Estimation of Time-Varying Instantaneous Total Mortality Rate Based on the Age-Structured Abundance Index

A method for estimating time-based instantaneous total mortality rate (Z) from multiple cohort catch per unit effort (CPUE) data was developed.  The Zs in different n continuous years, which were assumed constant in each n year, were estimated using the age-based CPUE data within these years.  Our simulation study found that the trends of the estimated time-based Z consist with the trends of the true Z values, and the estimated rates of change from this approach were close to the true change rates (the relative differences between the change rates of the estimated Zs and the true Zs were smaller than 10%).  Both variation of Z and recruitment can affect the estimate of Z and trend of Z over time.  When Z was increasing, the estimated Z was prone to be underestimated, and conversely when Z was decreasing the estimated Z would be overestimated.  If Z changed linearly or exponentially, the estimated results of Z could be impacted.  When Z was increasing from the same starting value, the absolute values of relative estimate error (REE) of estimated Z from the scenario of linearly increasing were smaller than those from the scenario of exponentially increasing.  Conversely, when Z was decreasing, the scenario of exponentially decreasing resulted in smaller absolute REE.  The most appropriate number of years in each band 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.  Further analyses suggested that selectivity and age estimation are also two factors that can impact the estimated values of Z if there is error in either of them, but the estimated trends of Z were still close to the true change rates (the relative differences between them were smaller than 10%).