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 $M$.

我们考虑估计自然死亡率的挑战， $米$, 在基于捕捞量和年龄丰度数据时间序列的标准统计鱼类资源评估模型中。尽管轶事证据和经验经验支持该参数可能难以估计的事实，但目前的文献缺乏理论依据。我们首先讨论一个时不变的可估计性$米$ 常数的理论和当前必要条件 $米$可识别。然后我们通过估计来研究它的实际用途$米$来自基于适合 19 个鱼类种群的模型的模拟数据。使用相同的数据集，我们接下来探索几个随时间变化的模型公式$米$，具有预先指定的平均值。交叉验证用于评估候选模型的预测性能。我们的结果表明，一个时不变的$米$ 对于一些时间序列较长且真实值通常较高的股票，可以以合理的精度进行估计 $米$. 然而，对于大多数股票，估计不确定性$米$非常大。对于时变$米$，我们发现与时间不变的模型相比，使用简单模型考虑年龄和时间的可变性显着提高了性能 $米$. 使用复杂模型并没有获得显着的改进，例如那些在平均值周围的可变性具有时间依赖性的模型$米$.