Global fish abundance estimation from regular sampling: the geostatistical transitive method

Abstract

This article deals with the estimation of fish biomass based on regular samplings. The geostatistical transitive method is a design-based spatially explicit method based on few and falsifiable assumptions concerning the sampling strategy. The falsifiability of a hypothesis corresponds to our capacity to control its adequacy to field data in practice. We first describe the basics of the method, mention the questions relative to the covariogram estimation, the units, and the projections of the coordinates, and explain how to fit the model to the experimental covariogram. We then apply the method to an ICES (International Council for the Exploration of the Sea) triennial mackerel egg survey, with regular sampling, and to a Moroccan octopus survey, with regular stratified sampling. To compare the present technique with existing methods, the number and the falsifiability of their respective hypotheses are considered in addition to the bias, the convergence, and the estimation variance. As is often the case, data are assumed to be synoptic, and we discuss two examples of spatiotemporal methods.