Model 3 contained a Beverton-Holt recruitment function, and Model 4 used a Ricker recruitment function. The best fitting model was Model 1. Model 1 had three parameters: an estimate of initial abundance (N0), an estimate of the scaling coefficient relating abundance to CPUE (q), and a recruitment parameter (a). The generalized likelihood ratio was used to place 95% confidence bounds around the parameter estimates from Model 1. These confidence bounds were very precise: Pr(240928 ≤ N0 ≤ 255374) ≈ 0.95; Pr(8.56 x 10-7 ≤ q ≤ 9.49 x 10-7) ≈ 0.95; and Pr(0.00804 ≤ a ≤ 0.00890) ≈ 0.95. Assuming that fishery removals should not be greater than the number of crabs that recruit to the fishery during the course of a fishing season, Bayesian statistics were used to evaluate alternative levels of a Total Allowable Catch (TAC) for the 1993/94 crab fishery. An optimal TAC was determined to be about 300 t. However, this TAC was conditional on the 1991/92 fishery data, and this data was limited to small temporal and spatial scales (about 4 mo. and 3600 n. mi.2). To extrapolate the estimated TAC to longer time periods information about the frequency and duration of the molting/mating event is required. To extrapolate the estimated TAC to larger areas (i.e. to estimate a TAC for all of South Georgia), it was necessary to determine whether growth or movement was predominantly responsible for recruitment. Monthly length frequency histograms were constructed and showed that growth was probably not the primary recruitment mechanism. Since movement may be important to the recruitment process, a TAC for all of South Georgia cannot be estimated by simple multiplication.