Title:
A Bayesian stable isotope mixing model for covariate selection

Abstract:
You are what you eat, conditional on selected covariates. We developed an
extended Bayesian mixing model with variable selection to infer
proportional contributions of diet sources to a consumer animal's diet
conditional on covariates, such as season and location. Our model performs
model selection to arrive at a parsimonious explanation of the diet.
Bayesian methods apply for arbitrary numbers of isotopes and diet sources
but existing models are somewhat limited as many can not condition on
covariates. The current state of the art is to fit many separate models for
each factor covariate combination and compare the separate posterior
estimates. Our model uses stable isotope ratios and concentrations of
carbon, nitrogen, and sulfur, isotopic fractionations, elemental
assimilation efficiencies, as well as prior information (expert opinion) to
inform the diet parameters within a single comprehensive model. Our model
appropriately accounts for parameter correlation, uncertainty, and prior
information at all levels of the analysis.