Caveats with estimating natural mortality rates in stock assessment models using age aggregated catch data and abundance indices

We consider the challenge in estimating the natural mortality, M, in a standard statistical fish stock assessment model based on time series of catch-and abundance-at-age data. Though anecdotal evidence and empirical experience lend support to the fact that this parameter may be difficult to estimate, the current literature lacks a theoretical justification. We first discuss the estimatability of a time-invariant M theoretically and present necessary conditions for a constant M to be identifiable. We then investigate the practical usefulness of this by estimating M from simulated data based on models fitted to 19 fish stocks. Using the same data sets, we next explore several model formulations of time varying M, with a pre-specified mean value. Cross validation is used to assess the prediction performance of the candidate models. Our results show that a time-invariant M can be estimated with reasonable precision for a few stocks with long time series and typically high values of the true M. For most stocks, however, the estimation uncertainty of M is very large. For time-varying M, we find that ac-counting for variability across age and time using a simple model significantly improves the performance compared to a time-invariant M. No significant improvement is obtained by using complex models, such as, those with time dependencies in variability around mean values of M.

Automated summary

The study investigates the challenge in estimating natural mortality M in fish stock assessment models, finding that a time-invariant M can be estimated with reasonable precision for a few stocks, but for most stocks, the estimation uncertainty of M is very large. It is also discovered that accounting for variability across age and time using a simple model significantly improves performance for time-varying M compared to time-invariant M.