A probabilistic procedure for estimating an optimal echo-integration threshold using the Expectation-Maximisation algorithm

To obtain reliable fish biomass estimates by acoustic methods, it is essential to filter out the signals from unwanted scatterers (e.g. zooplankton). When acoustic data are collected at more than one frequency, methods that exploit the differences in reflectivity of scatterers can be used to achieve the separation of targets. These methods cannot be applied with historical data nor recent data collected on board fishing vessels employed as scientific platforms, where only one transducer is available. Instead, a volume backscattering strength (S_v) threshold is set to separate fish from plankton, both for echogram visualisation or, more importantly, during echo-integration. While empirical methods exist for selecting a threshold, it often depends on the subjective decision of the user. A-47 dB threshold was empirically established in 2008 at the beginning of a series of surveys conducted by Mexico's National Fisheries Institute to assess the biomass of Pacific sardine in the Gulf of California. Until 2012, when a 120 kHz transducer was installed, only data collected at 38 kHz are available. Here, we propose a probabilistic procedure to estimate an optimal S_v threshold using the Expectation-Maximisation algorithm for fitting a mixture of Gaussian distributions to S_v data sampled from schools associated with small pelagic fish and their surrounding echoes. The optimal threshold is given by the Bayes decision function for classifying an S_v value in one of the two groups. The procedure was implemented in the R language environment. The optimal threshold found for 38 kHz data was -59.4 dB, more than 12 dB lower than the currently used value. This difference prompts the need to revise the acoustic biomass estimates of small pelagics in the Gulf of California.