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.

Otolith δ13C values as a metabolic proxy: approaches and mechanical underpinnings

“…This method provides the likelihood of a given M oto term determined using Bayesian methods and considering the uncertainty of the two sources in terms of d 13 C DIC and d 13 C diet variations. It also facilitates comparing metabolic performance (M oto term) between fish populations, and is easy to conduct within the well-established R software package MixSIAR (see https://github.com/brianstock/MixSIAR, accessed 21 March 2019; Stock et al 2018).…”

Exploring variability in the diet of depredating sperm whales in the Gulf of Alaska through stable isotope analysis

“…The trophic level calculation is represented by [38,63,64]. These models use Bayesian methods to account for uncertainty in input parameters, such as source isotope ratios and TEFs [37,38,64].…”

Food Web Structure and Trophic Dynamics of a Fish Community in an Ephemeral Floodplain Lake

“…To investigate the proportional contribution of resources underpinning Lake Liambezi food webs separately for each year, Bayesian mixing models (MixSIAR; Stock and Semmens, 2016;Stock et al, 2018) were run using stable isotope data from all primary consumers (and some secondary consumers) (see Table 1) with n ≥ 10 in both 2011 and 2012 (raw data), food sources (mean ± 1 SD) and discrimination factors of 1.5 ± 0.5‰ for δ 13 C and 3.2 ± 0.5‰ for δ 15 N as described above. The model was run with Markov chain Monte Carlo (MCMC) parameters of three chains of 300,000 iterations, a burn-in phase of 200,000 and a thinning of 100.…”

“…Convergence and diagnostic statistics were evaluated using the Gelman-Rubin test (all variables were ≤1.05). Note that while Bayesian mixing models can include some variability in predictions through the incorporation of error terms and informative priors (Parnell et al, 2010;Stock et al, 2018), there remains a mismatch in time integration between food resources and consumers, with the latter being typically more time integrated (Phillips et al, 2014). Thus, predicted proportional resource contributions to Lake Liambezi food webs will likely display some variation over time.…”