Estimation of recruitment in catch-at-age models

Management strategies must be designed to take into account the uncertainty inherent in fish populations and their assessments. Annual recruitment variation is an important component of uncertainty. Several methods that allow the estimation of annual recruitment in statistical catch-at-age models are described: (a) maximum likelihood estimation with no penalty on the annual recruitment residuals, (b) maximum likelihood estimation with a lognormal penalty on the annual recruitment residuals, (c) importance sampling to numerically approximate the marginal likelihood with a lognormal penalty on the annual recruitment residuals, and (d) full Bayesian integration using Markov Chain Monte Carlo with a lognormal prior on the annual recruitment residuals. Simulation analysis is used to test the performance of these methods. All four methods perform similarly at estimating quantities that are based on averaging or summing multiple estimates of annual recruitment; however the marginal likelihood method (c) and Bayesian integration (d) perform best at estimating annual recruitment and the standard deviation in annual recruitment residuals (sigma(R)) when catch-at-age data is missing for some years. The ability to estimate sigma(R) can be important for defining uncertainty when developing management strategies. The methods are applied to a New Zealand snapper (Pagrus auratus) stock and the estimate of sigma(R) is approximately 0.6.