Analyzing mixing systems using a new generation of Bayesian tracer mixing models

The ongoing evolution of tracer mixing models has resulted in a confusing array of software tools that differ in terms of data inputs, model assumptions, and associated analytic products. Here we introduce MixSIAR, an inclusive, rich, and flexible Bayesian tracer (e.g., stable isotope) mixing model framework implemented as an open-source R package. Using MixSIAR as a foundation, we provide guidance for the implementation of mixing model analyses. We begin by outlining the practical differences between mixture data error structure formulations and relate these error structures to common mixing model study designs in ecology. Because Bayesian mixing models afford the option to specify informative priors on source proportion contributions, we outline methods for establishing prior distributions and discuss the influence of prior specification on model outputs. We also discuss the options available for source data inputs (raw data versus summary statistics) and provide guidance for combining sources. We then describe a key advantage of MixSIAR over previous mixing model software—the ability to include fixed and random effects as covariates explaining variability in mixture proportions and calculate relative support for multiple models via information criteria. We present a case study of Alligator mississippiensis diet partitioning to demonstrate the power of this approach. Finally, we conclude with a discussion of limitations to mixing model applications. Through MixSIAR, we have consolidated the disparate array of mixing model tools into a single platform, diversified the set of available parameterizations, and provided developers a platform upon which to continue improving mixing model analyses in the future.

[1]  Daniel E. Schindler,et al.  Including source uncertainty and prior information in the analysis of stable isotope mixing models. , 2010, Environmental science & technology.

[2]  Michael T. Brett,et al.  Resource polygon geometry predicts Bayesian stable isotope mixing model bias , 2014 .

[3]  S. Hurlbert.  Pseudoreplication and the Design of Ecological Field Experiments , 1984 .

[4]  Donald A. Jackson.  COMPOSITIONAL DATA IN COMMUNITY ECOLOGY: THE PARADIGM OR PERIL OF PROPORTIONS? , 1997 .

[5]  M. McCarthy.  Bayesian Methods for Ecology: Frontmatter , 2007 .

[6]  A. Bond,et al.  Recent Bayesian stable-isotope mixing models are highly sensitive to variation in discrimination factors. , 2011, Ecological applications : a publication of the Ecological Society of America.

[7]  M. M. Szepanski,et al.  Assessment of anadromous salmon resources in the diet of the Alexander Archipelago wolf using stable isotope analysis , 1999, Oecologia.

[8]  Richard McElreath,et al.  Statistical Rethinking: A Bayesian Course with Examples in R and Stan , 2015 .

[9]  Richard Inger,et al.  Best practices for use of stable isotope mixing models in food-web studies , 2014 .

[10]  James T. Thorson.  Standardizing compositional data for stock assessment , 2014 .

[11]  Eric J Ward,et al.  Improving Bayesian isotope mixing models: a response to Jackson et al. (2009). , 2009, Ecology letters.

[12]  Eric J Ward,et al.  Habitat structure determines resource use by zooplankton in temperate lakes. , 2011, Ecology letters.

[13]  Maya S. deVries,et al.  Specialized morphology corresponds to a generalist diet: linking form and function in smashing mantis shrimp crustaceans , 2016, Oecologia.

[14]  John K Kruschke,et al.  Bayesian data analysis. , 2010, Wiley interdisciplinary reviews. Cognitive science.

[15]  Avner Vengosh,et al.  Environmental impacts of the Tennessee Valley Authority Kingston coal ash spill. 1. Source apportionment using mercury stable isotopes. , 2013, Environmental science & technology.

[16]  Brian Fry,et al.  Alternative approaches for solving underdetermined isotope mixing problems , 2013 .

[17]  Jake M. Ferguson,et al.  Estimating the Diets of Animals Using Stable Isotopes and a Comprehensive Bayesian Mixing Model , 2012, PloS one.

[18]  Donald L. Phillips,et al.  Mangrove-Exported Nutrient Incorporation by Sessile Coral Reef Invertebrates , 2009, Ecosystems.

[19]  David W. Welch,et al.  δ13C‐δ15N values as indicators of trophic position and competitive overlap for Pacific salmon (Oncorhynchus spp.) , 1993 .

[20]  Michael T. Brett,et al.  Quantitative estimates of isopod resource utilization using a Bayesian fatty acid mixing model , 2014 .

[21]  George W. Kling,et al.  Stable Isotopes Resolve the Drift Paradox for Baetis Mayflies in an Arctic River , 1993 .

[22]  Kiona Ogle,et al.  Beyond simple linear mixing models: process-based isotope partitioning of ecological processes. , 2014, Ecological applications : a publication of the Ecological Society of America.

[23]  Roger Jones,et al.  Seasonal changes in the importance of the source of organic matter to the diet of zooplankton in Loch Ness, as indicated by stable isotope analysis , 2001 .

[24]  C. Field,et al.  QUANTITATIVE FATTY ACID SIGNATURE ANALYSIS: A NEW METHOD OF ESTIMATING PREDATOR DIETS , 2004 .

[25]  FrancisR.I.C. Chris,et al.  Data weighting in statistical fisheries stock assessment models , 2011 .

[26]  Brian C Stock,et al.  Unifying error structures in commonly used biotracer mixing models. , 2016, Ecology.

[27]  M. J. V. Zanden,et al.  PRIMARY CONSUMER δ13C AND δ15N AND THE TROPHIC POSITION OF AQUATIC CONSUMERS , 1999 .

[28]  D. Phillips,et al.  Bayesian stable isotope mixing models , 2012, 1209.6457.

[29]  H. Schwarcz,et al.  Some theoretical aspects of isotope paleodiet studies , 1991 .

[30]  John Aitchison,et al.  The Statistical Analysis of Compositional Data , 1986 .

[31]  Donald L. Phillips,et al.  Combining sources in stable isotope mixing models: alternative methods , 2005, Oecologia.

[32]  Richard Inger,et al.  Source Partitioning Using Stable Isotopes: Coping with Too Much Variation , 2010, PloS one.

[33]  William H. Blake,et al.  Tracing crop-specific sediment sources in agricultural catchments , 2012 .

[34]  R. Tolosana-Delgado,et al.  Compositional data analysis with ‘R’ and the package ‘compositions’ , 2006, Geological Society, London, Special Publications.

[35]  Chris T. Darimont,et al.  Quantifying Inter- and Intra-Population Niche Variability Using Hierarchical Bayesian Stable Isotope Mixing Models , 2009, PloS one.

[36]  Brice X Semmens,et al.  Incorporating uncertainty and prior information into stable isotope mixing models. , 2008, Ecology letters.

[37]  David R. Anderson,et al.  Model selection and multimodel inference : a practical information-theoretic approach , 2003 .

[38]  A. Jansen.  Bayesian Methods for Ecology , 2009 .

[39]  Olaf P. Jensen,et al.  Bayesian estimation of predator diet composition from fatty acids and stable isotopes , 2015, PeerJ.

[40]  Michael T. Brett,et al.  A Fatty Acid Based Bayesian Approach for Inferring Diet in Aquatic Consumers , 2015, PloS one.

[41]  Ronald P. Barry,et al.  Analysis of stable isotope data : A K nearest-neighbors randomization test , 1998 .

[42]  Andrew Parnell,et al.  Bias in Diet Determination: Incorporating Traditional Methods in Bayesian Mixing Models , 2013, PloS one.

[43]  Terry D. Beacham,et al.  Overwinter shifts in the feeding ecology of juvenile Chinook salmon , 2017 .

[44]  Stuart Bearhop,et al.  Factors That Influence Assimilation Rates and Fractionation of Nitrogen and Carbon Stable Isotopes in Avian Blood and Feathers , 2002, Physiological and Biochemical Zoology.

[45]  Richard Inger,et al.  Statistical basis and outputs of stable isotope mixing models: Comment on Fry (2013) , 2013 .

[46]  Vladimir Batagelj,et al.  Compositional data analysis with R , 2003 .

[47]  Justin D. Yeakel,et al.  Tools for quantifying isotopic niche space and dietary variation at the individual and population level , 2012 .

[48]  Aki Vehtari,et al.  Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC , 2015, Statistics and Computing.

[49]  C. Layman,et al.  Size, sex and individual-level behaviour drive intrapopulation variation in cross-ecosystem foraging of a top-predator. , 2015, The Journal of animal ecology.

[50]  D. Phillips.  Mixing models in analyses of diet using multiple stable isotopes: a critique , 2001, Oecologia.

[51]  Andrew L Jackson,et al.  Erroneous behaviour of MixSIR, a recently published Bayesian isotope mixing model: a discussion of Moore & Semmens (2008). , 2009, Ecology letters.

[52]  D. Phillips,et al.  Source partitioning using stable isotopes: coping with too many sources , 2003, Oecologia.

[53]  M. Ben‐David,et al.  Annual and seasonal changes in diets of martens: evidence from stable isotope analysis , 1997, Oecologia.

[54]  Nicolaas Bouwes,et al.  A quantitative approach to combine sources in stable isotope mixing models , 2011 .

[55]  David T. Bilton,et al.  Intercolony movement of pre‐breeding seabirds over oceanic scales: implications of cryptic age‐classes for conservation and metapopulation dynamics , 2014 .

[56]  Martyn Plummer,et al.  JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling , 2003 .

[57]  A. Gelman.  Analysis of variance: Why it is more important than ever? , 2005, math/0504499.