A general framework for integrating environmental time series into stock assessment models: model description, simulation testing, and example

We present a method to integrate environmental time series into stock assessment models and to test the significance of correlations between population processes and the environmental time series. Parameters that relate the environmental time series to population processes are included in the stock assessment model, and likelihood ratio tests are used to determine if the parameters improve the fit to the data significantly. Two approaches are considered to integrate the environmental relationship. In the environmental model, the population dynamics process (e.g. recruitment) is proportional to the environmental variable, whereas in the environmental model with process error it is proportional to the environmental variable, but the model allows an additional temporal variation (process error) constrained by a log-normal distribution. The methods are tested by using simulation analysis and compared to the traditional method of correlating model estimates with environmental variables outside the estimation procedure. In the traditional method, the estimates of recruitment were provided by a model that allowed the recruitment only to have a temporal variation constrained by a log-normal distribution. We illustrate the methods by applying them to test the statistical significance of the correlation between sea-surface temperature (SST) and recruitment to the snapper (Pagrus auratus) stock in the Hauraki Gulf–Bay of Plenty, New Zealand. Simulation analyses indicated that the integrated approach with additional process error is superior to the traditional method of correlating model estimates with environmental variables outside the estimation procedure. The results suggest that, for the snapper stock, recruitment is positively correlated with SST at the time of spawning.