Analysis of stable isotope data: A K nearest-neighbors randomization test

The use of stable isotope analysis in ecological and wildlife studies is rapidly increasing. Studies include evaluating flow of nutrients in ecosystems and studying dietary composition of individual animals. Several mixing models have been developed to evaluate the relative contribution of different foods to the diet of consumers. All these mixing models require that all prey types will be significantly different in bivariate space. This requirement usually poses a problem in analyzing data of stable isotope ratios because sample sizes in most studies are small and seldom normally distributed. We propose a randomization test that we based on the K nearest-neighbor approach. Results from our simulations of power revealed that the K nearest-neighbor test appears to have high power even with small sample sizes and comparatively low displacement. The K nearest-neighbor test described here provides the preliminary statistical analysis necessary for the use of the mixing models, and therefore is a new powerful tool for analyzing stable isotope data. In evaluating the test performance on data collected from American martens (Martes americana) and their prey on Chichagof Island, Southeast Alaska, we were able to reject our null hypothesis that all samples of prey were drawn from identical populations (P = 0.05). A program written in Pascal or S-Plus is available from the authors to evaluate the K nearest-neighbor statistic for several groups.