Comparison of two length-based estimators of total mortality: A simulation approach

Length-based methods for estimating the total mortality rate, Z, are appealing due to their potential application in data-poor situations, particularly when assessing tropical and invertebrate fisheries where age composition data are lacking. We evaluated two length-based estimators attributed to Beverton and Holt (1956) and to Ehrhardt and Ault (1992) for precision and accuracy when applied to simulated length data generated under varying combinations of Z rates, growth rates, variability in length at age, and the degree of length truncation imposed by the data analyst. The Beverton-Holt method generally overestimated Z, with bias ranging from -5% to +40%, when the abundance of the oldest age-groups is less than that associated with a constant mortality rate. The bias in the Ehrhardt-Ault method ranged from -80% to +140%, depending on the combinations of Z and the von Bertalanffy growth coefficient K, the degree of imposed length truncation, and the method for mean length calculation. In general, the Ehrhardt-Ault estimator exhibited complex behavior, which made it difficult to summarize the direction and magnitude of the bias and the mean square error. The best length truncation to impose on the length samples to apply the Ehrhardt-Ault method often did not coincide with the “true” length of truncation especially with more realistic scenarios of variability in length at age. The Beverton-Holt method has the advantage of having known directional biases and predictable behavior. Use of the Ehrhardt-Ault estimator should be accompanied by a case-specific evaluation of its likely performance.