September 14th, 2010

SISUS: Stable Isotope Sourcing using Sampling




SISUS is a better way of doing what IsoSource does: provide feasible solutions to stable isotope mixing models without variation.

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

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] <>.
  • Getting Started: Erhardt, Erik Barry. “SISUS: Stable Isotope Sourcing using Sampling, Getting Started.” May 30, 2007 <>.


To estimate feasible proportional contributions of sources to a mixture using stable isotope data.

Paper Abstract

Stable isotope sourcing is used to estimate proportional contributions of sources to a mixture, such as in the analysis of animal diets, plant nutrient use, geochemistry, pollution, and forensics. We describe an algorithm implemented as SISUS software for providing a user-speci ed number of probabilistic exact solutions quickly from the basic mixing model. Our method outperforms IsoSource (Phillips and Gregg, 2003), a deterministic algorithm for providing approximate solutions to represent the solution polytope. Our method is an approximate Bayesian large sample procedure. SISUS software is freely available at and as an R package at

Visual distinction between IsoSource and SISUS

Bear example, brown bear hair as a mixture of S = 3 sources, salmon, meat, and fruit, using I = 2 isotopes of carbon (i = 1) and nitrogen (i = 2), reused from Koch and Phillips (2002, Table 1). Concentration for carbon is the proportion of carbon in dry matter, and concentration for nitrogen is the proportion crude protein in dry matter times the proportion nitrogen in protein. Assimilation for carbon is the digestible proportion of dry matter, and assimilation for nitrogen is the digestible proportion of dry matter times the protein digestibility proportion. The product of our these concentration and assimilation values are what Koch and Phillips (2002) report as Digest C and Digest N. Our results differ from theirs because they use Digest [C] and Digest [N] in their calculations, which is the Digest X divided by the proportion digestible dry matter.

                  Isotope Ratios  Discrim       Concent  Assim.Effic.
                       dC   dN    DC  DN    [C]   [N]     c     n
Mixture Brown Bear    -20.3 10.9
Source  Salmon        -20.5 13.2  1.2 2.3   0.548 0.118   1.00  1.00
Source  Meat          -21.5  3.9  4.9 4.0   0.515 0.141   1.00  1.00
Source  Fruit         -26.6 -0.9  3.3 4.1   0.45  0.0126  0.634 0.571

We analyze the bear example for the carbon isotope only, that is, excluding the nitrogen information, using the assimilation model (AECDMM) of (Martinez del Rio, Carlos and Wolf, Blair. O Starck, J Matthias and Wang, Tobias and Wang, Tobias (ed.) Mass-Balance models for animal isotopic ecology, chapter 6. Science Publishers, Inc., Enfield, NH, USA, 2005, 141-174). For the AECDMM using carbon only, the matrix needed for IsoSource is

Mixture = 0
Sources = 0.548 1.906 -0.856

The images below show the simplex and carbon hyperplanes and their intersection solution polytope as a line. Image (a) shows an example of the IsoSource deterministic sampling strategy, with a grid increment of 0.02 and tolerance of 0.1 where 117 of the 1326 points evaluated are determined approximate solutions. Image (b) shows one realization of R = 117 exact probabilistic solutions from SISUS which are qualitatively similar to deterministic approximate solutions of IsoSource, yet algorithmic advantages are clear. In practice, sample sizes of R = 1000 or R = 10000 might be used for an accurate representation of the solution polytope.

(a) IsoSource evaluates points on the lattice over the simplex, returning 117 approximate solutions of the 1326 evaluated points. Notice that the points evaluated are uniform over the simplex, but the approximate solutions provided are only roughly uniform near the solution polytope.

(b) SISUS samples exact solutions uniformly over the solution polytope. Here $sR=117$ solutions are requested to match IsoSource and to illustrate that the solutions are from a uniform distribution at random; samples converge quickly to a uniform distribution over the entire solution polytope.


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

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


Erik Barry Erhardt PIBBS HHMI

R RWUI Matthew Bohnsack

Comments are closed.