Estimating fish abundance from acoustic surveys: calculating variance due to acoustic backscatter and length distribution error

Estimation of fish abundance from acoustic surveys requires the estimation of total acoustic backscatter of the target species in the sampled region. Although the arithmetic mean of acoustic backscatter is an unbiased estimator of the mean backscatter for regular or random sampling designs, under the presence of spatial structure, its use leads to a loss of information and the estimation of its variance is not trivial. Here, we tackle these shortcomings by building a spatial model of acoustic backscatter using spline-based generalized additive models (GAMs). GAMs were used to provide local and global estimates of acoustic backscatter, and their precision was calculated by statistical simulations of the models' parameters. For a series of surveys performed off the western and Southern Iberian Peninsula, GAM estimates were unbiased and more precise than the arithmetic mean estimates. Simulations of the acoustic backscatter fields were combined with resampling of the trawls to provide confidence intervals for fish numbers and biomass. The relative standard errors of the estimates were within 13% and 46% (average 22%) for numbers and within 12% and 35% (average 19%) for biomass. Acoustic sampling error was the major contributor to the overall variance.