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Phillips, D.L. and P.L. Koch. 2001. Incorporating concentration dependence in stable isotope mixing models. Oecologia.130:114-125. WED-01-071

Stable isotopes are often used as natural labels to quantify the contributions of multiple sources to a mixture. For example, C and N isotopic signatures can be used to determine the fraction of three food sources in a consumerís diet. The standard dual isotope, three source linear mixing model assumes that the proportional contribution of a source to a mixture is the same for both elements (e.g., C, N). This may be a reasonable assumption if the concentrations are similar among all sources. However, one source is often particularly rich or poor in one element (e.g., N), which logically leads to a proportionate increase or decrease in the contribution of that source to the mixture for that element relative to the other element (e.g., C). We have developed a concentration-weighted linear mixing model, which assumes that for each element, a sourceís contribution is proportional to the contributed mass times the elemental concentration in that source. The model is outlined for two elements and three sources, but can be generalized to n elements and n + 1 sources. Sensitivity analyses for C and N in three sources indicated that varying the N concentration of just one source had large and differing effects on the estimated source contributions of mass, C, and N. The same was true for a case study of bears feeding on salmon, moose, and N-poor plants, in which the estimated biomass contribution of salmon was markedly less than the standard model estimated. Application of the model to a captive feeding study of captive mink fed on salmon, lean beef, and C-rich, N-poor beef fat reproduced very closely the known dietary proportions, whereas the standard model failed to yield a set of positive source proportions. Use of this concentration-weighted model is recommended whenever the elemental concentrations vary substantially among the sources.

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