Do commercial nitrogen-fixing and biostimulant inputs add agronomic value over standard fertilization? An equivalence-based reanalysis of three randomized field trials in the Brazilian Cerrado

Abstract Commercial inoculants based on associative diazotrophs and methylotrophic bacteria, and biostimulant programs, are marketed for broad use in cereal and fiber production, yet most field deployment occurs over already adequate mineral fertilization, where their marginal value is poorly quantified. We reanalyzed three randomized complete-block trials conducted at commercial scale in the Brazilian Cerrado (Sao Desiderio, Bahia) under full conventional fertilization: corn (seven treatments, four blocks; 2023/24), cotton (five treatments, four blocks; 2024/25), and soybean (four treatments, six blocks; 2024/25). Treatments evaluated Azospirillum brasilense, Methylobacterium symbioticum, Bradyrhizobium spp., a Bacillus phosphorus solubilizer, and biostimulants, applied via seed and foliar routes. Beyond conventional analysis of variance, we fit mixed models with block as a random effect, quantified effect sizes and coefficients of variation, computed the minimum detectable difference at 80% power, and applied two one-sided equivalence tests (TOST) against the untreated control at margins of plus or minus 10% and 15% of control yield. No treatment produced a statistically significant yield gain in any crop (all p greater than 0.8; fixed and mixed models concordant). In cotton, the best-powered trial (coefficient of variation 6%), all treatments were statistically equivalent to the untreated control within a 10% margin, an affirmative negative result. In corn and soybean the trials were underpowered (minimum detectable difference 21 to 26% of control), so non-significance is not equivalence; corn showed non-significant numerical gains up to 8.9% with phosphorus-solubilizer and methylotroph combinations that could not be excluded. Foliar nutrient concentrations (single composite per treatment, descriptive) showed no enrichment in inoculated treatments. Under standard fertilization, these commercial inputs delivered no detectable agronomic value where the data were adequately powered to test it. The results clarify the low empirical bar that current associative-fixation products meet in the field and, by extension, the agronomic threshold that engineered, plant-controlled nitrogen fixation must exceed to be useful.