Quantile Regression Estimates of Body Weight at Length in Walleye

Abstract

Quantile 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.

Summarizing quantile estimates of weight at length to compare condition: Geographic and temporal variation in Arctic Grayling

“…As in previous studies of fish body condition that involved the use of quantile regression (Cade et al 2008(Cade et al , 2011Crane et al 2015;Crane and Farrell 2017;Ranney 2018), we found extensive variation in the allometric exponents used to estimate weight at length of Arctic Grayling and consequent heterogeneity in the predicted distributions of weights at length. The percentile summaries that we used to partition distributions of weight at length from quantile predictions into quartiles constitute a simple device for collapsing predicted quantiles from many levels of a grouping factor (here, locations or years) to provide a more concise summary for comparative or diagnostic purposes.…”

“…Quantile regression estimates in linear models with any relevant grouping factors or continuous covariates provide a much more comprehensive and rigorous analysis of changes in weight at length, and there are multiple recent examples demonstrating this capability for fish condition analyses (Cade et al 2008(Cade et al , 2011Crane et al 2015;Crane and Farrell 2017;Ranney 2018;Neely et al 2021;Woodward et al 2021). Our percentile summary approach provides a method by which to concisely summarize estimates across multiple levels of a grouping factor.…”

“…We obtain a much more complete adjustment of weight conditional on length by allowing for heterogeneity in allometric exponents, thus allowing us to quantify heterogeneous variation in weights at length to enhance interpretations of condition (Cade et al 2008(Cade et al , 2011. Ranney (2018) demonstrated one method for using quantile regression estimates of weight at length for Walleye Sander vitreus to provide a reference standard for weight at length by pooling measures across 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.…”

“…2008, 2011). Ranney (2018) demonstrated one method for using quantile regression estimates of weight at length for Walleye Sander vitreus to provide a reference standard for weight at length by pooling measures across all sampled populations. This approach provides reference standards for weight at length that do not explicitly quantify variation among populations—as is often used, for example, in computing relative condition factor ( K n ).…”

Applications of deep convolutional neural networks to predict length, circumference, and weight from mostly dewatered images of fish

“…For example, when weight data are unavailable from the field, species‐specific length–weight regression formulas are used to generate weight data (Gerow, Anderson‐ Sprecher, & Hubert, 2005; Murphy, Brown, & Springer, 1990). Unfortunately, morphological variability both among fish and seasonally for individual fish can further reduce the precision of calculated weight estimates (Adams, Leaf, Wu, & Hernandez, 2018; Neumann & Murphy, 1992; Ranney, 2018). Finally, the time and effort required to obtain length and weight measurements in the field imposes limitations on the number of fish that can be sampled; which reduces the confidence in data capturing individual variability (Gutreuter & Krzoska, 1994).…”