Use of generalized linear Bayesian model to mitigate the impact of spatial contraction in fishing pattern on the estimation of relative abundance

We developed a hierarchical Bayesian generalized linear model (Delta model) for CPUE standardization and tested this model with Japanese longline fisheries data from 1975 to 2006 for south Pacific Ocean albacore tuna (Thunnus alalunga). The Delta model consists of binomial and lognormal sub-models and was developed to predict catch rates for areas bypassed by the fishery in some years. Incorporation of these predicted catch rates into the standardization process mitigates the impact of spatial contractions in fishing pattern on the estimation of abundance indices. The relative abundance of albacore as measured by the standardized and nominal CPUEs are similar for the early years when the spatial pattern of the fishing did not change. However, when the spatial coverage of fishing was decreasing, the standardized CPUEs without predicted catch rates and nominal CPUEs were similar in the first half of this period, but the standardized CPUE was lower than nominal CPUE in the remaining years of this period. In contrast, standardized CPUEs with the inclusion of predicted catch rates indicated significantly lower abundances than the nominal CPUEs for this entire period. Explanatory variables considered in this study were Year, Month, Area, Year–Area interaction, and Depth using hooks per basket (HPB) as a proxy variable. All variables except for HPB were important in explaining variations in catch rates. Comparison of model predicted probabilities and observed proportions of non-zero catches showed that the binomial sub-model fit was adequate, and calculated Bayesian p-values indicated that the lognormal sub-model fit was acceptable. We also show that model fitting can be improved by adding random process error into the relationship between the explanatory variables and the function of the expected values of the response variables.