Erik Erhardt

Publication Date



Stable isotope sourcing is used to estimate proportional contributions of sources to a mixture, such as in the analysis of animal diets, plant nutrient use, geochemistry, pollution, and forensics. We focus on animal ecology because of the particular complexities due to the process of digestion and assimilation. Parameter estimation has been a challenge because there are often many sources and few isotopes leading to an underconstrained linear system for the diet probability vector. This dissertation offers three primary contributions to the mixing model community. (1) We detail and provide an R implementation of a better algorithm (SISUS) for representing possible solutions in the underconstrained case (many sources, few isotopes) when no variance is considered (Phillips and Gregg, 2003). (2) We provide general methods for performing frequentist estimation in the perfectly-constrained case using the delta method and the bootstrap, which extends previous work applying the delta method to two- and three-source problems (Phillips and Gregg, 2001). (3) We propose two Bayesian models, the implicit representation model estimating the population mean diet through the mean mixture isotope ratio, and the explicit representation model estimating the population mean diet through mixture-specific diets given individual isotope ratios. Secondary contributions include (4) estimation using summaries from the literature in lieu of observation-level data, (5) multiple methods for incorporating isotope ratio discrimination (fractionation) in the analysis, (6) the use of measurement error to account for and partition more uncertainty, (7) estimation improvements by pooling multiple estimates, and (8) detailing scenarios when one model is preferred over another. We show that the Bayesian explicit representation model provides more precise diet estimates than other models when measurement error is small and informed by the necessary calibration measurements.

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Level of Degree


Department Name

Mathematics & Statistics

First Committee Member (Chair)

Edward John Bedrick

Second Committee Member

Ronald Christensen

Third Committee Member

Gabriel Huerta

Fourth Committee Member

Michele Guindani

Fifth Committee Member

Blair O. Wolf

Project Sponsors

Howard Hughes Medical Institute




Physiological ecology--Statistical methods, Animals--Food--Research--Statistical methods, Food preferences--Research--Statistical methods, Tissues--Analysis--Statistical methods, Stable isotopes--Analysis--Statistical methods, Mixture distributions (Probability theory), Bayesian statistical decision theory.

Document Type