Methodological uncertainty in resource mixing models for generalist fishes

Carbon and nitrogen stable isotope ratios are used to assess diet composition by determining bounds for the relative contributions of different prey to a predator's diet. This approach is predicated on the assumption that the isotope ratios of predator tissues are similar to those of dominant food sources after accounting for trophic discrimination (Delta (x) X), and is formulated as linear mixing models based on mass balance equations. However, Delta (x) X is species- and tissue-specific and may be affected by factors such as diet quality and quantity. From the different methods proposed to solve mass balance equations, some assume Delta (x) X to be exact values whilst others (based on Bayesian statistics) incorporate variability and inherent uncertainty. Using field data from omnivorous reef fishes, our study illustrates how uncertainty may be taken into account in non-Bayesian models. We also illustrate how dietary interpretation is a function of both absolute Delta (x) X and its associated uncertainty in both Bayesian and non-Bayesian isotope mixing models. Finally, collated literature illustrate that uncertainty surrounding Delta (x) X is often too restricted. Together, these data suggest the high sensitivity of mixing models to variation in trophic discrimination is a consequence of inappropriately constrained uncertainty against highly variable Delta (x) X. This study thus provides guidance on the interpretation of existing published mixing model results and in robust analysis of new resource mixing scenarios.