A method for calculating a meta-analytical prior for the natural mortality rate using multiple life history correlates

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The natural mortality rate M is an important parameter for understanding population dynamics, and is extraordinarily difficult to estimate for many fish species. The uncertainty associated with M translates into increased uncertainty in fishery stock assessments. Estimation of M within a stock assessment model is complicated by its confounding with other life history and fishery parameters which are also uncertain, some of which are typically estimated within the model. Ageing error and variation in growth, which may not be fully modelled, can also affect estimation of M, as can various assumptions, including the form of the stock-recruitment function (e.g. Beverton-Holt, Ricker) and the level of compensation (or steepness), which may be fixed (or limited by a prior) in the model. To avoid these difficulties, stock assessors often assume point estimates for M derived from meta-analytical relationships between M and more easily measured life history characteristics, such as growth rate or longevity. However, these relationships depend on estimates of M for a great number of species, and those estimates are also subject to errors and biases (as are, to a lesser extent, the other life history parameters). Therefore, at the very least, some measure of uncertainty in M should be calculated and used for evaluating uncertainty in stock assessments and management strategy evaluations. Given error-free data on M and the covariate(s) for a meta-analysis, prediction intervals would provide the appropriate measure of uncertainty in M. In contrast, if the relationship between the covariate(s) and M is exact and the only error is in the estimates of M used for the meta-analysis, confidence intervals would appropriate. Using multiple published meta-analyses of M's relationship with various life history correlates, and beginning with the uncertainty interval calculations, I develop a method for creating combined priors for M for use in stock assessment.

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