SISUS is a Bayesian statistical model and software aiming to provide a comprehensive solution to stable isotope sourcing inference and prediction problems.

You can use SISUS today by downloading the workbook template on the left, inputting your data, then submitting in the Execute page to return plots and numerical summaries.

You can contribute to the Stable Isotope Sourcing community Wiki by visiting SISUSWiki on the left, registering as a user, and adding and modifying content for our user community.

Awards: First place, Graduate Poster division, UNM Biology 16th Annual Research Day

Citing SISUS website documents

  • Website: Erhardt, Erik Barry. "SISUS: Stable Isotope Sourcing using Sampling." Retrieved [date] <http://statacumen.com/sisus/>.
  • Getting Started: Erhardt, Erik Barry. "SISUS: Stable Isotope Sourcing using Sampling, Getting Started." May 30, 2007 <http://statacumen.com/sisus/SISUS_Getting_Started_v0_08.pdf>.

Purpose

Stable Isotope Sourcing using Sampling (SISUS) is a Bayesian model and software extending the Phillips and Gregg (2003) IsoSource model and software for source partitioning using stable isotopes; SISUS aims to provide a comprehensive solution to stable isotope sourcing inference and prediction problems. 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 water sources used by a tree, or dietary sources for an animal. In general, the proportional contributions of n different sources can be uniquely determined by the use of k different isotope system tracers (e.g., d13C, d15N, d18O) with linear mixing models based on mass balance equations. Often, the number of potential sources exceeds k+1, which prevents finding a unique solution of source proportions.

Phillips and Gregg (2003) introduced a strategy to iterate over the n-1 dimensional simplex, determining proportions satisfying the mixing model equations. SISUS uses a sampling strategy to draw solutions uniformly from the convex polytope defined as the intersection of the simplex and the mass balance equation constraints. The Bayesian model allows specification of priors on the proportions, incorporation of variation in the isotope, concentration, and assimilation efficiency measurements, and probability statements about the proportions. SISUS output includes plots and numerical summaries describing the existence of solutions, and their distributional properties.

Examples

Examples taken from the literature demonstrating some of the many capabilities of SISUS.

The links are to pages that include the input workbook and the results produced when submitted to SISUS.

Some of these examples were produced using previous versions of the software. As such, the workbooks differ in format and will experience an error if submitted; instead, copy data from example workbooks to current workbook format.


Getting Started worksheet and results that appear in the current Getting Started guide in the menu.

  • GettingStarted_v0_08
  • Made up data to show some of the capabilities of SISUS, 3 mixtures, one with no solution (n=4, k=2)
    Concentration dependent Mixing Model with linear constraints, Dirichlet prior on simplex, error bars on Convex Hull.


Examples from Phillips' papers in Oecologia, where he and his coauthors developed mixing models for stable isotope sourcing. Papers and software here.

Donald L. Phillips. Oecologia (2001) 127:166--170.
Mixing models in analyses of diet using multiple stable isotopes: a critique
DOI 10.1007/s004420000571
  • P2001Wolf_3-2
  • Phillips in Oecologia (2001), p.167 Table 1 Wolf (n=3, k=2)
    Basic Mixing Model with Unique Solution.

  • P2001Mink_7-2
  • Phillips in Oecologia (2001), p.169 Table 2 Mink (n=7, k=2)
    Basic Mixing Model with Solution Space.
Donald L. Phillips and Jillian W. Gregg. Oecologia (2001) 127:171--179.
Uncertainty in source partitioning using stable isotopes (IsoError)
DOI 10.1007/s004420000578
  • PG2001CaneSoil12yr_2-1
  • Phillips and Gregg in Oecologia (2001) p.174 Table 2 CaneSoil 12yr (n=2, k=1)
    Basic Mixing Model with Unique Solution.

  • PG2001CaneSoil12yrVar_2-1
  • Phillips and Gregg in Oecologia (2001) p.174 Table 2 CaneSoil 12yr with variation (n=2, k=1)
    Basic Mixing Model with Solution Space.
    Solution space results from isotopic variation in mixture and sources. Asking for samples from the isotopic distributions (independent multivariate normals for the mixture and each source) by specifying the number of samples of isotope values using the n.samples.isotope.mvn parameter. Note: The results are skewed a little toward the Sugar cane when variation is allowed. This is because some of the samples from the isotope distributions don't lead to solutions (see process_info.txt "9575 of 10000 = 95.75 % samples lead to feasible solutions"), and the solutions that are not feasible are when Cane soil falls on the far side of Forest soil.
    **Results with variation are experimental.**

  • PG2001CaneSoil50yr_2-1
  • Phillips and Gregg in Oecologia (2001) p.174 Table 2 CaneSoil 50yr (n=2, k=1)
    Basic Mixing Model with Unique Solution.

  • PG2001CaneSoil50yrVar_2-1
  • Phillips and Gregg in Oecologia (2001) p.174 Table 2 CaneSoil 50yr with variation (n=2, k=1)
    Basic Mixing Model with Solution Space.
    Solution space results from isotopic variation in mixture and sources.
    **Results with variation are experimental.**

  • PG2001Wolf_3-2
  • Phillips and Gregg in Oecologia (2001), p.175 Table 3 Wolf (n=3, k=2)
    Basic Mixing Model with Unique Solution.

  • PG2001WolfVar_3-2
  • Phillips and Gregg in Oecologia (2001), p.175 Table 3 Wolf with variation (n=3, k=2)
    Basic Mixing Model with Solution Space.
    Solution space results from isotopic variation in mixture and sources.
    **Results with variation are experimental.**
    ** not confident that population isotopic variation was correctly backed-out from paper **

Donald L. Phillips and Paul L. Koch. Oecologia (2002) 130:114--125.
Incorporating concentration dependence in stable isotope mixing models (IsoConc)
DOI 10.1007/s004420100786 Donald L. Phillips and Jillian W. Gregg. Oecologia (2003) 136:261--269.
Source partitioning using stable isotopes: coping with too many sources (IsoSource)
DOI 10.1007/s00442-003-1218-3



Donald L. Phillips. IsoSource page (2003?).
Additional Constraints

SISUS incorporates linear constraints directly using the "Linear Constraints" worksheet within the input workbook.





I encourage you to send your examples to me to be included here. Please include full reference information.

Blair Wolf's Bear friend. (2006)
  • B2006Bears

  • Basic mixing model (5 mixtures at once)

Requirements

Microsoft Excel or other software (such as OpenOffice.org for Mac OS X, Linux, etc.) to read, modify, and write the input workbook in xls format.

When using OpenOffice.org, if an error occurs, first try setting the cell format of all numeric fields to Numeric.