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Marine Ecology Progress Series

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MEPS 490:285-289 (2013)  -  DOI:

Statistical basis and outputs of stable isotope mixing models: Comment on Fry (2013)

Brice X. Semmens1,*, Eric J. Ward2, Andrew C. Parnell3, Donald L. Phillips4, Stuart Bearhop5, Richard Inger6, Andrew Jackson7, Jonathan W. Moore8

1Scripps Institution of Oceanography, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92039-0202, USA
2Conservation Biology Division, Northwest Fisheries Science Center, National Marine Fisheries Service, National Oceanic and Atmospheric Administration, 2725 Montlake Blvd. East, Seattle, Washington 98112, USA
3School of Mathematical Sciences (Statistics), Complex and Adaptive Systems Laboratory, University College Dublin, Ireland
4U.S. Environmental Protection Agency, National Health and Environmental Effects Research Laboratory, Western Ecology Division, 200 SW 35th St., Corvallis, Oregon 97333, USA
5Centre for Ecology and Conservation, School of Biosciences, University of Exeter, Exeter EX4 4SB, UK
6Environment and Sustainability Institute, School of Biosciences, University of Exeter, Exeter EX4 4SB, UK
7Department of Zoology, School of Natural Sciences, and Centre for Biodiversity Research, Trinity College Dublin, Dublin 2, Ireland
8Earth to Ocean Research Group, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia V5A 1S6, Canada

ABSTRACT: Fry (2013; Mar Ecol Prog Ser 472:1–13) reviewed approaches to solving underdetermined stable isotope mixing systems, and presented a novel approach based on graphical summaries. He inaccurately characterized the statistics and interpretation of outputs from IsoSource and more recent Bayesian mixing model tools (e.g. SIAR, MixSIR), however, and as an alternative promoted an approach—not based on likelihood methods—that uses graphing and 2 new metrics for tracking source contributions to a mixture. Fry’s approach does not provide statistical probability densities associated with source contribution parameter estimates, has little applicability to complex mixing systems such as hierarchical models, and relies on the subjective interpretation of graphing products. We clarify the analytic theory underlying common mixing model approaches and provide an analysis of the 4-source, 2-tracer underdetermined mixing system example in Fry (2013), using both a Bayesian mixing model and Fry’s graphical analysis and summary metrics. We demonstrate that properly interpreted Bayesian approaches yield distributions of parameter estimates that can reflect multi-modality, covariance and parameter uncertainty.

KEY WORDS: Bayesian mixing model · SIAR · MixSIR · IsoSource

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Cite this article as: Semmens BX, Ward EJ, Parnell AC, Phillips DL and others (2013) Statistical basis and outputs of stable isotope mixing models: Comment on Fry (2013). Mar Ecol Prog Ser 490:285-289.

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