, Volume 136, Issue 2, pp 261–269 | Cite as

Source partitioning using stable isotopes: coping with too many sources

  • Donald L. PhillipsEmail author
  • Jillian W. Gregg
Ecosystems Ecology


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., δ13C, δ15N, δ18O) 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‰) 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


Stable isotope Mixing model Source partitioning 



We thank Merav Ben-David, Paul Koch, Todd Dawson, the EPA/Oregon State University "Isotopics" discussion group, and an anonymous reviewer for thoughtful reviews of this paper, and Merav Ben-David, Martin Kennedy, William Sturges, and Sandra Zencich for kindly allowing our use of their studies as examples. Robert Gibson of Computer Sciences Corporation wrote the IsoSource Visual Basic program. The information in this document has been funded by the U.S. Environmental Protection Agency. It has been subjected to Agency review and approved for publication. Mention of trade names or commercial products does not constitute endorsement or recommendation for use.


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Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  1. 1.U.S. Environmental Protection AgencyNational Health and Environmental Effects Research LaboratoryCorvallisUSA
  2. 2.Department of Forest ScienceOregon State UniversityCorvallisUSA

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