Correction of a bootstrap approach to testing for evolution along lines of least resistance

Abstract Testing for an association between the leading vectors of multivariate trait (co)variation within populations (the 'line of least resistance') and among populations is an important tool for exploring variational bias in evolution. In a recent study of stickleback fish populations, a bootstrap-based test was introduced that takes into account estimation error in both vectors and hence improves the previously available bootstrap method. Because this test was implemented incorrectly, however, I here describe the correct test protocol and provide a reanalysis of the original data set. The application of this new test protocol should improve future investigations of evolution along lines of least resistance and other vector comparisons.