Comparative Performance of Three Length‐Based Mortality Estimators

Abstract

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.

Urbanization correlates with altered growth and reduced survival of a small‐bodied, imperilled freshwater fish

“…Estimates were derived using summer 2017 and 2018 data only for which grouped sample sizes were sufficiently large ( n > 200). Mortality approaches were broadly grouped into those based on life‐history theory (Charnov et al, 2013; Cubillos et al, 1999; Taylor, 1958), those based on length‐ or weight‐at‐age data (Beverton & Holt, 1956, 1957; Hoenig, 1983; Huynh et al, 2018; Peterson & Wroblewski, 1984; Robson & Chapman, 1961), those based on abundance or density (CPUE used as a surrogate) data (as described in Power, 2007 and Skalski et al, 2005) and those based directly on age data (Robson & Chapman, 1961; Sekharan, 1975; Skalski et al, 2005). Mean population estimates of mortality across pooled adult age‐classes (considered here as ages 1 to 3+) were computed for each class of estimator following the methods described in the references above.…”

Multi-Indicator Harvest Strategies for Data-Limited Fisheries: A Practitioner Guide to Learning and Design

“…Model-based indicators typically rely on a mathematical representation of population dynamics, which is used in estimating quantities of interest (a variety of methods are summarized in Carruthers et al, 2014;Huynh et al, 2018;Pons et al, 2020). Thus, working with model-based indicators requires an awareness of modeling assumptions to avoid pitfalls and to provide context for when these methods can be expected to deliver reliable results (Geromont and Butterworth, 2015;Sagarese et al, 2019).…”

“…Thus, working with model-based indicators requires an awareness of modeling assumptions to avoid pitfalls and to provide context for when these methods can be expected to deliver reliable results (Geromont and Butterworth, 2015;Sagarese et al, 2019). For example, while length-based indicators can be used to guide decision-making toward fishery sustainability through estimation of spawning potential ratio and fishing mortality rate, an awareness of the limitations and pitfalls of length-based indicators is essential (Cope and Punt, 2009;Hordyk et al, 2016;Huynh et al, 2018). Such guidance is available based on simulation testing (Punt et al, 2001;Cope and Punt, 2009;Klaer et al, 2012;Carruthers et al, 2014Carruthers et al, , 2015Jardim et al, 2014;Hordyk et al, 2015;Rudd and Thorson, 2017;Sagarese et al, 2018).…”

Comparisons of mean length-based mortality estimators and age-structured models for six southeastern US stocks

“…With age-structured models, growth incorporates variability in size at age and parameters may be estimable within the model (Francis, 2016). In contrast, growth is fixed and assumed to be deterministic with age in the mean-length based models, although simulations have suggested robustness of the mean length-based models to this assumption (Then et al, 2015;Huynh et al, 2018). In many ASMs, including those presented here, natural mortality was parameterized to asymptotically decline with age.…”