Multi-source mixing models to quantify food web sources and pathways


S. C. Lubetkin, Quantitative Ecology and Resource Management, University of Washington, Seattle, WA 98195–2182, USA (fax +206 543 8798; e-mail


  • 1Biogeochemical tracers such as stable isotopes are often used to determine sources and pathways of organic matter through food webs, which may provide powerful indicators of environmental stress or insight into resource management issues. However, mixing models using such tracers are algebraically constrained and rarely attempted for more than two sources. This makes them of limited value for ecosystems that have numerous contributing sources.
  • 2We developed two complementary mixing models, SOURCE and STEP, which use linear programming techniques with multiple tracers, to estimate the dominant primary producer sources of consumers, and their diets and trophic levels, regardless of the number of sources and trophic steps.
  • 3SOURCE is used to estimate consumers’ direct and indirect uptake of autotrophic sources and their trophic levels. STEP calculates an estimate of a consumer's diet, which may include autotrophs and/or heterotrophs.
  • 4The two models were tested using simulated data sets of producer and consumer tracer values and then used with published δ13C, δ15N and δ34S data from a study tracing organic matter flows in a saltmarsh estuary.
  • 5SOURCE and STEP accurately estimated flows and trophic structures in the simulations, with average errors of 0·07–0·09 for SOURCE and 0·03–0·05 for STEP, depending on the number of tracers used.
  • 6We illustrate two resultant food webs for the saltmarsh estuary showing possible interpretations of the SOURCE and STEP estimates.
  • 7Synthesis and applications. SOURCE and STEP can be used with stable isotope data to estimate accurately consumers’ trophic levels, primary producer dependence and diets, even when the number of potential autotrophic sources or foods is larger than the number of tracers. SOURCE and STEP could be used to assess the roles played by individual species within food webs, to compare food webs across locations or over time, and to examine potential pollutant bioaccumulation in higher order consumers, among other potential applications. The s-plus code for both models is available at