## 2 Materials and Methods
### Nitrogenase Activity and Nutrient Solubilization Assays of Plant Growth-Promoting Bacteria  
Nitrogenase activity was measured by acetylene reduction assay (ARA). Ethylene absorption in ARA was determined spectrophotometrically since the change in the absorbance over time is linear with nitrogenase activity [48; 49; 50]. A total of 1 mL of NFB culture was added to a 13 mL glass vial with 1 mL of air replaced with the same volume of acetylene (99.99% purity). After culturing at 28 \({}^{\circ}\)C for 24 h, the bacterial sample was mixed with 2 mL of saturated NaCl solution. A total of 200 \(\mu\)L of the mixture (10% gas concentration) was then extracted and added to the absorption buffer (5.0 g/L CuSO\({}_{4}\), 5.3 g/L ammonia, 23 g/L NH\({}_{2}\)OH-HCl, 0.9 g/L gelatin, 31.6% ethanol). The optical density (OD) was measured at 548 nm after shaking the mixture for 5 min. Blank medium without NFB inoculation was used as the mock control.  
To measure inorganic phosphorus solubilization, bacterial strains were inoculated to inorganic phosphorus screening medium (10 g/L glucose, 0.5 g/L (NH\({}_{4}\))\({}_{2}\)SO\({}_{4}\), 0.2 g/L NaCl, 0.2 g/L KCl, 0.03 g/L MgSO\({}_{4}\)\(\cdot\)7H2O, 0.03 g/L MnSO\({}_{4}\), 0.003 g/L FeSO\({}_{4}\), 0.5 g/L yeast extract, 5.0 g/L Ca\({}_{3}\)(PO4)\({}_{2}\), 15 g/L agar, pH 6.8-7.0) and cultured at 30 \({}^{\circ}\)C for 3 d. Inorganic phosphorus solubilization was indicated by the emergence of clear halos on the plates, with halo sizes positively correlated to solubilization activity. Similarly, organic phosphorus solubilization was tested by inoculating the bacterium to egg yolk medium (10 g/L tryptone, 3.0 g/L beef extract, 5.0 g/L NaCl, 15 g/L agar, pH 7.0-7.5; add 3 mL of fresh egg yolk to a 50 mL medium plate before use) and checking the formation of turbid halos after incubation at 30 \({}^{\circ}\)C for 3 d.  
To measure potassium solubilization, bacterial strains were inoculated to silicate medium (10 g/L sucrose, 0.5 g/L yeast extract, 1.0 g/L (NH4)2 SO4, 2.0 g/L Na2 HPO4, 0.5 g/L MgSO4.7H2O, 1.0 g/L CaCO3, 1.0 g/L potash feldspar powder, 15 g/L agar) and incubated at 30 \({}^{\circ}\)C for 3 d. The emergence of clear halos on silicate plates indicated successful solubilization of inorganic potassium, with halo sizes positively correlated to bacterial potassium solubilization activity.  
Bacterial IAA production was quantified by using the [PERSON] reagent (a fresh mixture solution of 0.5 M FeCl3 and 35% HClO4) to generate a standard curve [51]. A total of 50 \(\upmu\)L of bacterial culture at the logarithmic growth phase was inoculated to the beef extract liquid medium containing 0.5 g/L tryptophan. After shaking at 140 rpm and 28 \({}^{\circ}\)C for 36 h, 50 \(\upmu\)L of activated bacterial culture at the logarithmic growth phase were mixed with the [PERSON] reagent and incubated (avoid light) at 25 \({}^{\circ}\)C for 30 min. Bacterial IAA production was indicated by the emergence of pink color in the solution. IAA-producing bacterial cultures were then centrifugated at 8000\(\times\)_g_ for 5 min. A total of 2 mL of supernatant from each strain was mixed with 4 mL of the Salkowski reagent and incubated (avoid light) at 25 \({}^{\circ}\)C for 30 min. IAA production was quantified by measuring ODs at 530 nm with three biological replicates performed for each sample. The standard curve was generated by using a concentration gradient of eight IAA standards for Salkowski reactions and subsequent OD measurements. In all inorganic/organic phosphorus and potassium solubilization and IAA production assays, all the bacterial samples were tested in the same batch to facilitate side-by-side activity comparisons.