Investigating trends in process error as a diagnostic for integrated fisheries stock assessments

Integrated stock assessments consist of fitting several sources of catch, abundance, and auxiliary biological information to estimate parameters of equations that describe the population dynamics of fish stocks. Stock assessments are subject to uncertainty, and it is a common practice to characterize uncertainty using alternative hypotheses and assumptions within an ensemble of models to develop scientific advice for fisheries management. In this context, there is the need to assign levels of plausibility to each of the combinations of factors that ultimately reflect the uncertainty on different biological and fishery processes. In this study, we describe and apply a model diagnostic to identify trends in process error in recruitment deviation estimates within ensembles of integrated assessment models of tropical tunas. We demonstrate that assessment model ensembles for tropical tunas contain distinct scenarios with significant trends in process error that are overlooked, with the associated implications for fisheries management. Using the Indian Ocean yellowfin as a case study, we found that trends in recruitment deviates are linked to extreme productivity scenarios which strongly diverged in scale from deterministic models fitted without recruitment deviates. This indicates that when recruitment deviates show an increasing trend, these can compensate for the loss of biomass in periods of high catch beyond the surplus production. In these cases, variation in recruitment is not a random process, but rather takes the function of a compensatory, systematic driver in productivity. Significant trends in recruitment were positively correlated with increased standard deviations and auto-correlation coefficient, non-random residual pattern in fits to abundance indices, and particularly poor performance of the Age-Structured Production Model (ASPM) diagnostic. We suggest that trends in recruitment deviates can be caused by misspecification of the biological parameters used as fixed values in integrated assessment models. The process error diagnostic described here can provide a statistical criterion in support for hypotheses and assumptions when using ensembles of models to develop fisheries management advice.