Comparative Performance of Three Length‐Based Mortality Estimators

Abstract

AbstractLength‐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.