Optimal effort allocation in stratified, large area trawl surveys, with application to shrimp surveys in the Barents Sea

Abstract

A method for optimal effort allocation in stratified trawl surveys with uncorrelated grid sampling is developed. Two related optimisation criteria are considered: (1) to minimise the coefficient of variation (CV) of the biomass index for a given available vessel time ( t) and (2) to minimise the vessel time needed in order to obtain a required CV value. The cost function model includes a constant trawl and handling time per station, and a stratum-dependent sailing time between successive stations. The benefit of the method is compared with a conventional design with proportional (to area) allocation. Simple formulas for reasonably close upper and lower bounds for the obtainable improvement are calculated. In general, the maximum relative reduction in t for a given CV value is larger than the obtainable relative reduction in CV for a given t. Applied to biomass data from conventional shrimp surveys in the Barents Sea (1992–1996), it is estimated that the mean CV value (averaged over years) could have been reduced from 7.0% (proportional allocation) to 6.4% (optimal allocation), which corresponds to a relative reduction of 8.7%. Correspondingly, a possible 10.9% reduction of t was found without loss of precision.