Incorporating spatial autocorrelation into the general linear model with an application to the yellowfin tuna (Thunnus albacares) longline CPUE data

Abstract

Catch-per-unit-effort (CPUE) data have often been used to obtain a relative index of the abundance of a fish stock by standardizing nominal CPUE using various statistical methods. The theory underlying most of these methods assumes the independence of the observed CPUEs. This assumption is invalid for a fish population because of their spatial autocorrelation. To overcome this problem, we incorporated spatial autocorrelation into the standard general linear model (GLM). We also incorporated into it a habitat-based model (HBM), to reflect, more effectively, the vertical distributions of tuna. As a case study, we fitted both the standard-GLM and spatial-GLM (with or without HBM) to the yellowfin tuna CPUE data of the Japanese longline fisheries in the Indian Ocean. Four distance models (Gaussian, exponential, linear and spherical) were examined for spatial autocorrelation. We found that the spatial-GLMs always produced the best goodness-of-fit to the data and gave more realistic estimates of the variances of the parameters, and that HBM-based GLMs always produced better goodness-of-fit to the data than those without. Of the four distance models, the Gaussian model performed the best. The point estimates of the relative indices of the abundance of yellowfin tuna differed slightly between standard and spatial GLMs, while their 95% confidence intervals from the spatial-GLMs were larger than those from the standard-GLM. Therefore, spatial-GLMs yield more robust estimates of the relative indices of the abundance of yellowfin tuna, especially when the nominal CPUEs are strongly spatially autocorrelated.