Comparative Performance of Three Length-Based Mortality Estimators

Length-based methods provide alternatives for estimating the instantaneous total mortality rate (Z) in exploited marine populations when data are not available for age-based methods. We compared the performance of three equilibrium length-based methods: the length-converted catch curve (LCCC), the Beverton–Holt equation (BHE), and the length-based spawning potential ratio (LB-SPR) method. The LCCC and BHE are two historically common procedures that use length as a proxy for age. From a truncated length-frequency distribution of fully selected animals, the LCCC estimates Z with a regression of the logarithm of catch at length by the midpoint of the length-bins, while the BHE estimates Z as a function of the mean length. The LB-SPR method is a likelihood-based population dynamics model, which—unlike the LCCC and BHE—does not require data truncation. Using Monte Carlo simulations across a range of scenarios with varying mortality and life history characteristics, our study showed that neither the LCCC nor the BHE was uniformly superior in terms of bias or root mean square error across simulations, but these estimators performed better than LB-SPR, which had the largest bias in most cases. Generally, if the ratio of natural mortality (M) to the von Bertalanffy growth rate parameter (K) is low, then the BHE is most preferred, although there is likely to be high bias and low precision. If M/K is high, then the LCCC and BHE performed better and similarly to each other. Differences in performance among commonly used truncation methods for the LCCC and BHE were small. The LB-SPR method did not perform as well as the classical methods but may still be of interest because it provides estimates of a logistic selectivity curve. The M/K ratio provided the most contrast in the performance of the three methods, suggesting that it should be considered for predicting the likely performance of length-based mortality estimators. Length-based methods for assessing exploited marine populations are of significant interest largely because of their applicability to the study of data-limited stocks for which age-based methods may not be available or suitable (Punt et al. 2013). Hard tissues, such as scales and otoliths, may lack distinct growth marks, for example, in tropical fish species. Such species are often assessed using length-based methods (Pauly 1984c) because length measurements are collected both easily and nonlethally. Historically, the most common methods used to estimate the total instantaneous mortality rate (Z; year ) from length composition data have been the length-converted catch curve (LCCC; Pauly 1983, 1984a, 1984b) and the Beverton–Holt equation (BHE; Beverton and Holt 1956, 1957). Subject editor: Patrick J. Sullivan, Cornell University, Ithaca, New York *Corresponding author: q.huynh@oceans.ubc. ca Received October 10, 2017; accepted March 23, 2018 This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. Marine and Coastal Fisheries: Dynamics, Management, and Ecosystem Science 10:298–313, 2018