Functional Data Analysis of Foliar Biostimulant Effects on Cucumber (Cucumis sativus) Yield Dynamics in Hydroponic Greenhouse Cultivation

This study evaluated the effect of foliar application of biostimulants on cucumber crops (Cucumis sativus var. Centauro) under greenhouse conditions in a hydroponic system with a substrate. Applications were made every 15 days after transplanting to analyze the influence of biostimulants on fruit productivity over four cuts. Treatments were as follows: T1 (control, water), T2 (algal extract with bioactive compounds from Ascophyllum nodosum, N, K, B and Zn), T3 (foliar formulation with a high concentration of Mg, B and Zn), and T4 (a mixture of T2 and T3). Additionally, a nutrient solution with 14N, 1.5P, 7K, 8Ca, 2.5Mg and 3S was supplied during the production cycle. This study also applied Functional Data Analysis (FDA) to evaluate the dynamic responses of accumulated cucumber yield. Raw data were converted into continuous functions and functional principal component analysis (FPCA) was used to decompose yield trajectories into principal components for each treatment. FDA revealed significant (p = 0.04) treatment effects, with biostimulant treatments exhibiting shapes similar to each other but different from T1. Functional principal component analysis (FPCA) identified one major variation mode (94.3% variance) linked to an increased response or acceleration between the second and third cut, particularly for T4. Functional ANOVA also confirmed significant (p < 0.01) treatment effects between these cuts, which was not observed with traditional repeated-measures ANOVA, as total harvest weight per cut was not affected by the application of biostimulants (P≥0.9). T4 (algal extract + Mg-B-Zn) maximized yield via early-phase acceleration. FDA captured continuous yield dynamics, revealing inflection points commonly missed by traditional methods.