VPA with ad hoc tuning: implementation for disaggregated fleet data, variance estimation, and application to the Namibian stock of Cape horse mackerel Trachurus trachurus capensis

Abstract

The arbitrariness of Virtual Population Analysis (VPA) solutions in the absence of objectively based procedures to tune both oldest-age and most-recent-year terminal fishing mortalities is demonstrated. The formalism for tuning the latter set of mortalities with effort data from one or more participating fleets is presented, and procedures for estimating the variance of the resultant solution for Laurec-Shepherd tuning are proposed. These methods are applied to the stock of Cape horse mackerel off Namibia. Overall biomass trends are poorly determined. A multiple-fleet disaggregated-data VPA for the Polish and Soviet effort series estimates the 1989 F _0.1 Total Allowable Catch (TAC) to be a little in excess of 700 000 tons, with an associated negatively biased 95-per-cent confidence interval estimate of [220; 3 500] thousand tons. This enormous imprecision suggests that F _0.1 TAC estimation based on a VPA should be abandoned as the basis for management recommendations for the resource. A replacement-yield harvesting strategy is advocated as an interim measure; the associated TAC estimated would be 517 (SE 19) thousand tons using data on catch per unit effort and estimated average biomass from VPA. A status-quo F harvesting strategy, and the possibilities for direct surveys of the resource, merit consideration.