Testing for a change in diet using fatty acid signatures

Determining whether the diet of predators has changed is an important ecological problem and appropriate methodology is needed in order to test for differences or changes in diet. It is known that the fatty acid (FA) signature in a predator's adipose tissue predictably reflects the prey consumed and that, consequently, a change in the FA signatures can be largely attributed to changes in the predator's diet composition. The use of FA signatures as a means of detecting change in diet presents some statistical challenges however, since the FA signatures are compositional and sample sizes relative to the dimension of a signature are often small due to biological constraints. Furthermore, the FA signatures often contain zeros precluding the direct use of traditional compositional data analysis methods. In this paper, we provide the methodology to carry out valid statistical tests for detecting changes in FA signatures and we illustrate both independent and paired cases using simulation studies and real life seabird and seal data. We conclude that the statistical challenges using FA data are overcome through the use of nonparametric tests applied to the multivariate setting with suitable test statistics capable of handling the zeros that are present in the data.