Recommendations for Catch-Curve Analysis

Although catch curves and related methods for estimating total mortality rate, Z, have been studied extensively, there are a number of unresolved methodological issues. We used analytical methods and Monte Carlo simulation to evaluate four criteria (Peak, Peak Plus, χ² test, and Z-test) for identifying the age of full recruitment in a cross sectional analysis.  We evaluated the regression, Chapman-Robson and Heincke mortality estimators. The regression estimator was evaluated with four different methods of right data truncation. Heincke’s method performed poorly in terms of bias and mean squared error and is not recommended in general. A two-tailed χ² test for full selectivity based on the formulation of Chapman and Robson did not perform well and is not recommended. The one-tailed Z-test also proposed by Chapman and Robson (or the corresponding one-tailed χ² test) performed much better than the two-tailed χ² test but was not preferred overall.  The Chapman-Robson mortality estimator with age of full recruitment set equal to the age one year older than the age of maximum catch (Peak Plus criterion) generally provided the best estimates of Z based on minimum mean squared error.  It is to be preferred over regression estimators except possibly when Z is thought to be very high.  The regression estimator of variance of Z is generally precise and slightly negatively biased regardless of age of full recruitment selection criterion and right truncation method.  The Chapman-Robson variance estimator is generally precise but has a large negative bias if not corrected for overdispersion.  Once corrected, the Chapman-Robson variance estimator performs as well or better than all other methods under all evaluated scenarios.