An Exploration of Temporal Yield Dynamics in Hydroponic Cucumber Treated with Foliar Biostimulants Using Functional Data

Abstract

The present study explored the dynamic effects of foliar biostimulants on cucumber (Cucumis sativus var. Centauro) accumulated yield curves using a novel statistical approach: Functional Data Analysis (FDA). Four treatments were tested: T1 (control, water), T2 (seaweed extract with N, K, B, Zn), T3 (high Mg, B, Zn), and T4 (T2 + T3). Yield was measured over four harvest cuts. FDA modelled cumulative yield as continuous functions. Functional principal component analysis identified one major mode of variation, revealing an accelerated yield response between the second and third cuts, especially for T4. A functional generalized regression detected significant treatment effects (p = 0.029), which were not detected by a traditional repeated-measures ANOVA (p = 0.074). The results showed that FDA captures subtle, time-dependent growth dynamics missed by conventional methods. The combination treatment (T4) maximized yield via early-phase acceleration, highlighting a synergistic biostimulant effect. FDA provided a superior analytical framework for understanding continuous crop responses to biostimulants.