No abstract

Stable isotopes are increasingly being used as tracers in environmental studies. One application is to use isotopic ratios to quantitatively determine the proportional contribution of several sources to a mixture, such as the proportion of various pollution sources in a waste stream. In general, the proportional contributions of n+1 different sources can be uniquely determined by the use of n different isotope system tracers (e.g., delta13C, delta15N, delta18O) with linear mixing models based on mass balance equations. Often, however, the number of potential sources exceeds n+1, which prevents finding a unique solution of source proportions. What can be done in these situations? While no definitive solution exists, we propose a method that is informative in determining bounds for the contributions of each source. In this method, all possible combinations of each source contribution (0-100%) are examined in small increments (e.g., 1%). Combinations that sum to the observed mixture isotopic signatures within a small tolerance (e.g., +/-0.1 per thousand ) are considered to be feasible solutions, from which the frequency and range of potential source contributions can be determined. To avoid misrepresenting the results, users of this procedure should report the distribution of feasible solutions rather than focusing on a single value such as the mean. We applied this method to a variety of environmental studies in which stable isotope tracers were used to quantify the relative magnitude of multiple sources, including (1) plant water use, (2) geochemistry, (3) air pollution, and (4) dietary analysis. This method gives the range of isotopically determined source contributions; additional non-isotopic constraints specific to each study may be used to further restrict this range. The breadth of the isotopically determined ranges depends on the geometry of the mixing space and the similarity of source and mixture isotopic signatures. A sensitivity analysis indicated that the estimated ranges vary only modestly with different choices of source increment and mass balance tolerance parameter values. A computer program (IsoSource) to perform these calculations for user-specified data is available at http://www.epa.gov/wed/pages/models.htm.

Stable isotope mixing models are increasingly used to quantify consumer diets, but may be misused and misinterpreted. We address major challenges to their effective application. Mixing models have increased rapidly in sophistication. Current models estimate probability distributions of source contributions, have user-friendly interfaces, and incorporate complexities such as variability in isotope signatures, discrimination factors, hierarchical variance structure, covariates, and concentration dependence. For proper implementation of mixing models, we offer the following suggestions. First, mixing models can only be as good as the study and data. Studies should have clear questions, be informed by knowledge of the system, and have strong sampling designs to effectively characterize isotope variability of consumers and resources on proper spatio-temporal scales. Second, studies should use models appropriate for the question and recognize their assumptions and limitations. Decisions about source grouping or incorporation of concentration dependence can influence results. Third, studies should be careful about interpretation of model outputs. Mixing models generally estimate proportions of assimilated resources with substantial uncertainty distributions. Last, common sense, such as graphing data before analyzing, is essential to maximize usefulness of these tools. We hope these suggestions for effective implementation of stable isotope mixing models will aid continued development and application of this field.

Fifty years ago, GE Hutchinson defined the ecological niche as a hypervolume in n‐dimensional space with environmental variables as axes. Ecologists have recently developed renewed interest in the concept, and technological advances now allow us to use stable isotope analyses to quantify these niche dimensions. Analogously, we define the isotopic niche as an area (in δ‐space) with isotopic values (δ‐values) as coordinates. To make isotopic measurements comparable to other niche formulations, we propose transforming δ‐space to p‐space, where axes represent relative proportions of isotopically distinct resources incorporated into an animal's tissues. We illustrate the isotopic niche with two examples: the application of historic ecology to conservation biology and ontogenetic niche shifts. Sustaining renewed interest in the niche requires novel methods to measure the variables that define it. Stable isotope analyses are a natural, perhaps crucial, tool in contemporary studies of the ecological niche.

In this paper, we review recent advances in stable isotope mixing models (SIMMs) and place them into an overarching Bayesian statistical framework, which allows for several useful extensions. SIMMs are used to quantify the proportional contributions of various sources to a mixture. The most widely used application is quantifying the diet of organisms based on the food sources they have been observed to consume. At the centre of the multivariate statistical model we propose is a compositional mixture of the food sources corrected for various metabolic factors. The compositional component of our model is based on the isometric log‐ratio transform. Through this transform, we can apply a range of time series and non‐parametric smoothing relationships. We illustrate our models with three case studies based on real animal dietary behaviour. Copyright © 2013 John Wiley & Sons, Ltd.