Estimating time-based instantaneous total mortality rate based on the age-structured abundance index

Abstract

The instantaneous total mortality rate (Z) of a fish population is one of the important parameters in fisheries stock assessment. The estimation of Z is crucial to fish population dynamics analysis, abundance and catch forecast, and fisheries management. A catch curve-based method for estimating time-based Z and its change trend from catch per unit effort (CPUE) data of multiple cohorts is developed. Unlike the traditional catch-curve method, the method developed here does not need the assumption of constant Z throughout the time, but the Z values in n continuous years are assumed constant, and then the Z values in different n continuous years are estimated using the age-based CPUE data within these years. The results of the simulation analyses show that the trends of the estimated time-based Z are consistent with the trends of the true Z, and the estimated rates of change from this approach are close to the true change rates (the relative differences between the change rates of the estimated Z and the true Z are smaller than 10%). Variations of both Z and recruitment can affect the estimates of Z value and the trend of Z. The most appropriate value of n can be different given the effects of different factors. Therefore, the appropriate value of n for different fisheries should be determined through a simulation analysis as we demonstrated in this study. Further analyses suggested that selectivity and age estimation are also two factors that can affect the estimated Z values if there is error in either of them, but the estimated change rates of Z are still close to the true change rates. We also applied this approach to the Atlantic cod (Gadus morhua) fishery of eastern Newfoundland and Labrador from 1983 to 1997, and obtained reasonable estimates of time-based Z.