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

• Published in: North American Journal of Fisheries Management
• Main Authors: Mainguy, Julien, Moral, Rafael de Andrade
• Format: Article in Journal/Newspaper
• Language: English
• Published: Wiley 2021
• Subjects: Arctic; Canada; Conway; Salvelinus alpinus
• Online Access: http://dx.doi.org/10.1002/nafm.10665; https://onlinelibrary.wiley.com/doi/pdf/10.1002/nafm.10665; https://onlinelibrary.wiley.com/doi/full-xml/10.1002/nafm.10665; https://afspubs.onlinelibrary.wiley.com/doi/pdf/10.1002/nafm.10665

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 (GLM Poisson ) 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 GLM Poisson 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 (GLM GP ) extensions; the GLM CMP and GLM GP were the most appropriate to model underdispersed data, whereas the GLM Poisson 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 GLM Poisson extension was applied. Altogether, the proposed GLM‐based method should help to circumvent the ...