Measuring repeatability of compositional diet estimates: An example using quantitative fatty acid signature analysis

By measuring the temporal consistency, or repeatability, in the diets of predators, we can gain a better understanding of the degree of individual specialization in resource utilization and implications for predator-prey interactions, population dynamics, and food web structure. To measure repeatability, we require repeated diet estimates of individuals over time, such as those derived from quantitative fatty acid signature analysis (QFASA), a popular diet estimation technique. However, diet estimates are often lengthy compositional vectors with many zeros, as some prey will not be consumed by all individuals, precluding the use of previously proposed measures of repeatability. In this paper, we propose a novel approach for inferring repeatability for multivariate data and, in particular, compositional diet estimates. We extend the commonly used measure of repeatability for univariate data to the multivariate compositional setting by utilizing the mean squares obtained from a nonparametric multivariate analysis of variance, and an appropriate choice of statistical distance. Our measure and its extension are compatible with both balanced and unbalanced data sets. Associated confidence intervals via nonparametric bootstrapping are also developed for the case of QFASA diet estimates that incorporate both sampling error and measurement error, where the latter error arises because the diets of predators are estimated. Simulation study results suggest that for practical levels of repeatability, our methods yield confidence intervals with the desired coverage probability even when the sample size relative to the dimension of the data (i.e., number of prey species eaten) is small. We tested our methods using QFASA diet estimates for free-ranging Northwest Atlantic grey seals. Given the importance of understanding how predator diets vary over time and space, our method may find broad application to other compositional diet estimates, including those derived from the stomach or fecal contents, and stable isotope analyses.