Estimating Mortality from Mean Length Data in Nonequilibrium Situations, with Application to the Assessment of Goosefish

Abstract

The Beverton–Holt length-based mortality estimator has received widespread use primarily due to its applicability in data-limited situations. The mean length of animals that are fully vulnerable to the sampling gear can be used to estimate total mortality from basic growth parameters and a known length at first capture. This method requires equilibrium conditions because the mean length of a population will change only gradually after a change in mortality. In this study, we derive the transitional behavior of the mean length statistic for use in nonequilibrium conditions. We investigate conditions affecting the reliability of the Beverton–Holt results and then develop a new procedure that allows a series of mortality rates to be estimated from mean length data representing nonequilibrium conditions in multiple years. We then examine an assessment of goosefish Lophius americanus that was criticized for its use of the Beverton–Holt estimator under nonequilibrium conditions. Using data from the 1963–2002 National Marine Fisheries Service annual fall groundfish surveys off the northeastern United States and assuming a single change in total mortality, we used the maximum likelihood method to estimate that the total mortality of goosefish in the southern assessment region increased from 0.31 to 0.60 per year in 1977. Estimates of the new mortality rate made three or more years after the change were relatively stable and only ranged from 0.55 to 0.71 per year, while estimates from the standard Beverton–Holt approach ranged from 0.37 to 1.1 per year. The results for goosefish in the northern assessment region showed that total mortality changed from 0.14 to 0.29 per year in 1978 and then to 0.55 per year in 1987. The new nonequilibrium estimator allows a change in mortality to be characterized reliably several years faster than would occur with the use of the Beverton–Holt estimator.