Variations in predator diets is important in ecology to help us understand their top-down effects on the ecosystem. In predator diets, their fatty acid signatures reflect the proportions of prey consumed. Since fatty acid signatures are compositional and often longer than the sample size, a standard MANOVA test is unsuitable. Here, non-parametric MANOVA techniques are developed to test for differences in fatty acid signatures among locations, years, and seasons which infer differences in diets. Simulations show that the test has good power and appropriate type I error rates. The tests developed were applied to data on Greenland Sharks to test for differences in diets between individuals from Cumberland Sound, Canada, versus those from Svalbard, Norway and whether there is a yearly and/or seasonal effect on the diets. Diet compositions were found to vary between the locations, seasons and years, possibly caused by differing prey species distributions, migrations, and climate change.