Recommendations for estimating and detecting time-varying spawner-recruit dynamics in fish populations

Models that account for time-varying dynamics are increasingly used in population assessments in recognition of changing biological and environmental conditions. We performed a systematic simulation analysis based on a semelparous life history to evaluate the performance of various Ricker spawner-recruit models including stationary, random-walk, and regime shift models, that offer various interpretations of time-varying dynamics. Estimation models that allowed parameters to vary following random-walks tended to perform equally well or outperform regime shift and stationary models. However these results were not consistent across all scenarios examined. We also evaluated the performance of model selection criteria commonly used to identify time-varying processes. Both likelihood based model selection criteria (AICc and BIC) and cross-validation methods (LFO) were found to be unreliable, with a few exceptions. Changes in productivity were more identifiable than changes in capacity or both parameters, which were often indiscernible from stationary dynamics. The results were sensitive to the magnitude of parameter change and extent of residual variability (unexplained error), with greater changes and lower error being easier to accurately estimate and select. Given this context dependence for the accuracy of parameter estimates with time-varying models, and unreliable nature of selection criteria, we recommend that analysts conduct case-specific simulation-evaluations when model choices may have important and divergent management implications.