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 delta13C and delta15N 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 (delta13C-delta15N biplots), but the statistical method can readily be applied to univariate and multivariate cases.