When isotopes aren't enough: Using additional information to constrain mixing problems

Stable isotopes are often used as chemical tracers to determine the relative contributions of sources to a mixture. Ecological examples include partitioning pollution sources to air or water bodies, trophic links in food webs, plant water use from different soil horizons, sources of respired C from ecosystems, etc. With n isotopic tracers, mixing models based on isotopic mass balance can solve for n+1 source contributions. With >n+1 sources, there is no unique solution but mixing models can still place bounds on source contributions. Often these bounds are wide, limiting ecological insights based on isotopic evidence alone. However, researchers often have other ecological knowledge that can be used to further constrain these broad limits of source contributions. For example, in an animal dietary study, data on gut contents, prey abundance, etc. may be applied to filter out sets of source proportions that are not ecologically feasible even if they satisfy isotopic mass balance. One approach is to use the IsoSource model to provide the full range of solutions that satisfy isotopic mass balance, then to trim these results by imposing other non-isotopic constraints. We outline the specific procedure for this approach, and demonstrate it on three varied ecological studies that utilized stable isotope analysis to quantify source contributions. The first example analyzes contributions of various organic C pools to CO₂ release in a forest fire, reflecting C pool sizes and logical rankings of the completeness of combustion (e.g., bark>wood). The second example examines plant water use from different soil horizons, constrained by soil water potential. The third example analyzes food sources for a carnivore, with constraints on prey availability. These examples demonstrate that other types of information can be fruitfully combined with stable isotope data to provide improved resolution of source contributions in mixing problems.