A quantitative approach to combine sources in stable isotope mixing models

Abstract

Abstract. Stable isotope mixing models, used to estimate source contributions to a mixture, typically yield highly uncertain estimates when there are many sources and relatively few isotope elements. Previously, ecologists have either accepted the uncertain contribution estimates for individual sources or addressed the problem in an ad hoc way by combining either related sources prior to analysis or the estimated proportions of related sources following analysis. Neither of these latter approaches explicitly account for uncertainty in source combinations within the likelihood framework. In this paper we incorporate uncertainty in both the number of source groups and group assignment within a formal Bayesian mixing model framework. By dynamically exploring model complexity due to aggregating sources based on shared proportional contributions, we can estimate posterior probabilities of alternative group configurations, and construct posterior dendrograms of group membership. We apply this method to simulated data, and illustrate applications to two consumer datasets (rainbow trout, coastal mink). Our results demonstrate that estimating, rather than fixing, the number of proportional contributions in a mixing model can improve model inference and reduce bias in estimates of source contributions to a mixture.

Bias in Diet Determination: Incorporating Traditional Methods in Bayesian Mixing Models

“…It is well known in Bayesian analysis that prior information may strongly affect the posterior distribution only when the data contain a modest amount of information allowing discriminate single prey contributions to the diet [29]. The latter would happen when prey isotopic contents have a large overlap in isotopic space [48–50], as it is the case of Argentine anchovy and Argentine shortfin squid (Figure 2). In such cases where overlapping isotopic data does not allow differentiating the relative contribution of each prey species, the SIMM-UP renders each of these preys have a similar importance in the predators’ diets, with a relative large uncertainty shows as a wide CIs (Figure 1).…”

“…We believe that the only answer to the potential biases induced by prior information in SIMMs can come from using extensive knowledge on the natural histories of studied species and of habitats so as to interpret potential differences in the posterior distributions arising from using different priors [50]. Our studied objects were two sympatric pinnipeds species breeding in rookeries along the Uruguayan coast.…”

Intrapopulation variations in diet and habitat use in a marine apex predator, the broadnose sevengill shark Notorynchus cepedianus

“…Quantitative mixing models were not used because of the poor source geometry of mixing models, coupled with the relatively large number of prey species consumed in each area (Barnett et al 2010b). Moreover the relative uncertainty of δ 13 C and δ 15 N trophic fractionation for elasmobranchs means that mixing models will not lead to conclusive results if used to determine the diet composition (Phillips & Gregg 2003, Bond & Diamond 2011, Ward et al 2011. Also, sevengills seasonally move out of these coastal habitats (Barnett et al 2011), and this coupled with the relatively slow turnover rate of elasmobranch muscle (MacNeil et al 2006) means that muscle isotope composition will not fully equilibrate with local sources and will not accurately reflect the diet in these habitats.…”

Is Bocourt’s Terrific Skink Really So Terrific? Trophic Myth and Reality

“…Moreover, because δ 13 C and δ 15 N discrimination factors (i.e. the difference between the isotopic signature of the consumer and that of its prey) remain relative uncertain for terrestrial reptiles (and especially P. bocourti ), mixing models will not lead to conclusive results if used to determine the diet composition [43,51-53]. To date, only one study has estimated this parameter in skinks and only for carbon [54,55].…”