Several indices based on catch rate as measured by CPUE are used in the VPA of Atlantic bluefin tuna, as described in the International Commission for the Conservation of Atlantic Tunas (ICCAT) report (ICCAT, 1993; table 3 gives the annual values). These indices are of critical importance because their trends are influential in determining the final trend in population parameters from the analysis. The committee wanted to evaluate the uncertainty in these indices and therefore obtained data from three indices, as explained below. The methods used to obtain the indices were examined and as a consequence, the committee performed analyses to reestimate annual values for the indices. In addition, hypothesis of trends in the CPUE data and abundance indices were made, using a robust procedure described below. This trend analysis was performed on the new information as well as the abundance indices from Table 3 of the ICCAT report.
The use of CPUE as an index of abundance relies on the direct relationship CPUE = C/E = qN, where C is catch, E is effort, q is the catchability coefficient, and N is abundance, biomass, or density. A common problem has been that the value of q may depend on various fishing methods, gear types, and environmental conditions. When annual indices of abundance are desired, the annual trend in CPUEs will reflect the abundance trend only if q is constant over years. However, because fishing techniques and environmental conditions may vary annually, CPUEs need to be standardized so that their trend is independent of these other factors. The annual trend in standardized CPUEs will reflect changes in CPUEs that are not attributable to the standardization factors. Therefore, the annual trend of the standardized CPUEs is attributable to factors not used in the standardization procedure, the most important of which is abundance. Nonlinear relationships between CPUE and abundance were not considered in this report owing to data limitations, but it is true that the presence of nonlinear relationships would induce additional uncertainty about population status and should be considered further.
One popular technique for standardizing catch rates is the use of general linear models. Usually, the CPUEs are transformed so that the annual effects and standardization factors will be multiplicative; for example,