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

Abstract

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.

Resource use of great hammerhead sharks (Sphyrna mokarran) off eastern Australia

“…Once corrected for trophic enrichment, the stable‐isotope values of δ 13 C, δ 15 N and δ 34 S of great hammerhead tissues were generally within the isoscape produced by the stable‐isotope values of the potential sources included here, meeting the assumption that Bayesian isotope mixing models should not be outside the isoscape (Phillips et al ., ; Stock et al ., ). Great hammerhead liver tissues were more depleted in 13 C and 15 N than muscle tissues from the same individuals and the δ 34 S values of liver tissues were more variable than those of muscle tissues (Figure ).…”

“…Prior to running Bayesian stable‐isotope mixing models, reducing the number of possible sources can reduce noise and inaccuracies in the results (Parnell et al ., ; Stock et al ., ). Since we had isotopic data on three dimensions (each isotope tracer) that were not independent from each other for each potential source, a pairwise permutational analysis of variance (PERMANOVA) was run using the vegan package in R using the pairwise.adonis function (Dixon, ).…”

“…The total number of sources is still lower than the > seven recommended upper limit outlined in Stock et al . ().…”

“…To determine the contribution of the sampled prey items to the short‐term (liver) and long‐term (muscle) diets of great hammerheads, δ 13 C, δ 15 N and δ 34 S values were analysed with a Bayesian mixing model using the MixSIAR package in R (Stock et al ., ). Tissue type (muscle or liver) was used as a fixed factor to differentiate temporal contributions to diets.…”

“…Model run length was set to very long to assure Gelman and Geweke diagnostics were within acceptable ranges as explained in Stock et al . (). All analyses were conducted in R version 3.4.4.…”