Improved Models for Predicting Walleye Abundance and Setting Safe Harvest Quotas in Northern Wisconsin Lakes

Abstract

In Wisconsin, the management of Walleyes Sander vitreus relies on a set of log-linear regressions to predict Walleye abundance and to set safe harvest. The regression models predict mean Walleye abundance from lake area, but they ignore variability among years; they also predict equal Walleye populations in lakes with the same size and recruitment source. We evaluated three alternative models in terms of predictive accuracy and the risk of overharvest. We used 899 mark–recapture population estimates (collected between 1953 and 2013) from 219 lakes to develop and evaluate (1) a log-linear mixed-effects model that used all individual observations and estimated adult Walleye abundance from lake area and lake-specific deviations from the overall intercept; (2) a mixed-effects model that builds on model 1 by adding a linear fixed effect of sampling year; and (3) a mixed-effects model that builds on model 1 by adding a random year effect. Walleye abundance was positively correlated with lake area in all models and was negatively correlated with sampling year (when included). Alternative models improved predictive accuracy by 17–22% over the current regression model. Restricting data to those collected during the most recent 20 years improved model responsiveness to new data and reduced the value of including a linear time trend. When all data were used for model construction, the relative risk of overharvest was lowest under the mixed-effects model with a linear time trend; when the most recent 20 years of data were used, the risk was lowest under the mixed-effects model with a random year effect. Accounting for variability among years would allow harvest to track changing Walleye populations and would allow management to be more adaptive. We recommend using the mixed-effects model with a random year effect and restricting the data inputs to the most recent 20 years.

Received May 20, 2015; accepted September 17, 2015

ACKNOWLEDGMENTS

We thank current and former employees of the WDNR and the GLIFWC for collecting and analyzing the data used for this analysis. Special thanks to Mark Luehring, Joe Dan Rose, and Rick Madsen for their thorough and thoughtful comments on the analysis and resultant improvements to the manuscript. We are grateful to Paul Rasmussen for extensive statistical consultation and manuscript review and to Mike Hansen, Dan Isermann, and four anonymous referees for their reviews, which much improved the final product. This study was funded by a Federal Aid in Sportfish Restoration Program (U.S. Fish and Wildlife Service) grant to the WDNR (Project F-95-P, Study SSBW).