Effect of Measurement Error on Tests of Density Dependence of Catchability for Walleyes in Northern Wisconsin Angling and Spearing Fisheries

Abstract

AbstractWe sought to determine how much measurement errors affected tests of density dependence of spearing and angling catchability for walleye Sander vitreus by quantifying relationships between spearing and angling catch rates (catch/h) and walleye population density (number/acre) in northern Wisconsin lakes. The mean measurement error of spearing catch rates was 43.5 times greater than the mean measurement error of adult walleye population densities, whereas the mean measurement error of angling catch rates was only 5.6 times greater than the mean measurement error of adult walleye population densities. The bias‐corrected estimate of the relationship between spearing catch rate and adult walleye population density was similar to the ordinary‐least‐squares regression estimate but differed significantly from the geometric mean (GM) functional regression estimate. In contrast, the bias‐corrected estimate of the relationship between angling catch rate and total walleye population density was intermediate between ordinary‐least‐squares and GM functional regression estimates. Catch rates of walleyes in both spearing and angling fisheries were not linearly related to walleye population density, which indicated that catch rates in both fisheries were hyperstable in relation to walleye population density. For both fisheries, GM functional regression overestimated the degree of hyperdepletion in catch rates and ordinary‐least‐squares regression overestimated the degree of hyperstability in catch rates. However, ordinary‐least‐squares regression induced significantly less bias in tests of density dependence than GM functional regression, so it may be suitable for testing the degree of density dependence in fisheries for which fish population density is estimated with mark– recapture methods similar to those used in our study.