Beyond simple linear mixing models: Process-based isotope partitioning of ecological processes

Stable isotopes are valuable tools for partitioning the components contributing to ecological processes of interest, such as animal diets and trophic interactions, plant resource use, ecosystem gas fluxes, streamflow, and many more. Stable isotope data are often analyzed with simple linear mixing (SLM) models to partition the contributions of different sources, but SLM models cannot incorporate a mechanistic understanding of the underlying processes and do not accommodate additional data associated with these processes (e.g., environmental covariates, flux data, gut contents). Thus, SLM models lack predictive ability. We describe a process-based mixing (PBM) model approach for integrating stable isotopes, other data sources, and process models to partition different sources or process components. This is accomplished via a hierarchical Bayesian framework that quantifies multiple sources of uncertainty and enables the incorporation of process models and prior information to help constrain the source-specific proportional contributions, thereby potentially avoiding identifiability issues that plague SLM models applied to "too many" sources. We discuss the application of the PBM model framework to three diverse examples: temporal and spatial partitioning of streamflow, estimation of plant rooting profiles and water uptake profiles (or water sources) with extension to partitioning soil and ecosystem CO2 fluxes, and reconstructing animal diets. These examples illustrate the advantages of the PBM modeling approach, which facilitates incorporation of ecological theory and diverse sources of information into the mixing model framework, thus enabling one to partition key process components across time and space.