Abstract
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 accounting 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.
Highlights
Time series of catch at age and abundance at age indices are critical input for assessing commercially important fish stocks
In a more flexible model, we let the natural mortality rate vary by both age and year by the separable structure Ma,y = Maage + Myyear, with constraint My0ear = 0, where Maage, a = 1, ..., A is a set of parameters that depend on age a and Myyear, y = 1, ..., Y is another set of parameters that depend on year y
We present a general stock assessment model that is to be estimated on catch and survey index data only
Summary
Time series of catch at age and abundance at age indices are critical input for assessing commercially important fish stocks. For this type of data, the assessment models in use for management advice are typically variants of statistical catch at age models, where processes for the fishing mortality rate F, the natural mortality rate M and possibly recruitment are modelled as stochastic processes We compare the prediction performance of models with (i) pre-specified M, (ii) estimated M and (iii) time-varying M around a pre-specified level, by fitting them to real data for the same 19 fish stocks in a cross validation experiment
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