Including source uncertainty and prior information in the analysis of stable isotope mixing models

Stable isotope mixing models offer a statistical framework for estimating the contribution of multiple sources (such as prey) to a mixture distribution. Recent advances in these models have estimated the source proportions using Bayesian methods, but have not explicitly accounted for uncertainty in the mean and variance of sources. We demonstrate that treating these quantities as unknown parameters can reduce bias in the estimated source contributions, although model complexity is increased (thereby increasing the variance of estimates). The advantages of this fully Bayesian approach are particularly apparent when the source geometry is poor or sample sizes are small. A second benefit to treating source quantities as parameters is that prior source information can be included. We present findings from 9 lake food-webs, where the consumer of interest (fish) has a diet composed of 5 sources: aquatic insects, snails, zooplankton, amphipods, and terrestrial insects. We compared the traditional Bayesian stable isotope mixing model with fixed source parameters to our fully Bayesian model-with and without an informative prior. The informative prior has much less impact than the choice of model-the traditional mixing model with fixed source parameters estimates the diet to be dominated by aquatic insects, while the fully Bayesian model estimates the diet to be more balanced but with greater importance of zooplankton. The findings from this example demonstrate that there can be stark differences in inference between the two model approaches, particularly when the source geometry of the mixing model is poor. These analyses also emphasize the importance of investing substantial effort toward characterizing the variation in the isotopic characteristics of source pools to appropriately quantify uncertainties in their contributions to consumers in food webs.