Optimal partition of sampling effort between observations of fish density and migration speed for a riverine hydroacoustic duration-in-beam method

The duration-in-beam model has long been used in fisheries acoustics. For instance, the Pacific Salmon Commission uses this model for the hydroacoustic data collected at Mission, BC, Canada to estimate daily salmon passages in the Fraser River for in-season salmon management. The fish flux is calculated as the product of fish density times the migration speed. These two components are measured separately with the same acoustical sampling system. As the system can only acquire either density or speed data at any given time, an optimal sampling design is needed to partition the sampling effort for acoustical measurements of fish density and migration speed. In this paper, we present a method to estimate the optimal allocation of sampling effort between the density and speed measurements. The optimum was achieved by minimizing the variance of the estimated fish flux. The theoretical optimization method was applied to the hydroacoustic data collected in the 1998 fishing season to obtain an estimated optimal sampling design. This optimal design was adopted for the hydroacoustic sampling program at Mission, BC in the 1999 salmon migration season. The statistical results from the 1999 data were examined and compared with that from the 1998 data acquired according to a non-optimized sampling plan. It was found that the optimized sampling plan reduced the relative variance by 20%. Therefore, the methodology of this optimal design for sampling effort is a useful addition to the duration-in-beam model in fisheries acoustics.