A general hypothesis-testing framework for stable isotope ratios in ecological studies

We propose a framework for hypothesis-testing of stable isotope ratios in ecological studies. Statistical procedures are based on analysis of nested linear models and a residual permutation procedure (RPP) that is employed to evaluate probabilities associated with test statistics. We used simulated examples and a real data set to illustrate the utility and generality of the method. First, we developed a test for differences in centroid location and dispersion of δ¹³C and δ¹⁵N values within and among groups of isotopic data. Second, we evaluated magnitude and direction of change in centroid position (termed "path") of a pair of isotopic samples separated in space/time relative to paths of other paired sample sets. Third, we compared attributes of path trajectories (size, direction, and shape) over sample sets containing more than two samples to provide a quantitative description of how patterns of isotopic ratios change in response to spatial and temporal gradients. Examples are limited to the bivariate case (δ¹³C-δ¹⁵N biplots), but the statistical method can readily be applied to univariate and multivariate cases.