Empirical dynamic modeling for sustainable benchmarks of short-lived species

Abstract The abundance dynamics of short-lived marine species often exhibit large-amplitude fluctuations, potentially driven by unknown but important species interactions and environmental effects. These complex dynamics pose challenges in forecasting and establishing robust reference points. Here, we introduce an empirical dynamic modeling (EDM) framework using time-delay embeddings to recover unspecified species interactions and environmental effects, and use walk-forward simulations with varying harvest rates to estimate maximum sustainable yield (MSY). Firstly, we apply our framework to simulated data under various dynamics scenarios and demonstrate the statistical robustness of EDM-based MSY. Secondly, we apply our framework to abundance and catch time series (30 years) of federally managed brown shrimp stocks in the US Gulf of Mexico. We identify nonlinear signals and achieve high prediction accuracy in the empirical dynamics of brown shrimp. Lastly, based on the EDM of brown shrimp dynamics, we obtain MSY for timely and effective management. Our results highlight the utility of EDM in deriving reference points for short-lived species, particularly in situations where stock abundance and catch dynamics are influenced by unobserved species interactions and environmental effects in a complex ecosystem.