Incorporating uncertainty into a length-based estimator of natural mortality in fish populations

Natural mortality (M) is one of the most important life history attributes of functioning fish populations. The most common methods to estimate M in fish populations provide point estimates which are usually constant across sizes and ages. In this article, we propose a framework for incorporating uncertainty into the length-based estimator of mortality that is based on von Bertalanffy growth function (VBGF) parameters determined with Bayesian analysis and asymmetric error distributions. Two methods to incorporate uncertainty in M estimates are evaluated. First, we use Markov chains of the estimated VBGF parameters directly when computing M and second, we simulate the posterior distribution of VBGF parameters with the copula method. These 2 approaches were applied and compared by using the extensive database available on age and growth for southern blue whiting (Micromesistius australis) harvested in the southeast Pacific. The copula approach provides advantages over Markov chains and requires far less computational time, while conserving the underlying dependence structure in the posterior distribution of the VBGF parameters. The incorporation of uncertainty into length-based estimates of mortality provides a promising way for modeling fish population dynamics.