Quantifying learning in biotracer studies.

Mixing models have become requisite tools for analyzing biotracer data, most commonly stable isotope ratios, to infer dietary contributions of multiple sources to a consumer. However, Bayesian mixing models will always return a result that defaults to their priors if the data poorly resolve the source contributions, and thus, their interpretation requires caution. We describe an application of information theory to quantify how much has been learned about a consumer's diet from new biotracer data. We apply the approach to two example data sets. We find that variation in the isotope ratios of sources limits the precision of estimates for the consumer's diet, even with a large number of consumer samples. Thus, the approach which we describe is a type of power analysis that uses a priori simulations to find an optimal sample size. Biotracer data are fundamentally limited in their ability to discriminate consumer diets. We suggest that other types of data, such as gut content analysis, must be used as prior information in model fitting, to improve model learning about the consumer's diet. Information theory may also be used to identify optimal sampling protocols in situations where sampling of consumers is limited due to expense or ethical concerns.