The selection and analysis of fatty acid ratios: A new approach for the univariate and multivariate analysis of fatty acid trophic markers in marine pelagic organisms

Fatty acid (FA) compositions provide insights about storage and feeding modes of marine organisms, characterizing trophic relationships in the marine food web. Such compositional data, which are normalized to sum to 1, have values—and thus derived statistics as well—that depend on the particular mix of components that constitute the composition. In FA studies, if the set of FAs under investigation is different in two separate studies, all the summary statistics and relationships between the FAs that are common to the two studies are artificially changed due to the normalization, and thus incomparable. Ratios of FAs, however, are invariant to the particular choice of FAs under consideration—they are said to be subcompositionally coherent. Here, we document the collaboration between a biochemist (M.G.) and a statistician (M.J.G.) to determine a suitable small set of FA ratios that effectively replaces the original data set for the purposes of univariate and multivariate analysis. This strategy is applied to two FA data sets, on copepods and amphipods, respectively, and is widely applicable in other contexts. The selection of ratios is performed in such a way as to satisfy substantive requirements in the context of the respective data set, namely to explain phenomena of interest relevant to the particular species, as well as the statistical requirement to explain as much variance in the FA data set as possible. Benefits of this new approach are (1) univariate statistics that can be validly compared between different studies, and (2) a simplified multivariate analysis of the reduced set of ratios, giving practically the same results as the analysis of the full FA data set.