The effect of non-linear relationships between CPUE and abundance on the management procedure performance for northeast porbeagle

One potential problem with applying any Management Procedure that requires an index of abundance is that there is only one potential CPUE series, a Spanish longline series that is likely available in the future for management of the eastern Atlantic porbeagle stock. In this fishery, Porbeagle shark are a bycatch species so that there are concerns about the index not being representative of the non-target species. To address this concern, we run a set of simulations across a range of non-linear relationships between CPUE and abundance from hyperstable to hyperdeplete. We test a set of MPs that have previously demonstrated to meet minimum satisficing standards of having a least a 50% change that the stock is above the CITES Appendix 2 threshold of 20% SSB0, at least a 50% chance that the stock is above the level that supports maximum sustained yield, and at least a 50% of chance that fishing mortality is below the fishing mortality that produces maximum sustained yield. We show that for model-free MPs, the effect of hyper stability on MP performance is minimal. For the model-based MPs, performance is adequate provided that there is not excessive hyperstability or excessive hyperdepletion. A key research recommendation for northeast porbeagle is to analyze the Spanish longline index to determine if there is evidence for hyperstability of hyperdepletion, and to see if such effects can be removed through the standardization process.