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Managing the Essential Zeros in Quantitative Fatty Acid Signature Analysis

  • Connie Stewart
  • Christopher Field
Article

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.

Key Words

Bootstrap Compositional data Diet estimation Parametric mixture model Pseudo-seal 

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References

  1. Aitchison, J. (1986), The Statistical Analysis of Compositional Data, New York: Chapman and Hall. MATHGoogle Scholar
  2. Aitchison, J. (1989), “Measures of Location of Compositional Data Sets,” Mathematical Geology, 21, 787–790. CrossRefGoogle Scholar
  3. — (1992), “On Criteria for Measures of Compositional Difference,” Mathematical Geology, 24, 365–379. MathSciNetMATHCrossRefGoogle Scholar
  4. — (2000), “Logratio Analysis and Compositional Distance,” Mathematical Geology, 32, 271–275. MATHCrossRefGoogle Scholar
  5. 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. MathSciNetMATHCrossRefGoogle Scholar
  6. Azzalini, A., and Dalla Valle, A. (1996), “The Multivariate Skew-normal Distribution,” Biometrika, 83, 715–726. MathSciNetMATHCrossRefGoogle Scholar
  7. Billheimer, D., Guttorp, P., and Fagan, W. F. (2001), “Statistical Interpretation of Species Composition,” Journal of the American Statistical Association, 96, 1205–1214. MathSciNetMATHCrossRefGoogle Scholar
  8. 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. CrossRefGoogle Scholar
  9. 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. CrossRefGoogle Scholar
  10. Davison, A. C., and Hinkley, D. V. (1997), Bootstrap Methods and their Application, Cambridge: Cambridge University Press. MATHGoogle Scholar
  11. DiCiccio, T., and Romano, J. (1990), “Nonparametric Confidence-limits by Re-sampling Methods and Least Favorable Families,” International Statistical Review, 58, 59–76. MATHCrossRefGoogle Scholar
  12. 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. MathSciNetCrossRefGoogle Scholar
  13. 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. CrossRefGoogle Scholar
  14. 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. CrossRefGoogle Scholar
  15. 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. CrossRefGoogle Scholar
  16. Mateu-Figueras, G., and Pawlowsky-Glahn, V. (2008), “A Critical Approach to Probability Laws in Geochemistry,” Mathematical Geosciences, 40, 489–502. MATHCrossRefGoogle Scholar
  17. Pawlowsky-Glahn, V., and Egozcue, J. J. (2001), “Geometric Approach to Statistical Analysis,” Stochastic Environmental Research and Risk Assessment, 15, 384–398. MATHCrossRefGoogle Scholar
  18. Stewart, C. (2005), “Inference on the Diet of Predators Using Quantitative Fatty Acid Signature analysis,” Ph.D. thesis, Dalhousie University. Google Scholar

Copyright information

© International Biometric Society 2010

Authors and Affiliations

  1. 1.University of New Brunswick (Saint John)Saint JohnCanada
  2. 2.Dalhousie UniversityHalifaxCanada

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