Managing the Essential Zeros in Quantitative Fatty Acid Signature Analysis

Abstract

Quantitative fatty acid signature analysis (QFASA) is a recent diet estimation method that depends on statistical techniques. QFASA has been used successfully to estimate the diet of predators such as seals and seabirds. Given the potential species in the predator's diet, QFASA uses statistical methods to obtain point estimates of the proportion of each species in the diet. In this paper, inference for a population of predators is considered. The estimated diet is compositional and often with zeros corresponding to species that are estimated to be absent from the diet. Zeros of this type (referred to as essential zeros) are troublesome since typical methods of dealing with compositional data involve logarithmic transformations. In this paper, we develop mixture models that can be used to model compositional data with essential zeros. We then present inference procedures for the true diet of a predator that are based on the developed models and designed for the difficult but practical setting in which sample sizes are small. Simulations using "pseudo-seals" are carried out to assess the fit of our models and our confidence intervals. Two real-life data sets involving seabirds and seals illustrate the usefulness of our confidence interval methods in practice. Supplemental materials for this article are available online. © 2010 International Biometric Society.