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. Stable isotopes are increasingly being used as tracers of ecological processes potentially providing relevant information to environmental management issues. An application of the methodology consists in relating the stable isotopic composition of a sample mixture to that of sources. The number of stable isotopes, however, is usually lower than that of potential sources existing in an ecosystem, which creates mathematical difficulties in correctly tracing sources. We discuss a linear programming model which efficiently derives information on the contribution of sources to mixtures for any number of stable isotopes and any number of sources by addressing multiple sources simultaneously. The model identifies which sources are present in all, present in a subset of the samples or absent from all samples simultaneously and calculates minimum and maximum values of each source in the mixtures. We illustrate the model using a data set consisting of the isotopic signatures of different plant sources ingested by primary consumers in tropical riverine habitat in Asia. The model discussed may contribute to extend the scope of stable isotopes methodology to a range of new problems dealing with multiple sources and multiple tracers. For instance, in food web studies, if particular organic matter sources disappear or decrease in availability (e.g. climate change scenarios) the model allows simulation of alternative diets of the consumers providing potentially relevant information for managers and decision makers.

Stable isotopes as ecological tracers: an efficient method for assessing the contribution of multiple sources to mixtures