A Bayesian framework for stable isotope mixing models

Stable isotope sourcing is used to estimate proportional contributions of sources to a mixture, such as in the analysis of animal diets and plant nutrient use. Statistical methods for inference on the diet proportions using stable isotopes have focused on the linear mixing model. Existing frequentist methods provide inferences when the diet proportion vector can be uniquely solved for in terms of the isotope ratios. Bayesian methods apply for arbitrary numbers of isotopes and diet sources but existing models are somewhat limited as they assume that trophic fractionation or discrimination is estimated without error or that isotope ratios are uncorrelated. We present a Bayesian model for the estimation of mean diet that accounts for uncertainty in source means and discrimination and allows correlated isotope ratios. This model is easily extended to allow the diet proportion vector to depend on covariates, such as time. Two data sets are used to illustrate the methodology. Code is available for selected analyses.