Mathematical Assessment of Three-Year Field Performance and Growth Promotion Efficiency of Bacillus pumilus and Bacillus thuringiensis in Brassica juncea

<title>Abstract</title> <p> Yellow leaf disease caused by <italic>Fusarium equiseti</italic> has emerged as a serious constraint to mustard ( <italic>Brassica juncea</italic> L.) production, resulting in substantial reductions in plant growth and yield. The present study aimed to identify the causal pathogen of yellow leaf disease and evaluate the plant growth-promoting, biocontrol, and induced systemic resistance (ISR) potential of two rhizospheric bacterial isolates. Diseased mustard leaves collected from Uttar Dinajpur district, West Bengal, India, yielded a fungal isolate (MUSLD-01), which was identified as <italic>Fusarium equiseti</italic> through morphological, scanning electron microscopic, and molecular analyses. Two rhizospheric bacterial isolates were identified as <italic>Bacillus pumilus</italic> (GenBank accession ON783696) and <italic>Bacillus thuringiensis</italic> (GenBank accession OQ415951) based on 16S rDNA sequencing. Both isolates exhibited multiple plant growth-promoting traits, including indole-3-acetic acid production, phosphate solubilization, siderophore production, and catalase activity. In vitro dual culture assays demonstrated pronounced antagonistic activity against <italic>F. equiseti</italic> , with <italic>B. thuringiensis</italic> exhibiting comparatively greater inhibition of mycelial growth. GC–MS analysis of ethyl acetate extracts of bacterial culture filtrates revealed diverse antifungal bioactive metabolites associated with pathogen suppression. A three-year field evaluation (2023–24 to 2025–26) involving three mustard varieties (B-9, B-54, and NYC) demonstrated consistent improvements in plant height, leaf length, root length, and seed yield following PGPR inoculation. Among the tested treatments, <italic>B. pumilus</italic> produced the greatest growth promotion and yield enhancement, while both bacterial isolates substantially reduced the adverse effects of <italic>F. equiseti</italic> under field conditions. Mathematical assessment of growth response indicated approximately 19–20% improvement in vegetative growth, 34–36% enhancement in seed yield, and about 31–33% greater root development in PGPR-treated plants compared with untreated controls. Enhanced activities of phenylalanine ammonia-lyase, peroxidase, chitinase, and β-1,3-glucanase further confirmed activation of induced systemic resistance. Collectively, the integration of microbiological, biochemical, mathematical, and multi-year field evidence demonstrates that <italic>B. pumilus</italic> and <italic>B. thuringiensis</italic> are promising eco-friendly biocontrol agents and plant growth-promoting rhizobacteria for the sustainable management of mustard yellow leaf disease and improvement of crop productivity. </p>