Zero-inflated beta distribution for modeling the proportions in quantitative fatty acid signature analysis

Quantitative fatty acid signature analysis (QFASA) produces diet estimates containing the proportion of each species of prey in a predator's diet. Since the diet estimates are compositional, often contain an abundance of zeros (signifying the absence of a species in the diet), and samples sizes are generally small, inference problems require the use of nonstandard statistical methodology. Recently, a mixture distribution involving the multiplicative logistic normal distribution (and its skew-normal extension) was introduced in relation to QFASA to manage the problematic zeros. In this paper, we examine an alternative mixture distribution, namely, the recently proposed zero-inflated beta (ZIB) distribution. A potential advantage of using the ZIB distribution over the previously considered mixture models is that it does not require transformation of the data. To assess the usefulness of the ZIB distribution in QFASA inference problems, a simulation study is first carried out which compares the small sample properties of the maximum likelihood estimators of the means. The fit of the distributions is then examined using ‘pseudo-predators’ generated from a large real-life prey base. Finally, confidence intervals for the true diet based on the ZIB distribution are compared with earlier results through a simulation study and harbor seal data.