. 2023 Feb 3;13:1041124. doi: 10.3389/fmicb.2022.1041124

Table 10.

Different methodologies and principles to assess biological N-fixation.

S.No.	Method	Principle	Formula	References
1.	N differences	The difference in total N accumulation in the shoot of the legume crop and control crop is determined as symbiotic N fixation	Q = [N yield (legume) – N yield (control)] + [N soil (legume) – N soil (control)]	Peoples et al. (1989)
2.	Nodule tissue	Total N plant α nodule tissue formed (weight)	Regression equation: NF = b X	Döbereiner (1966)
3.	N yields	Linear relationships with N yields	BNF (kg N ha⁻¹year⁻¹) $= [α c u l t \times \frac{Y}{N H I} + β c u l t] \times B G N$	Anglade et al. (2015)
4.	Isotope dilution method
a.	Natural ¹⁵N abundance	With increasing N fixation, there is a decline in the abundance of ¹⁵N in the N₂-fixing plant as N assimilation from the soil is diluted by atmospheric N of lower ¹⁵N abundance fixed in root nodules of plant	$P = 100 \times \frac{δ^{15} N (s o i l N) - δ^{15} N (l e g u m e N)}{(δ^{15} N (s o i l N) - B)}$	Peoples et al. (1989)
			$% N = 100 \times \frac{(^{15} N_{r e f}) - (^{15} N_{l e g})}{(^{15} N_{r e f} - B)}$	Chalk and Craswell (2018)
b.	¹⁵N enrichment method		$P = 100 \times 1 - \frac{(a t o m s %^{15} N e x c e s s i n l e g u m e N)}{(a t o m s %^{15} N e x c e s s i n s o i l d e r i v e d N)}$	Peoples et al. (1989)
5.	Acetylene reduction by the enzyme nitrogenase	Detection of nitrogenase activity (as nitrogenase reduces acetylene to ethylene)	ARA = Nitrogenase activity × dry weight of the nodules	Chalk and Craswell (2018)
6.	Xylem (Ureide) solute technique	Differences in xylem N solute concentration between symbiotic plants and non-nodulated plants to assess their dependency on N fixation/soil mineral N	$R e l a t i v e u r e i d e i n d e x (%) = \frac{(U r e i d e N)}{(T o t a l s a p N)} \times 100$	Peoples et al. (1989)
7.	Empirical models	Pre-defined N fixation rate α to harvested yield, plant N concentration and total N derived from N fixation	Nfix = α · DM · f_leg · N_con · %Ndfa · (1 + R_root)	Liu et al. (2011)
8.	Simulation models	Pre-defined N fixation rate (Nfix) is estimated concerning response functions (soil/plant water status, soil temperature, soil/plant N concentration, C supply and growth stage of the crop)	Nfix = Nfixpot fT fW fN fC fgro	Liu et al. (2011)

2^* NF, N fixed; b, regression slope of total plant N with nodule weight; X, corresponding nodule weight.

3^* α_cult and β_cult, slope and intercept coefficients; Y, yield (kg N ha⁻¹ year⁻¹); NHI, N harvest index; BG, factor determining below-ground contributions, i.e., nodules, roots and rhizodeposition (factor 1.3 for pulses).

4^* P, percentage of pulse N fixed from atmospheric N; δ¹⁵N (soil N), obtained from non-N fixing plant grown in the same soil as a pulse; B, δ¹⁵N of N fixing plant grown with N as the sole source of N (values varies with different legumes); ¹⁵N_ref, abundance of the ¹⁵N isotope in the reference plant; ¹⁵N_leg, abundance of the ¹⁵N isotope in the pulse.

7^* DM, yield; f_leg, legume proportion (if intercropped); N_con, N concentration in pulse; %Ndfa, total N proportion derived from N fixation; R_root, ratio of fixed N below and above ground.

8^* Nfixpot, N fixation rate (g N fixed day⁻¹); fT – Soil temperature function, fW – Soil water status function; fN – Soil mineral N/root substrate N concentration function; fC – Substrate C concentration in plant/root function; fgro – Crop growth stage.