Model Selection Uncertainty and Bayesian Model Averaging in Fisheries Recruitment Modeling

Stock recruitment (SR) modeling is the central part of fisheries population dynamics analysis. Models and modeling techniques on SR relationships have been evolving for decades, and have moved from traditional SR models, such as the Ricker and Beverton-Holt models to measurement error models, and Kalman filter time series models. Though SR models are evolving, people still typically select a specific model and then proceed as if the selected model had generated the data. This approach ignores the uncertainty in the model selection, leading to overconfident inferences and decisions with higher risk than expected. Bayesian model averaging (BMA) provides a coherent mechanism for accounting for this model uncertainty. In this study, Lake Erie walleye (Sander vitreus) fishery was used as an example. Six mathematical models were developed, which included a Ricker model, a hierarchical Ricker model, a residual auto-regressive model, a Kalman filter random walk model, a Kalman filter autoregressive model, and a Ricker measurement error model. The posterior distributions of estimated productivity and recruitment from these models were weighted based on the Deviance Information Criterion (DIC) to provide our predictive posterior distribution of population productivity and recruitment over time. To test the efficiency of the Bayesian averaging approach and the uncertainty from model selection, a further simulation study was done based on the example fishery. Our results showed that model selection uncertainty is high and BMA explained the data reasonably well. We suggest that BMA is more appropriate in simulating SR models. The framework developed here can be used for other species population SR analysis. We also suggest that the model selection uncertainty be considered and the BMA be applied to other stock assessment models and even in the fisheries management decision making in the future.