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.

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>.

e-mail: "Erik Barry Erhardt" <erik AT StatAcumen.com>

Purpose

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

Paper Abstract

Mass-balance mixing models for stable isotope sourcing provide a mechanistic, and hence predictive, foundation for describing animal ecology and other applications where sources assimilate into a mixture. The goal of the mixing models described here is to estimate feasible proportions of biomass consumed of sources by a consumer. The mixing models used in stable isotope sourcing problems have a common linear structure, which we emphasize here. These models define the relationship between the isotopic data space and the source-proportion solution space. Often, the number of sources n is many more than the number of stable isotopes k, n > k + 1, resulting in an infinite number of source-proportion solutions, a region we call the solution polytope. The most popular software for providing solutions to underconstrained mixing models is IsoSource (Phillips and Gregg, 2003), a deterministic algorithm for providing approximate solutions to represent the solution polytope. Here, we describe an algorithm implemented as SISUS software for providing a user-specified number of probabilistic exact solutions quickly which accurately represents the solution polytope. Both methods provide qualitatively similar results, though the differences arguably favor the probabilistic approach. Additionally, we show how IsoSource can be used to provide approximate solutions to the Assimilation Efficiency Concentration-Dependent Mixing Model, a more developed model than the Basic Mixing Model. SISUS software is freely available at http://StatAcumen.com/sisus.

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 
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 advanages 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.

Requirements

Microsoft Excel or other software (such as OpenOffice.org for Mac OS X, Linux, Windows, 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.