Weight-Length Relationships in Fisheries Studies: The Standard Allometric Model Should Be Applied with Caution

Abstract

The standard allometric weight-length relationship W = aL^b is widely used in fisheries science to estimate the weight of fish of known length and to compute body condition indices. This relationship is used in abundance surveys such as acoustic surveys to convert abundance at length into estimates of population biomass. Although fitting this relationship to weight-length data over a broad range of body sizes is common practice, the fit of this relationship often does not receive careful scrutiny. We explored the fit of the allometric model as well as alternative weight-length relationships to data from acoustic surveys of walleye pollock Theragra chalcogramma from the North Pacific and found a subtle but persistent lack of fit for the allometric relationship, particularly for the largest and smallest fish in the population. This lack of fit results in biased estimates of population biomass. Analysis of weight-length measurements of 10 additional species indicates that these biases are not restricted to walleye pollock; indeed, the lack of fit of the allometric weight-length relationship is likely to be a general concern. Our results suggest that the allometric relationship should not be applied to generate weight-length relations over a broad range of body sizes without careful examination of the potential consequences. In some applications, such as the walleye pollock surveys examined here, use of alternative, less biased, methods to estimate mean weight at length will be beneficial. Such methods include fitting the allometric relationship in a piecewise fashion over restricted size or age intervals and simply computing the mean weight at length. In applications with spawning fish, incorporating the maturity state in weight-length prediction methods is likely to further improve predictions of weight at length.