Simplex-centroid mixture design reveals pathogen-dependent interaction structure in a camphene–d-limonene–eucalyptol system against three phytopathogenic fungi and oomycetes

The increasing limitations of synthetic fungicides have intensified interest in sustainable, plant-derived alternatives. A simplex–centroid mixture design with Scheffé special-cubic modelling was used to optimize a ternary monoterpene system (camphene, d -limonene, eucalyptol) against three phytopathogenic fungi and oomycetes representing diverse infection strategies: Macrophomina phaseolina , Phytophthora infestans , and Verticillium dahliae . Twelve formulations (pure compounds, binary blends, and ternary mixtures) were assayed by broth microdilution. Individually, the three monoterpenes were weak antifungal agents (MIC 150–500 µg/mL); ternary formulations reduced MIC values markedly, to 12.5 µg/mL at two of the design points used to fit the M. phaseolina model. The fitted models were statistically significant for all three targets (R 2 = 0.8940, 0.9604 and 0.9400; R 2 adj = 0.7668, 0.9130 and 0.8680; p = 0.0023–0.0246); because the modal-MIC reporting convention yields zero pure error, lack of fit could not be tested, and the models are presented as descriptive representations of the response surface within the tested compositional region rather than as externally validated predictors. They revealed pathogen-dependent interaction structure: binary interactions dominated for M. phaseolina , a ternary interaction dominated for P. infestans , and both contributed for V. dahliae , indicating that antifungal activity is primarily driven by non-additive mixture effects, that is, significant departures from linear blending of the pure components, rather than by single-compound dominance. Desirability-based optimization identified an interior formulation (camphene 0.3643, d -limonene 0.2967, eucalyptol 0.3390) with a composite desirability of 0.998; because the individual desirabilities saturate once their targets are met, this composition lies within a broader domain of near-equivalent blends rather than being a unique optimum. At this composition the model predicted MIC values of 16 ± 45 µg/mL for M. phaseolina , 41 ± 22 µg/mL for P. infestans and 74 ± 11 µg/mL for V. dahliae (predicted value ± standard error of prediction). This composition was then prepared and assayed independently of the design runs, in three biological replicates on separate days; the experimentally determined MIC values were 15.625 µg/mL (modal) for M. phaseolina , 50 µg/mL (median of 31.25, 50 and 62.5 µg/mL) for P. infestans and 62.5 µg/mL (modal) for V. dahliae , each within one two-fold dilution step of its prediction (observed/predicted = 1.00, 1.22 and 0.85, respectively; t(6) = 0.861, p = 0.422; t(6) = 1.166, p = 0.288; t(6) = − 1.841, p = 0.115). Relative to the most active pure monoterpene assayed in parallel, the optimised blend was 16.0-fold more potent against M. phaseolina , 5.0-fold against P. infestans and 2.4-fold against V. dahliae , and the three pathogens differed in susceptibility to it (one-way ANOVA F(2,6) = 12.24, p = 0.0076). Overall, this study demonstrates that mixture-design-driven statistical optimization can identify monoterpene compositions with substantially lower in vitro MIC values than their individual components. These in vitro results provide a quantitative starting point for future greenhouse and field evaluation, phytotoxicity assessment, and formulation development, none of which is reported here.