An Improved Method for the Estimation and Comparison of Mortality Rates in Fish from Catch-Curve Data

Abstract

Catch-curve analyses are routinely used to estimate instantaneous mortality (Z) in fish, and as the age-frequency data are often overdispersed, the application of a variance bias-correction factor has been recommended. The extensions of the Poisson generalized linear model (GLMPoisson) may, however, constitute a better alternative, as they model the variance (SE) in counts more adequately with their specific dispersion parameter for more accurate estimations and statistical comparisons. To test this idea, simulated age-frequency data generated under four dispersion scenarios were analyzed according to six currently available methods and compared with the results of a GLMPoisson and five of its extensions to evaluate each method-specific bias in Z ± SE estimates. Empirical age-frequency data from sampled Walleye Sander vitreus and Arctic Char Salvelinus alpinus populations in Québec, Canada, were then used to illustrate the applicability of our GLM-based method, which relies on the behavior of Pearson residuals to assess model adequacy and an information-theoretic approach for model selection. All analyses revealed that Z-estimates were generally accurate among the methods considered, except under the most likely situation of quadratic overdispersion met in ecological studies, for which only the negative binomial type 2 and the mean-parametrized Conway–Maxwell–Poisson (CMP) extensions were adequate to estimate both Z and its SE. Linearly overdispersed data were best modeled by the negative binomial type 1 and generalized Poisson (GLMGP) extensions; the GLMCMP and GLMGP were the most appropriate to model underdispersed data, whereas the GLMPoisson adequately modeled equi-dispersed data, similar to the Chapman and Robson (1960) method. Statistical comparisons of Z ± SE for grouping factors, such as year or site, were correctly achieved when the most adequate and statistically supported GLMPoisson extension was applied. Altogether, the proposed GLM-based method should help to circumvent the identified issues related to SE estimation for statistical inferences about mortality rates for fisheries management decision making.