Modeling temporal variation in recruitment in fisheries stock assessment: A review of theory and practice

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Recruitment is one of the most variable biological processes driving fisheries population dynamics and the characteristics and drivers of the variation differ among stocks. Understanding, describing (modeling), estimating, and predicting (forecasting) this variation is essential to appropriate stock assessment and fisheries management. Most modern stock assessments estimate annual variation in recruitment, particularly those that include age or size composition data. Changes over time are often partitioned into those related to the spawning biomass due to density dependence (the stock-recruitment relationship) and those related to other factors such as environmental conditions. Several methods have been used to model recruitment inside stock assessment models, and they differ by how recruitment is represented and how statistical inference is conducted. Virtual population analyses make few statistical assumptions about recruitment and instead calculate recruitment as the sum of the mortality-adjusted catches of a cohort while surplus production models generally imply a stock-recruitment relationship in their production function. Integrated statistical stock assessment models have modelled recruitment using a stock-recruitment relationship, autocorrelation, a function of covariates, regime shifts, or a combination of these. Statistical inference has typically been conducted using state-space (hierarchical) models, whether using Bayesian or maximum likelihood methods, or inferences are approximated using penalized likelihood approaches, which may not be statistically reliable. All these methods have specific issues that need to be addressed and there are tradeoffs in their use. Future temporal variation also needs to be considered when providing management advice. We review the theory and practice of modelling temporal variation in recruitment in fisheries stock assessment, provide advice on good practices, and recommend important research.