# Stable Isotope Mixing Models for Estimating Source Proportions

Stable isotope analysis can be used in ecological studies to trace chemical movement through the environment. A common application is to use the isotopic composition of a mixture to determine the proportions of various sources in the mixture, using mathematical mixing models. Examples include quantifying the importance of various pollutant sources to contaminated water, or the importance of various prey species in a predator’s diet.

The links below provide information and download files for three stable isotope analysis tools: IsoError, IsoConc, and IsoSource.

- IsoError
### IsoError: Confidence interval calculation for source partitioning using stable isotopes

ISOERROR1_04 is a Microsoft Excel 2000™ spreadsheet that calculates estimates and confidence intervals of source proportional contributions to a mixture, using stable isotope analyses.

Examples include the quantifying proportions of:

- different pollution sources to contaminated air or water bodies
- food sources in an animal’s diet
- C
_{3}vs. C_{4}plant inputs to soil organic carbon, etc.

Linear mixing models are used to partition two sources with a single isotopic signature (e.g., δ

^{13}C) or three sources with a second isotopic signature (e.g., δ^{15}N).The user supplies the mean, standard deviation, and number of samples from each of the source and mixture populations for each isotopic signature. For dual isotope studies, the correlations of the two isotopes within each population can also be specified, but are not required. The spreadsheet calculates the estimate proportion for each source (0-1), standard errors for these estimates, and approximate 95% confidence intervals. Confidence intervals are truncated at 0 and 1.

- IsoConc
### IsoConc: Concentration-dependent stable isotope mixing model

ISOCONC1_01.xls is a Microsoft Excel 2000™ spreadsheet which performs calculations for the concentration-weighted stable isotope mixing model. This dual-isotope model takes into account isotopic element concentration differences among the sources in determining the proportional contributions of sources to a mixture. The user supplies the isotopic signatures for each source and the mixture, as well as the isotopic element concentrations for each source. Separate estimates are made of the contributions of each source for total mass and each isotopic element.

- IsoSource
### IsoSource: stable isotope mixing model for partitioning an excess number of sources

IsoSource version 1.3 is a Microsoft Visual Basic™ software package which calculates ranges of source proportional contributions to a mixture based on stable isotope analyses when the number of sources is too large to permit a unique solution (> number of isotope systems + 1). [It may also be used for other non-isotopic tracers such as concentrations of trace chemicals.]

Examples include partitioning of:

- pollutant sources in a waste stream
- food sources in an animal’s diet,
- water sources for plant uptake,
- carbon sources in soil organic matter, and many others.

This software provides the distribution of source proportions which are consistent with isotopic mass balance.

The user supplies the isotopic signatures (e.g., atom %, isotopic ratios, or δ values) for the mixture and each of the sources. The user also supplies the source increment (e.g., entering a value of 1% specifies examination of all possible combinations of sources contributions from 0-100% in increments of 1%), and the mass balance tolerance (e.g., entering a value of 0.1‰ specifies that all source combinations that result in predicted mixture signatures within 0.1‰ of the observed signature are considered as feasible solutions).

IsoSource provides output files which list each feasible solution, descriptive statistics about the distribution of these solutions (number of solutions, mean, standard deviation, minimum, maximum, 1%ile, median, and 99%ile for each source), and histograms of these distributions. Output files can be viewed on-screen, printed, or read into other applications such as Microsoft Excel™ for further viewing or manipulation.

Additional non-isotopic constraints can be incorporated by extracting appropriate subsets of solutions from the IsoSource output. Additional information on this post-processing is given in the "Additional constraints.pdf" link shown at the bottom of the page."

**NOTE - Each of the individual solutions represents a combination of source proportions which satisfies isotopic mass balance in the mixing model. Descriptive statistics are provided simply as a way to characterize this entire distribution of feasible solutions. 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.**

Download IsoSource Version 1.3.1(9 MB) [IsoSource software in a zip file - Unzip the file and run Setup.exe]Additional constraints: procedures for post-processing IsoSource results.

## Further Information

Publications: Publications describing these methods and related applications

**Contact:** For further information on any of these models contact Don Phillips at phillips.donald@epa.gov.