Combining sources in stable isotope mixing models: alternative methods

Abstract

Stable isotope mixing models are often used to quantify source contributions to a mixture. Examples include pollution source identification; trophic web studies; analysis of water sources for soils, plants; or water bodies, and many others. A common problem is having too many sources to allow a unique solution. We discuss two alternative procedures for addressing this problem. One option is a priori to combine sources with similar signatures so the number of sources is small enough to provide a unique solution. Aggregation should be considered only when isotopic signatures of clustered sources are not significantly different, and sources are related so the combined source group has some functional significance. For example, in a food web analysis, lumping several species within a trophic guild allows more interpretable results than lumping disparate food sources, even if they have similar isotopic signatures. One result of combining mixing model sources is increased uncertainty of the combined end-member isotopic signatures and consequently the source contribution estimates; this effect can be quantified using the IsoError model (http://www.epa.gov/wed/pages/models/isotopes/isoerror1_04.htm). As an alternative to lumping sources before a mixing analysis, the IsoSource mixing model (http://www.epa.gov/wed/pages/models/isosource/isosource.htm) can be used to find all feasible solutions of source contributions consistent with isotopic mass balance. While ranges of feasible contributions for each individual source can often be quite broad, contributions from functionally related groups of sources can be summed a posteriori, producing a range of solutions for the aggregate source that may be considerably narrower. A paleo-human dietary analysis example illustrates this method, which involves a terrestrial meat food source, a combination of three terrestrial plant foods, and a combination of three marine foods. In this case, a posteriori aggregation of sources allowed strong conclusions about temporal shifts in marine versus terrestrial diets that would not have otherwise been discerned.

Resource partitioning among top predators in a Miocene food web

“…Because the carnivoran teeth analysed here were found as isolated fossils in Batallones-1 and it was not possible to group the teeth by individuals, we treated each carnivoran tooth as a different individual and compared their d 13 C values to the average d 13 C values of feasible prey in terms of body size (see below). In ISOSOURCE, it is desirable that dietary sources exhibit distinctly different d 13 C values in order to obtain clear discrimination among potential prey [48,51]. Although our results show considerable overlap among potential prey species, the ISOSOURCE analysis was useful in estimating the proportional contributions of each prey species to a particular carnivoran diet [51].…”

“…In ISOSOURCE, it is desirable that dietary sources exhibit distinctly different d 13 C values in order to obtain clear discrimination among potential prey [48,51]. Although our results show considerable overlap among potential prey species, the ISOSOURCE analysis was useful in estimating the proportional contributions of each prey species to a particular carnivoran diet [51].…”

Stable nitrogen isotope patterns of trees and soils altered by long-term nitrogen and phosphorus addition to a lowland tropical rainforest

“…As a result of the elimination of DON as a potential source, a better constrained two-source mixing model termed IsoError (Phillips et al 2005) was used on a plot level instead. This Excel-based model propagates plot-scale variances associated with plant and soil measurements as it solves for the proportional fraction (f ) of mineral N used by each species following mass balance mixing models:…”

Water uptake from different soil depths for halophytic shrubs grown in Northern area of Ningxia plain (China) in contrasted water regimes

“…To determine the fractional contribution of water sources to studied species, the IsoSource program was used (http://www.epa.gov/wed/pages/models/ stableIsotopes/isosource/isosource.htm) (Phillips et al 2005). Totally, there were 11 source endpoints, i.e.…”