A Revised Alverson and Carney Model for Estimating the Instantaneous Rate of Natural Mortality

Abstract

The Alverson and Carney (AC) model for estimating the instantaneous rate of natural mortality (M) was reformulated to include β and t ₀ parameters. The revised Zhang and Megrey (ZM) model could be used for the estimation of M instead of the AC model since von Bertalanffy and allometric growth parameters are readily available for most exploited fish stocks. It was determined from the new formulation that the ratios of the age at maximum biomass (t _mb) to the maximum age (t _max) for pelagic and demersal species were significantly different from 0.38, the value originally proposed by Alverson and Carney. The ratios for these two ecological groups were 0.302 and 0.440, respectively, and were significantly different. We examined the sensitivity and bias in M from the new formulation relative to those from the AC model, which assumed that β = 3.0 and t ₀ = 0. Estimates of M from the AC model are most sensitive to the assumption that growth starts at t ₀ = 0 when growth rates are high as well as to the β and t _mb assumptions. The performance of the revised ZM model was evaluated by comparing calculated M values from the two models based on a paired-sample t-test. The results of the two statistical analyses showed that the ZM model produced values of M closer to published estimates than did the AC model. Thus, the ratio t _mb/t _max for specific ecological groups should be used rather than Alverson and Carney's constant 0.38. Analyses of exploited stock dynamics might be conducted using the possible range of M instead of the constant value. The range could be estimated from the ZM model using the mean ratio t _mb/t _max ± SD to get the t _mb for each subgroup or by explicit variance calculations.