## Theory of Estimate Calculation

In stable N tracer studies, only the two 14N and 15N isotopes are available, thus only two sources can be identified. If more than two sources are present, only the contribution of two aggregated pools can be identified (Shearer and Kohl 1993). The fractional contribution of source A to a sink S can be calculated by a simple linear interpolation of the sink 15N abundance between the two extreme poles represented by the abundance of the two sources. The following calculation is used (alternatively, atom% N or d15N can be used):

d15N source B — d15N source A

In natural abundance studies, the isotopic discrimination is likely to have a strong influence on the results of the estimation, since isotopic alteration is of the same order of magnitude as the difference between sources. The closer the 15N abundance of the two sources, the more important it becomes to take the isotopic discrimination into account.

Isotopic discrimination can lead not only to a shift in isotopic composition of the N actually transformed, but also to an alteration of the original 15N abundance of sources as a consequence of isotope accumulation due to different transformation rates. The N source can only be identified if the 15N abundance of N sources is measurably different after they have undergone isotopic discrimination. Thus, in natural abundance studies, it is fundamental that calculations refer to d15N of the sources after isotopic discrimination has altered both the N flow and the source N abundance (Shearer and Kohl 1993). When evaluating the contribution of a source to an N flow, it may also be important to evaluate the real variability of sources and sinks, not only the measurement error. Examples of calculations can be found in Shearer and Kohl (1993).

As previously explained, with only two tracers, no more than two sources can be discriminated. However, this drawback can be overcome by using the isotopes of other elements as additional tracers. Oxygen, carbon or others are commonly used (Oelmann et al. 2007). The use of more than one isotope is also useful for distinguishing between the processes that contribute to a certain product (Kool et al. 2009, 2011).

In the following sections, three applications to estimate the source contribution to a sink are presented (1) tracing N in landscapes, (2) symbiotic N2 fixation and (3) quantification of N dynamics in soil-plant systems.