Proposed Standard Weight (Ws) Equations for Arctic Grayling

Abstract

AbstractRelative 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.