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Objective: We developed a novel, simple approach to summarize variation in quantile regression estimates of weight at length across multiple levels of grouping factors (locations or years) and demonstrate its utility for comparing fish condition using Arctic Grayling Thymallus arcticus data. We compared condition among 28 geographic locations of Arctic Grayling populations and among 12 and 25 years for two populations. Methods: We summarized variation among locations and among years within locations using percentiles (maximum, 75th, 50th, 25th, and minimum) of predicted quantiles of weight at length, allowing us to simplify the distributions of predicted quantiles of weight into highest to lowest fourths (quartiles) across locations or years. One part of this summary information, 75th percentiles of median (0.50 quantile) predicted weights at length across populations, is identical to summary statistics used to develop standard weight equations for computing relative weights. However, our approach avoids biases inherent in fitting a single standard weight equation and can accommodate among‐fish variation in weight at length via multiple quantiles when developing reference standards for comparative or diagnostic purposes. A selected new weight at length can be compared with the distribution of quantile predictions among locations in terms of weights or as proportionate weights similar to relative weight. Result: Arctic Grayling in 28 geographic locations, from the southern limit of their distribution in Montana and Wyoming north through Canada and Alaska to the Arctic coast, had considerable variation in allometric exponents in weight–length relationships and in predicted weights at length. Predicted weights of Arctic Grayling for heavier fish (0.90 quantiles) in populations with less (lower quartiles) to greater (upper quartiles) weights were 127–194 g and 336–510 g at total lengths = 250 and 350 mm, respectively. Lighter fish (0.10 quantiles) in populations with less to greater weights were 100–133 g and 259–364 g, at the same total lengths, respectively. We provide statistical code and tabled values that can be used as reference standards as a replacement for standard weight equations for comparing new samples of fishes. We also quantified annual variation in condition within two intensively sampled populations, the Kuparuk River in Alaska (25 years, 1985–2012) and Red Rock Creek, Montana (12 years, 1994–2016). Annual distributions of weights at length were greater for Arctic Grayling in Red Rock Creek than those in the Kuparuk River. Variation in predicted distributions of weights at length among years was also greater for Red Rock Creek, although fish from both locations exhibited substantial among‐year variation that exceeded half the variation estimated among geographic locations. Conclusion: Our estimates indicated that there was substantial spatial and temporal variation in condition of Arctic Grayling that might be investigated further to help understand constraints on populations to aid conservation and management of the species. Our summary approach can be easily extended to other investigations of fish weight at length relationships where multiple quantile estimates are made across many levels of grouping factors. Impact statementFish condition based on measures of their weight and length is commonly used to assess the health and status of fish populations and response to management actions. Our new approach summarizing across percentiles of weight at length allows fisheries biologists to better understand variation in lighter to heavier fish at a given length within and among populations to aid our understanding about factors that impact condition. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]