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.

Effects of phylogeny and prey type on fatty acid calibration coefficients in three pinniped species: implications for the QFASA dietary quantification technique

“…In both our NFS and SSL samples, higher CCs were indeed associated with higher variance. This observation is particularly important given the recent interest in using bootstrapping resampling techniques for dietary FA investigations (Stewart & Field 2011, Thiemann et al 2011.…”

An approach to measure distance between compositional diet estimates containing essential zeros

“…To examine the effect of essential zeros on the stress, we used a reduced prey base containing eight important species, as described in [18]. This allowed us to vary the amount of zeros in the true diets and produce diet estimates that are generally closer to the true diet than would be expected if the larger prey database was used.…”

“…Pseudo-predators were first introduced in [8] and a modified algorithm was developed in [18]. A pseudo-predator is created by sampling with replacement from a prey database with probability weights given by a selected 'true' diet.…”

“…Since the diet estimates often contain many zeros and these zeros represent an estimated absence of a species from the diet, the recommended and usual approach is to treat the zeros as essential zeros rather than replacing them with an arbitrary amount [18]. While strategies for replacing rounded zeros by appropriate values have been developed (see [13,15], for example), these are not recommended for essential zeros.…”

A Logistic Normal Mixture Model for Compositional Data Allowing Essential Zeros

“…Work by Stewart and Field (2011) uses a multiplicative logistic normal mixture model that allows them to consider the univariate log odds for the i th component to be normally distributed where the i th component is not zero. It works well for their applications, in particular regression, but does not capture covariance easily.…”