Estimating fishing and natural mortality rates, and catchability coefficient, from a series of observations on mean length and fishing effort

Gedamke and Hoenig (2006) (Transactions of the American Fisheries Society, 135: 476-487) developed a non-equilibrium version of the Beverton and Holt estimator of total mortality rate, Z, based on mean length and thereby increased the usefulness of length-based methods. In this study, we extend their model by replacing period-specific Z parameters with the year-specific parameterization Z y = qf y + M where q is the catchability coefficient, f y is the fishing effort in year y, F (=qf) is the fishing mortality rate, and M is the natural mortality rate. Thus, the problem reduces to estimating just three parameters: q, M and residual variance. We used Monte Carlo simulation to study the model behaviour. Estimates of q and M are highly negatively correlated and may or may not be reliable; however, the estimates of corresponding Z's are more precise than estimates of F and are generally reliable, even when uncertainty about the mean lengths is high. This length-based method appears to work best for stocks with rapid growth rate. Contrast in effort data may not be necessary for reliable estimates of Z's. This approach forms a bridge between data-limited models and more complex models. We apply the method to the Norway lobster Nephrops norvegicus stock in Portugal as an example