Reducing Bias and Filling in Spatial Gaps in Fishery-Dependent Catch-per-Unit-Effort Data by Geostatistical Prediction, I. Methodology and Simulation

Geostatistical prediction can address two difficult issues in interpreting fishery-dependent catch per unit effort (CPUE): the lack of a sampling design and the need to fill spatial gaps. In this paper we demonstrate the spatial weighting properties of geostatistics for treating data collected without a sampling design or with a selection bias, two basic traits of fishery-dependent data. We then examine the bias and precision of geostatistical prediction of CPUE based on fishery-dependent data through simulation. We create data sets with known variograms, sample them with a preference for sites with high abundance, and then estimate variograms and CPUE as the geostatistical mean relative abundance. The variograms obtained from the simulated fishery samples correctly estimated the range but underestimated the sill, and the geostatistical mean substantially improved the estimation of CPUE over the arithmetic mean. Though the geostatistical mean still overestimated the true value, the error was primarily due to prediction into unsampled locations, where predictions revert toward the arithmetic mean. The geostatistical variance at a point, which is a function of spatial autocorrelation and the location of adjacent samples, provides a measure of uncertainty. This variance measures the degree to which predictions are derived from nearby data versus distant observations, which translates the spatial extent of extrapolation into probabilistic terms. In conjunction with conventional standardization methods that account for factors affecting catchability, geostatistical prediction provides an additional tool that reduces but does not eliminate biases inherent in fishery-dependent data and supports the need to predict CPUE in unsampled areas.