Integrated models are able to combine several sources of data into a single analysis using joint likelihood functions, fostering the consistency of assumptions among analyses and the ability to diagnose goodness of fit and model-misspecification. Owing to their capacity to consistently combine diverse information, integrated models could detect the variability induced by external drivers, such as various environmental drivers, on key components of the stock dynamics (e.g. recruitment) in cases where these external drivers are relevant but not yet identified or incorporated into the modelling exercise. This diagnosing power could then be used to explore causality between fishery dynamics, as estimated by the integrated model, and external drivers. To achieve this aim, a correlation analysis is neither necessary nor sufficient to prove causation. An alternative statistical concept, Granger-causality, provides a framework that uses predictability, rather than correlation, to give more evidence of causation between time-series variables.
A two-step procedure to investigate external forcings in stock dynamics is proposed. First, an integrated model is implemented to detect anomalies that cannot be explained by the internal dynamics of the stock. Then, in a second step, Granger-causality is used to detect the external origin of these anomalies. This two-step procedure is explored using the European anchovy in the Gulf of Cádiz as an example population where the external (environmental) drivers are well documented. The fishery dynamics is first estimated through an age-length model (Gadget). Then Granger-causality is used to assess the predictive power of different environmental drivers on recruitment. The results indicate that this is a powerful procedure, although also with important limitations, to determine predictability and that it can be implemented in a wide variety of stocks and external drivers. Moreover, once Granger-causality has been identified, it is shown that it can be used to forecast by making few modifications of the integrated model used for diagnosis.