Theoretical Ecology

, Volume 8, Issue 1, pp 1–13 | Cite as

A generalized perturbation approach for exploring stock recruitment relationships

ORIGINAL PAPER

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.

Keywords

Compensatory dynamics Generalized modeling Stock-recruitment relationships Shepherd function Neimark-Sacker bifurcation 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Center for Stock Assessment Research and Department of Ecology and Evolutionary BiologyUniversity of California Santa CruzSanta CruzUSA
  2. 2.Santa Fe InstituteSanta FeUSA
  3. 3.Center for Stock Assessment Research and Department of Applied Mathematics and StatisticsUniversity of California Santa CruzSanta CruzUSA
  4. 4.Department of BiologyUniversity of BergenBergenNorway

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