Natural mortality diagnostics for state-space stock assessment models

Stock assessment models often require an external estimate of the natural mortality rate (M) that is usually assumed to be the same for all ages and years in the model. Although the fixed M assumption can be a major oversimplification, model diagnostics (e.g. profile likelihoods) that can help provide an understanding of how the choice of M affects model fit are often not used in practice. In the state-space setting, model diagnostics are especially complicated because of the complex dependencies in the data caused by process errors. To get a better understanding of the effect of broad changes in M across all ages and years on the state-space model fit, we develop new methods that provide profile likelihoods for individual data sources (surveys, landings, age compositions) by decomposing the state-space integrated likelihood. We also use local influence diagnostics to assess the influence of age and year specific changes in M on model fit. We jointly call these methods M diagnostics and apply them to a case study for American plaice (Hippoglossoides platessoides) on the Grand Bank of Newfoundland. The M diagnostics indicate that most input data sources are fit better with a higher M in recent years. We suggest that M diagnostics should be routinely examined when formulating an assessment model.