Northwest Fisheries Science Center

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Document Type: Journal Article
Center: NWFSC
Document ID: 8410
Title: An explicit solution for calculating optimum spawning stock size from Ricker's stock recruitment model
Author: M. D. Scheuerell
Publication Year: 2016
Journal: PeerJ
Volume: 4
Pages: e1623
Keywords: Ricker model,maximum sustainable yield,harvest,Lambert W,MSY

Stock-recruitment models have been used for decades in fisheries management as a means of formalizing the expected number of offspring that recruit to a fishery based on the number of parents. In particular, Ricker’s stock recruitment model is widely used due to its flexibility and ease with which the parameters can be estimated. After model fitting, the spawning stock size that produces the maximum sustainable yield (SMSY) to a fishery, and the harvest corresponding to it (UMSY), are two of the most common biological reference points of interest to fisheries managers. However, to date there has been no explicit solution for either reference point because of the transcendental nature of the equation needed to solve for them. Therefore, numerical or statistical approximations have been used for more than 30 years. Here I provide explicit formulae for calculating both SMSY and UMSY in terms of the productivity and density-dependent parameters of Ricker’s model.

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Theme: Recovery and rebuilding of marine and coastal species
Foci: Develop methods to use physiological, biological and behavioral information to predict population-level processes.
Characterize the population biology of species, and develop and improve methods for predicting the status of populations.