Quantile Regression Estimates of Body Weight at Length in Walleye

Abstract

AbstractQuantile regression is a method of estimating fish weight at length for alternate portions of a probability distribution, but it is an approach that has not received much attention in fisheries literature. Quantile regression can provide estimates of any quantile of weight at length without bias (including the 75th quantile, which was often the focus of standard weight [Ws] equations), and this is more advantageous than previously defined Ws equations derived from linear or quadratic regression methods. The goal of this study was to demonstrate the utility of quantile regression as a tool to assess fish weight at length at various portions of the probability distribution without bias using Walleye Sander vitreus as a case study. Quantile regression models at the 75th quantile were developed for three randomly selected Walleye populations from Georgia and South Dakota and compared with a large (N = 33,589) reference population. Bootstrap resampling procedures indicated that only one population from the state of Georgia had an intercept and slope similar to the reference population. For the one population that had similar intercept and slope to the reference population, predictions of weight at various lengths still fell below the 95% CIs for predicted weights of the reference population, suggesting that slight differences in intercepts and slopes in allometric relationships can result in predicted weights that still differ at some lengths. Predicted weights of Walleye derived from the 10th, 25th, 50th, 75th, and 90th quantiles were used to demonstrate how individuals and populations may be compared at different management targets. Overall, this study demonstrates the relative ease with which quantile regression may be used to compare fish body condition between populations without bias.