Why natural mortality is estimable, in theory if not in practice, in a data-rich stock assessment

Abstract

The process equations of a stock assessment model that predict catch at age and survey CPUE at age can be recast as a single set of equations for the change in survey CPUE of a cohort from one year to the next. Given deterministic data, these equations can be solved for the model parameters by applying the EM algorithm, even when almost all of the age-specific survey catchabilities and natural mortality rates are free parameters. This exercise shows that the usual stock assessment data, if error-free, do contain the information necessary to estimate natural mortality, even age-specific rates, but only if the data contain adequate variation in fishing mortality rates. The EM calculations break down when applied to stochastic data; they are not an alternative to numerical model fitting for parameter estimation.