Table 1 Approaches to partitioning more than two sources*.

From: A dual-isotope approach to allow conclusive partitioning between three sources

Approach

Limitations †

Advantages

For example

1. Additive approach: Include treatments without a given component, and then subtract the effects of the simpler system from the more complex system to estimate the effect of the component alone

Excludes the potential to detect any interactive effects and thus will not work for systems where components behave differently when isolated—that is, does not truly allow for three-source partitioning

Does not require additional treatments; likely least expensive method due to fewer isotopically labelled components

36, 37

2. Modelling approach: Use modelling to calculate a range of possible partitions and their associated probabilities

Can only provide a range of solutions, which may not be optimal for some study questions

Provides probability distribution of solutions; explicitly accounts for natural underlying variation in isotopic composition of the sources

6, 13, 14

3. Multiple element approach: Use combinations of multiple elements (for example, C and/or N and/or O)

The range of applications is limited to systems where the different elements persist and/or cycle together

Does not require additional treatment; could provide additional insight due to multiple elements

8, 38

4. Multiple isotope approach: Use two stable isotopes and a radioisotope (for example, 12C, 13C and 14C)

14C in soils is highly heterogeneous at natural abundance levels; enriched levels of 14C are highly regulated and generally cannot be used outside the laboratory; analyses can be expensive

Allows for conclusive three-source partitioning; highly enriched 14C could allow for high sensitivity

39

5. Combined sources approach: Collapse into what is effectively a two-source system, where all but one source (or groups of sources) have the same isotopic signature. To isolate individual components, the labelled source can be switched

Requires that at least two pairs of different sources are found or created with identical isotopic signatures without changing their other properties; some sources (particularly, soil) are extremely difficult to label evenly; even if the two sources have the same bulk isotopic signature, it is virtually impossible to find two sources that generate the same isotopic signal over time and space when they are controlled by different external factors (for example, soil CO2 emissions versus plant root respiration); likely requires isotopically labelled materials

In the right system, can allow conclusive three-source partitioning

40, 41

6. Three-source dual-isotope approach: Use dual treatments with different isotope ratios for the same component

Likely requires isotopically labelled materials

Allows for conclusive three-source partitioning

This study

  1. *Further examples, including a worked example of the additive approach, can be found in Supplementary Note 1, Supplementary Table 1 and Supplementary Fig. 1.
  2. †All stable isotopic methods suffer from the limitation that isotopic fractionation may occur during biological and chemical transformations. Thus, identifying the appropriate end-members, or isotopic signatures, for the sources is essential.
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