Unlocking the triad of age, year, and cohort effects for stock assessment: Demonstration of a computationally efficient and reproducible framework using weight-at-age

Abstract

Many demographic processes vary by age and over time, but are also hypothesized to exhibit cohort-specific patterns in variation; accounting for this variation within fisheries management remains a key challenge for contemporary stock assessments. Although there is evidence for time, age, and cohort-specific patterns in the variation of various components within stock assessment (e.g., selectivity, growth), methods are sparsely documented or are lacking to simultaneously estimate autocorrelation over time, among ages, and by cohort while also quantifying residual variation. We demonstrate an approach that facilitates the simultaneous estimation of autocorrelation for time, age, and cohort correlations, and provide two options to estimate the pointwise variance of this process (termed conditional and marginal variance). Using eastern Bering Sea walleye pollock (Gadus chalcogrammus) as a case-study, we develop factorial model formulations to demonstrate differences in predicted weight-at-age values from models that estimate different combinations of correlation parameters along three axes (age, year, cohort). We show that traditional model selection tools can be used to identify the relative evidence for, and magnitude of, age, time, and cohort correlations, and demonstrate that this method can be easily integrated as a routine option within next-generation stock assessments. Code to replicate our analysis is provided in a GitHub repository (https://github.com/chengmatt/GMRF_WAA), and includes a Template Model Builder function for assembling the precision matrix to facilitate easy adoption in other software packages.