Estimating Total Mortality Rates from Mean Lengths and Catch Rates in Nonequilibrium Situations (vol 146, pg 803, 2017)

A series of estimates of the total mortality rate (Z) can be obtained by using the Beverton-Holt nonequilibrium-based approach of Gedamke and Hoenig (2006) on observations of population mean length over time (ML model). In contrast, only relative mortality rates (not absolute values) can be obtained from a time series of catch rates. We derived the transitional behavior of the catch rate following a change in total mortality in the population. From this derivation, we developed a new-method to estimate Z that utilizes both mean lengths and catch rates (MLCR model). Both theML model and the MLCR model assume constant recruitment in the population. We used a simulation study to test performance when recruitment is variable. Simulations over various scenarios of Z and recruitment variability showed that there may be correlated residuals in the mean lengths and catch rates arising from fluctuations in recruitment. However, the root mean square errors of the Z estimates and the change point (i.e., the year when mortality changed) were smaller in the MLCR model than in the ML model, indicating that the MLCR model can better account for variable recruitment. Both methods were then applied to Mutton Snapper Lutjanus analis in Puerto Rico to illustrate their potential application to assess data-limited stocks. The ML model estimated an increase in Z, but the MLCR model also estimated a subsequent reduction in Z when the catch rate data were considered.