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Historical development of stable isotope mixing models in ecology
Citation:
PHILLIPS, D. L. Historical development of stable isotope mixing models in ecology. Presented at Bayesian Mixing Model Workshop, 7th Internationa Conference on Applications of Stable Isotope Techniques to Ecological Studies, Fairbanks, AK, August 08 - 13, 2010.
Impact/Purpose:
More than 40 years ago, stable isotope analysis methods used in geochemistry began to be applied to ecological studies. One common application is using mathematical mixing models to sort out the proportional contributions of various sources to a mixture.
Description:
More than 40 years ago, stable isotope analysis methods used in geochemistry began to be applied to ecological studies. One common application is using mathematical mixing models to sort out the proportional contributions of various sources to a mixture. Examples include contributions of prey to the diet of a consumer, pollution sources to air or water bodies, carbon sources to soil organic matter, soil horizons to plant water use, and many others. Modelers have continued to develop additional capabilities for mixing models over the years. The simplest algebraic model used a single isotopic value (e.g., δ13C) to uniquely partition the contributions of two sources to a mixture. Expanding this algebraic system to n isotopic values allowed partitioning of n+1 sources. Other methods based on geometric distances in isotope space (e.g., δ15N and δ13C axes) were devised, but they were shown to be mathematically flawed and are no longer used. Error propagation calculations provided statistical confidence intervals around the point estimates of source proportions (e.g., IsoError). Concentration-dependent models incorporated elemental concentrations and allowed for independent assessment of the contributions of sources to each element (e.g., C and N) in the mixture (e.g., IsoConc). Other models, using various types of algorithms, allowed more sources to be included (>n+1 for n isotopic values). Even though there is not a unique solution, some of these methods put bounds on the possible range of source contributions (e.g., IsoSource, SOURCE/STEP, SISUS), while others focused on single values to represent the central tendencies of these distributions (e.g., Moore-Penrose pseudoinverse). Other developments included additional processing of mixing model results to summarize the contributions of groups of related sources, or to consider other non-isotopic constraints. Recently, Bayesian methods were first applied to stable isotope mixing models, holding the promise of providing a rigorous statistical framework and allowing flexible specification of mixing models of varying complexity. This is the subject of this workshop and the remaining presentations.