A Bayesian stable isotope mixing model for coping with multiple isotopes, multiple trophic steps and small sample sizes

Abstract

We introduce a Bayesian stable isotope mixing model for estimating the relative contributions of different dietary components to the tissues of consumers within food webs. The model is implemented with the probabilistic programming language Stan. The model incorporates isotopes of multiple elements (e.g. C, N, H) for two trophic levels, when the structure of the food web is known. In addition, the model allows inclusion of latent trophic levels (i.e. for which no empirical data are available) intermediate between sources and measured consumers. Running the model in simulations driven by a real dataset from Finnish lakes, we tested the sensitivity of the posterior distributions by altering critical prior parameters and assumptions in the data-generating process. Importantly, we found that the model estimations were particularly sensitive to the assigned prior value for ω (the fraction of H in aquatic consumer tissue that is derived from environmental water rather than diet) so that reliable empirical data for this parameter are required. When reliable information is not available for ω, we suggest that an uninformative prior should be used. The proposed model and inferences are suitable for studies where resources for collecting new data are limited, but useful prior information for each specific trophic level is available from earlier studies.