Abstract
Models of stock-recruitment relationships (SRRs) are often used to predict fish population dynamics. Commonly used SRRs include the Ricker, Beverton-Holt, and Cushing functional forms, which differ primarily by the degree of density-dependent effects (compensation). The degree of compensation determines whether recruitment respectively decreases, saturates, or increases at high levels of spawning stock biomass. In 1982, J.G. Shepherd united these dynamics into a single model, where the degree of compensation is determined by a single parameter. However, the difficulty in relating this parameter to biological data has limited its usefulness. Here, we use a generalized modeling framework to show that the degree of compensation can be related directly to the functional elasticity of growth, which is a general quantity that measures the change in recruitment relative to a change in biomass. We show that the elasticity of growth can be calculated from perturbations in fish biomass, is robust to observation error, and can be used to determine general attributes of the SRR in both continuous time production models, as well as discrete time age-structured models.
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Acknowledgements
We thank S. Allesina, M.P. Beakes, D. Braun, T. Gross, C. Kuehn, T. Levi, A. MacCall, J.W. Moore, S. Munch, M. Novak, C.C. Phillis, and A.O. Shelton for many helpful discussions and comments. We also thank the Dynamics of Biological Networks Lab at the Max-Planck Institute for the Physics of Complex Systems and the University of Bristol for sharing the ideas and knowledge that inspired this work. This project was partially funded by the Center for Stock Assessment and Research, a partnership between the Fisheries Ecology Division, NOAA Fisheries, Santa Cruz, CA and the University of California, Santa Cruz and by NSF grant EF-0924195 to M.M.
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Yeakel, J.D., Mangel, M. A generalized perturbation approach for exploring stock recruitment relationships. Theor Ecol 8, 1–13 (2015). https://doi.org/10.1007/s12080-014-0230-z
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DOI: https://doi.org/10.1007/s12080-014-0230-z