Biogeosciences www.biogeosciences.net 1726-4170 1726-4189 5 5 2008 10.5194/bg-5-1351-2008 http://www.biogeosciences.net/5/1351/2008/ http://www.biogeosciences.net/5/1351/2008/bg-5-1351-2008.html http://www.biogeosciences.net/5/1351/2008/bg-5-1351-2008.pdf 1351 1359 2008-09-25 Stable isotopes as ecological tracers: an efficient method for assessing the contribution of multiple sources to mixtures M. N. Bugalho migbugalho@isa.utl.pt P. Barcia M. C. Caldeira J. O. Cerdeira Centro de Ecologia Aplicada "Baeta Neves", Instituto Superior de Agronomia, Universidade Técnica de Lisboa, Portugal Faculdade de Economia, Universidade Nova de Lisboa, Lisboa, Portugal Centro de Estudos Florestais, Instituto Superior de Agronomia, Universidade Técnica de Lisboa, Portugal Departamento Florestal, Instituto Superior de Agronomia, Universidade Técnica de Lisboa, Portugal Departamento de Matemática, Instituto Superior de Agronomia, Universidade Técnica de Lisboa, Portugal 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. 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