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.
Similar content being viewed by others
References
Aitchison, J. (1986), The Statistical Analysis of Compositional Data, New York: Chapman and Hall.
Aitchison, J. (1989), “Measures of Location of Compositional Data Sets,” Mathematical Geology, 21, 787–790.
— (1992), “On Criteria for Measures of Compositional Difference,” Mathematical Geology, 24, 365–379.
— (2000), “Logratio Analysis and Compositional Distance,” Mathematical Geology, 32, 271–275.
Azzalini, A., and Capitanio, A. (1999), “Statistical Applications of the Multivariate Skew-normal Distribution,” Journal of the Royal Statistical Society: Series B (Statistical Methodology), 61, 579–602.
Azzalini, A., and Dalla Valle, A. (1996), “The Multivariate Skew-normal Distribution,” Biometrika, 83, 715–726.
Billheimer, D., Guttorp, P., and Fagan, W. F. (2001), “Statistical Interpretation of Species Composition,” Journal of the American Statistical Association, 96, 1205–1214.
Bowen, W. D., Tully, D., Boness, D. J., Bulhier, B., Marshall, G., and Blanchard, W. (2002), “Prey-dependent Foraging Tactics and Prey Profitability in a Marine Mammal,” Marine Ecology Progress Series, 244, 235–245.
Budge, S. M., Iverson, S. J., Bowen, W. D., and Ackman, R. G. (2002), “Among—and within—Species Variation in Fatty Acid Signatures of Marine Fish and Invertebrates on the Scotian Shelf, Georges Bankand Southern Gulf of St. Lawrence,” Canadian Journal of Fisheries and Aquatic Sciences, 59, 886–898.
Davison, A. C., and Hinkley, D. V. (1997), Bootstrap Methods and their Application, Cambridge: Cambridge University Press.
DiCiccio, T., and Romano, J. (1990), “Nonparametric Confidence-limits by Re-sampling Methods and Least Favorable Families,” International Statistical Review, 58, 59–76.
Egozcue, J. J., Pawlowsky-Glahn, V., Mateu-Figueras, G., and Barceló-Vidal, C. (2003), “Isometric Logratio Transformations for Compositional Data Analysis,” Mathematical Geology, 35, 279–300.
Iverson, S. J., Field, C., Bowen, D. W., and Blanchard, W. (2004), “Quantitative Fatty Acid Signature Analysis: A New Method of Estimating Predator Diets,” Ecological Monographs, 72, 211–235.
Iverson, S. J., Springer, A. M., and Kitaysky, A. S. (2007), “Seabirds as Indicators of Food Web Structure and Ecosystem Variability: Qualitative and Quantitative Diet Analyses Using Fatty Acids,” Marine Ecology Progress Series, 352, 235–244.
Martín-Fernández, J. A., Barceló-Vidal, C., and Pawlowsky-Glahn, V. (2003), “Dealing with Zeros and Missing Values in Compositional Data Sets Using Nonparametric Imputation,” Mathematical Geology, 35, 253–278.
Mateu-Figueras, G., and Pawlowsky-Glahn, V. (2008), “A Critical Approach to Probability Laws in Geochemistry,” Mathematical Geosciences, 40, 489–502.
Pawlowsky-Glahn, V., and Egozcue, J. J. (2001), “Geometric Approach to Statistical Analysis,” Stochastic Environmental Research and Risk Assessment, 15, 384–398.
Stewart, C. (2005), “Inference on the Diet of Predators Using Quantitative Fatty Acid Signature analysis,” Ph.D. thesis, Dalhousie University.
Author information
Authors and Affiliations
Corresponding author
Electronic Supplementary Material
Below are the links to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Stewart, C., Field, C. Managing the Essential Zeros in Quantitative Fatty Acid Signature Analysis. JABES 16, 45–69 (2011). https://doi.org/10.1007/s13253-010-0040-8
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13253-010-0040-8