A comparison of SIMM assumptions and features among commonly used SIMMs.

<p>Four mixing model assumptions (italics) commonly violated when estimating the proportional dietary contribution of sources to the diets of animals, and the model feature that addresses each violated assumption. A list of other features included in SIMMs and their definitions. X denotes the model addresses the assumption or includes the feature and Y indicates the feature is not explicitly included (e.g., model may account for error using an arbitrary tolerance measure). MCMC (Markov chain Monte Carlo), SIR (sequential importance resampling), and ML (maximum likelihood) denotes sampling method used when estimating parameters.</p>a<p>X denotes that the model provides solutions when sources exceed <i>n</i>+1, but solutions are not comparable to other models (i.e., output lists ranges of potential solutions, not parameter estimates).</p>b<p>X indicates Ward et al. (35) was the first study to use this approach. However, this model (35) has recently been introduced; therefore, it has not been commonly used.</p

Dietary estimates generated by IsotopeR and the Semmens et al. model.

<p>Proportional dietary estimates (marginal posterior probability distributions) for individual bears (<i>n</i> = 11) estimated by IsotopeR (blue lines) and the Semmens et al. model (orange lines). Dotted lines denote population-level dietary estimates.</p

Isotopic mixing space for FC black bears sampled in Yosemite National Park.

<p>Isotope values (δ¹³C and δ¹⁵N) for male bears (open circles) captured in YNP and their estimated food sources. Estimated means for source aggregates (100% plant diet [green circle], 100% animal diet [orange circle], 100% human food diet [blue circle]) and process error (1 SD; dashed ovals) were estimated by IsotopeR and defined the vertices of the dietary mixing triangle; the shape of each source aggregate illustrates the degree of estimated isotopic correlation of observations used to define each source (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0028478#pone-0028478-g004" target="_blank">Fig. 4</a>). Variations in dietary contributions (%) of plants (P), animals (A), and human food (HF) are shown along the edge of the mixing triangle (solid gray line) that connects estimated source means; labels denote the contribution of diet when consumers lie at the intersection of the mixing triangle edge and gray dashed iso-diet lines (within the triangle). The black dashed triangle illustrates the approximate total mixing space at 1 SD. Measurement error (not shown) was also estimated by IsotopeR and applied to each source observation when estimating source aggregates and to each bear in the mixing space. The inset illustrates the isotopic mixing space if concentration dependence was not included in the analysis.</p

Model comparisons.

<p>Means and 95% credible intervals (denoted by error bars) calculated by IsotopeR (blue circles) and other Bayesian (orange circles) models. The blue dashed line and gray bar indicates the estimated mean and 95% credible interval for the full IsotopeR model, respectively. Frequentist (open black circles with confidence intervals) and data cloning estimates (open green circles) are also illustrated.</p

Selecting the best stable isotope mixing model to estimate grizzly bear diets in the Greater Yellowstone Ecosystem

<div><p>Past research indicates that whitebark pine seeds are a critical food source for Threatened grizzly bears (<i>Ursus arctos</i>) in the Greater Yellowstone Ecosystem (GYE). In recent decades, whitebark pine forests have declined markedly due to pine beetle infestation, invasive blister rust, and landscape-level fires. To date, no study has reliably estimated the contribution of whitebark pine seeds to the diets of grizzlies through time. We used stable isotope ratios (expressed as <i>δ</i>¹³C, <i>δ</i>¹⁵N, and <i>δ</i>³⁴S values) measured in grizzly bear hair and their major food sources to estimate the diets of grizzlies sampled in Cooke City Basin, Montana. We found that stable isotope mixing models that included different combinations of stable isotope values for bears and their foods generated similar proportional dietary contributions. Estimates generated by our top model suggest that whitebark pine seeds (35±10%) and other plant foods (56±10%) were more important than meat (9±8%) to grizzly bears sampled in the study area. Stable isotope values measured in bear hair collected elsewhere in the GYE and North America support our conclusions about plant-based foraging. We recommend that researchers consider model selection when estimating the diets of animals using stable isotope mixing models. We also urge researchers to use the new statistical framework described here to estimate the dietary responses of grizzlies to declines in whitebark pine seeds and other important food sources through time in the GYE (e.g., cutthroat trout), as such information could be useful in predicting how the population will adapt to future environmental change.</p></div