Relative weight (Wr) is an index that is commonly used by fisheries managers to evaluate the condition within and among fish populations. Managers also use Wr comparisons to assess condition dynamics among species. Rather than using population-level mean Wr for comparisons, standard length categories are frequently used to evaluate mean Wr differences among length categories. To establish Wr values for a species, a species-specific standard weight (Ws) equation is required. Regression-line-percentile (RLP) and empirical-percentile (EmP) methods were used with length–weight data that were collected from 50 Arctic Grayling Thymallus arcticus populations in the United States and Canada. The RLP method yielded a Ws equation of log₁₀Ws(g) = −5.241 + 3.083 log₁₀TL(mm) and the EmP method of log₁₀Ws(g) = −5.279 + 3.096 log₁₀TL(mm). These equations were developed to calculate relative weights (Wr) for fish measuring 150 mm total length (TL) and greater. Subsequent analysis did not reveal significant systematic length-related bias in the application of either Ws equation. Furthermore, differences in Ws calculations between the methods were at most 2.2% over the lengths that we observed. Our findings highlight the relative importance of using a robust data set when calculating Ws equations over the method used to calculate Ws. We suggest that both equations are valid and managers should report which Ws equation was used.

中文翻译：

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北极鳟的建议标准重量 (Ws) 方程

相对权重 ( Wr ) 是渔业管理者常用的一个指标，用于评估鱼类种群内部和种群之间的状况。管理人员还使用Wr比较来评估物种之间的条件动态。标准长度类别通常用于评估长度类别之间的平均Wr差异，而不是使用总体水平的平均Wr进行比较。要为一个物种建立Wr值，需要一个物种特定的标准重量 ( Ws ) 方程。回归线百分位数（RLP）和经验百分位数（EMP）的方法用由50个北极格雷林收集该长度量数据中使用茴arcticus美国和加拿大的人口。的RLP方法产生了Ws的日志的方程_10个Ws的（G）= -5.241 + 3.083日志₁₀ TL（mm）与日志的EMP方法₁₀ Ws的（G）= -5.279 + 3.096日志₁₀ TL（毫米）。开发这些方程是为了计算总长度 (TL) 为 150 毫米及以上的鱼的相对重量 ( Wr )。随后的分析在应用任一Ws方程时均未发现与长度相关的显着系统偏差。此外，Ws 的差异在我们观察到的长度上，方法之间的计算最多为 2.2%。我们的发现强调了在计算Ws方程时使用稳健数据集的相对重要性，而不是用于计算Ws的方法。我们建议这两个方程都是有效的，管理者应该报告使用了哪个Ws方程。