Adjusting Mercury Concentration for Fish-Size Covariation: A Multivariate Alternative to Bivariate Regression

Abstract

Regression-based methods like analysis of covariance (ANCOVA) are frequently used to adjust one variable for the correlated influence of a second less interesting variable (e.g., mercury concentration and fish size). However, the influence of the covariate (i.e., fish size) is not removed unequivocally when regression slopes are not parallel. Using data on tissue-mercury concentration and fish size from 30 populations of lake trout (Salvelinus namaycush), we show that data adjusted to a common size with bivariate regression can retain information associated with the original size differences. As an alternative, we use univariate and bivariate summary statistics from each population as raw data in a multivariate analysis to search for differences among populations. Ordination axes resulting from this analysis exhibited both small- and large-scale spatial autocorrelation. Localized spatial patterns probably reflect similar geochemical features of the watersheds of neighbouring lakes in small geographic areas. In contrast, regional spatial autocorrelation suggested broad-scale patterns that may implicate atmospheric inputs of mercury. As an extension of this multivariate approach, both regional and local patterns could be compared with environmental variables to reveal correlations that may suggest new cause-and-effect hypotheses.