Is catch-per-unit-effort proportional to abundance?

We compiled 297 series of catch-per-unit-effort (CPUE) and independent abundance data (as estimated by research trawl surveys) and used observation error and random effects models to test the hypothesis that CPUE is proportional to true abundance. We used a power curve, for which we were interested in the shape parameter (beta). There was little difference among species, ages, or gear types in the distributions of the raw estimates of beta for each CPUE series. We examined three groups: cod, flatfish, and gadiformes, finding strong evidence that CPUE was most likely to remain high while abundance declines (i.e., hyperstability, where beta < 1). The range in the mean of the random effects distribution for beta was quite small, 0.64-0.75. Cod showed the least hyperstability, but still, 76% of the mass of the random effects distribution was below 1. Based on simulations, our estimates of beta are positively biased by approximately 10%; this should be considered in the application of our findings here. We also considered the precision of CPUE indices through a meta-analysis of observation error variances. The most precise indices were those from flatfish (median coefficient of variation of approximately approximate to0.42).