Simulation testing a new multi-stage process to measure the effect of increased sampling effort on effective sample size for age and length data

Ocean management involves monitoring data that are used in biological models, where estimates inform policy choices. However, few science organizations publish results from a recurring, quantitative process to optimize effort spent measuring fish age. We propose that science organizations could predict the likely consequences of changing age-reading effort using four independent and species-specific analyses. Specifically we predict the impact of changing age collections on the variance of expanded age-composition data ("input sample size", Analysis 1), likely changes in the variance of residuals relative to stock-assessment age-composition estimates ("effective sample size", Analysis 2), subsequent changes in the variance of stock status estimates (Analysis 3), and likely impacts on management performance (Analysis 4). We propose a bootstrap estimator to conduct Analysis 1 and derive a novel analytic estimator for Analysis 2 when age-composition data are weighted using a Dirichlet-multinomial likelihood. We then provide two simulation studies to evaluate these proposed estimators and show that the bootstrap estimator for Analysis 1 underestimates the likely benefit of increased age reads while the analytic estimator for Analysis 2 is unbiased given a plausible mechanism for model misspecification. We conclude by proposing a formal process to evaluate changes in survey efforts for stock assessment.