Non-linearity in stock–recruitment relationships of Atlantic cod: insights from a multi-model approach

Camilla Sguotti,Christian Möllmann,Ethan Deyle,Saskia A Otto,George Sugihara,Xochitl Cormon,Karl M Werner,Gary Griffith

doi:10.1093/icesjms/fsz113

Abstract

Abstract The stock–recruitment relationship is the basis of any stock prediction and thus fundamental for fishery management. Traditional parametric stock–recruitment models often poorly fit empirical data, nevertheless they are still the rule in fish stock assessment procedures. We here apply a multi-model approach to predict recruitment of 20 Atlantic cod (Gadus morhua) stocks as a function of adult biomass and environmental variables. We compare the traditional Ricker model with two non-parametric approaches: (i) the stochastic cusp model from catastrophe theory and (ii) multivariate simplex projections, based on attractor state-space reconstruction. We show that the performance of each model is contingent on the historical dynamics of individual stocks, and that stocks which experienced abrupt and state-dependent dynamics are best modelled using non-parametric approaches. These dynamics are pervasive in Western stocks highlighting a geographical distinction between cod stocks, which have implications for their recovery potential. Furthermore, the addition of environmental variables always improved the models’ predictive power indicating that they should be considered in stock assessment and management routines. Using our multi-model approach, we demonstrate that we should be more flexible when modelling recruitment and tailor our approaches to the dynamical properties of each individual stock.

Highlights

Forecasting complex trajectories of marine resources is essential to fishery management and one of the major challenges of our time (Schindler and Hilborn, 2015; Ye et al, 2015)
The two preliminary tests of the empirical dynamic modelling (EDM), necessary to perform the multivariate simplex projection (MSP), revealed on average significantly non-linear dynamics in recruitment of Atlantic cod stocks, and an appropriate choice of explanatory variables (Supplementary Figures S4 and S5), allowing us to proceed with the analyses
We investigated (i) whether recruitment dynamics in Atlantic cod stocks are better predicted by non-parametric, statedependent, or catastrophic statistical methodology compared to traditional parametric, linear approaches such as the Ricker stock–recruitment model and (ii) whether using climate variables as predictors in addition to spawning-stock biomass (SSB) improves the predictive performance of such models

Summary

Introduction

Forecasting complex trajectories of marine resources is essential to fishery management and one of the major challenges of our time (Schindler and Hilborn, 2015; Ye et al, 2015). SRRs are based on the assumption that recruitment (the number of fish that enter the adult population) is directly related to adult stock size (Kraus et al, 2000; Jennings et al, 2001) Parametric approaches, such as the Ricker model, were developed around the 1950s (Ricker, 1954) and in some cases still represent the method of choice in stock assessments (ICES, 2017). These models are very specific in the type of functional response curve to describe the SRR, and are linear, in the sense that, the relationship between recruitment and VC International Council for the Exploration of the Sea 2019.

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Discussion

Conclusion