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 identified issues related to SE estimation for statistical inferences about mortality rates for fisheries management decision making.

中文翻译：

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从捕捞曲线数据估计和比较鱼类死亡率的改进方法

捕获曲线分析通常用于估计鱼的瞬时死亡率 ( Z )，并且由于年龄频率数据经常过度分散，因此建议应用方差偏差校正因子。然而，泊松广义线性模型 (GLM _Poisson )的扩展可能构成更好的替代方案，因为它们使用特定的离散参数更充分地对计数中的方差 (SE) 进行建模，以便进行更准确的估计和统计比较。为了测试这个想法，根据六种当前可用的方法分析了在四种分散情况下生成的模拟年龄频率数据，并与 GLM_泊松及其五个扩展的结果进行比较，以评估Z 中每种方法特定的偏差± SE 估计。然后使用来自加拿大魁北克的采样 Walleye Sander vitreus和 Arctic Char Salvelinus alpinus种群的经验年龄频率数据来说明我们基于 GLM 的方法的适用性，该方法依赖于 Pearson 残差的行为来评估模型的充分性和信息- 模型选择的理论方法。所有分析表明，在所考虑的方法中，Z估计通常是准确的，除了在生态研究中最可能遇到的二次过分散情况下，只有负二项式类型 2 和均值参数化 Conway-Maxwell-Poisson (CMP)扩展足以估计Z和它的 SE。线性过度分散的数据最好由负二项式类型 1 和广义泊松 (GLM _GP ) 扩展建模；GLM _CMP和 GLM _GP最适合模拟欠分散数据，而 GLM _Poisson充分模拟了等分散数据，类似于 Chapman 和 Robson (1960) 方法。当最充分和统计支持的 GLM _Poisson时，正确实现了Z ± SE 的分组因素（例如年份或地点）的统计比较扩展已应用。总而言之，提议的基于 GLM 的方法应有助于规避与 SE 估计相关的已识别问题，以便对渔业管理决策的死亡率进行统计推断。