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Development of stable isotope mixing models in ecology - Perth
Citation:
PHILLIPS, D. L. Development of stable isotope mixing models in ecology - Perth. Presented at Edith Cowan University - invited oral presentation, Perth, AUSTRALIA, May 13, 2011.
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, incorporating the previous model developments in a statistical framework that allows flexible specification of mixing models of varying complexity. The user specifies prior knowledge (if any) about source proportion values and defines the mixing model, which may include any number of sources, and trophic enrichment corrections and concentration effects as well. Means and SDs are input for the isotopic values, correction factors, and concentrations, and the model estimates probability distributions for the source proportions that incorporate both the prior knowledge and the data. These models likely will be used increasingly as they become better known.