A quantitative approach to combine sources in stable isotope mixing models

Stable isotope mixing models, used to estimate source contributions to a mixture, typically yield highly uncertain estimates when there are many sources and relatively few isotope elements. Previously, ecologists have either accepted the uncertain contribution estimates for individual sources or addressed the problem in an ad hoc way by combining either related sources prior to analysis or the estimated proportions of related sources following analysis. Neither of these latter approaches explicitly account for uncertainty in source combinations within the likelihood framework. In this paper we incorporate uncertainty in both the number of source groups and group assignment within a formal Bayesian mixing model framework. By dynamically exploring model complexity due to aggregating sources based on shared proportional contributions, we can estimate posterior probabilities of alternative group configurations, and construct posterior dendrograms of group membership. We apply this method to simulated data, and illustrate applications to two consumer datasets (rainbow trout, coastal mink). Our results demonstrate that estimating, rather than fixing, the number of proportional contributions in a mixing model can improve model inference and reduce bias in estimates of source contributions to a mixture.