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

Abstract

Abstract.-The Alverson and Carney (AC) model for estimating the instantaneous rate of natural mortality (M) was reformulated to include b 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 b ¼ 3.0 and t 0 ¼ 0. Estimates of M from the AC model are most sensitive to the assumption that growth starts at t 0 ¼ 0 when growth rates are high as well as to the b 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 6 SD to get the t mb for each subgroup or by explicit variance calculations.

Population ecology parameters and biomass of golden grey mullet (Liza aurata) in Iranian waters of the Caspian Sea

“…Estimate of the instantaneous coefficient of natural mortality for golden grey mullet obtained from the ZM method (Zhang and Megrey, 2006) was 0.350 year −1 .…”

“…The instantaneous coefficient of natural mortality (M) was estimated using the ZM model (Zhang and Megrey, 2006) with von Bertalanffy growth parameters and a maximum age (t max ) of 12 for golden grey mullet (Ghadirnejad, 1996;Caspian Sea Biodiversity, 2006). The equation of ZM model is…”

“…whereˇthe power parameter of the length-weight relationship, t 0 is the hypothetical age for L t = 0, and t mb is the critical age, which can be estimated as t mb = 0.440t max (Zhang and Megrey, 2006). The instantaneous coefficient of fishing mortality (F) was calculated as…”

Estimation of mortality coefficients and survivorship curves for minke whales (Balaenoptera acutorostrata) in Korean waters

“…Based on the assumption that the age structure of the bycaught population is representative of the natural or equilibrium state of population, assuming random distribution and random selectivity, we used bycatch data to estimate the mortality coefficient and survival rate of this population. The instantaneous coefficient of natural mortality (M) was estimated from the following equation (Zhang and Megrey 2006), based on the assumption that life history of early stage cetaceans is similar to that of fish:…”

Estimating rates of mortality in stocks of Metapenaeus macleayi in estuaries of eastern Australia

“…Growth and M may be correlated; i.e. fast-growing fish tend to have higher rates of M than slower-growing fish (Zhang and Megrey, 2006). Life history analyses associate life-history parameters of many closely related species to environmental parameters (e.g.…”