Optimization of Organic and Inorganic Fertilizer Mixtures for Improving Potato Yield Using A Simplex-Centroid Mixture Design

Declining soil fertility and poor fertilizer management practices are among the common production limiting factors in potato (Solanum tuberosum L.). Combined use of organic and inorganic fertilizers under integrated nutrient management has been suggested as a sustainable approach to improve crop productivity while conserving soil health. The study was conducted to assess the combined effect of organic and inorganic fertilizer mixtures on marketable potato tubers design in a simplex-centroid mixture structure arranged in randomized complete block design. Eight fertilizer treatments consisting of farmyard manure (FYM), Diammonium Phosphate (DAP), Baraka, Yara and Farmer’s Practice were evaluated over two growing seasons. Linear and Quadratic Scheffè models were fitted to characterize component effects and interactions using the Simple Centroid mixture design.
The linear model showed that the fitted model was statistically significant (F = 52.18, df = 3, 37, 𝑝 < 0.001 ), indicating that the mixture components jointly influence potato yield in the first season. It also showed that in the second season all three components significantly influence the marketable number of tubers.
A quadratic Scheffé mixture model was fitted to investigate the combined effects of fertilizer component proportions on marketable number of tubers. In the first season, the fitted quadratic model was statistically significant (F = 30.29, df = 5, 35, 𝑝 < 0.001), indicating that the mixture terms collectively influence potato yield. The model explained approximately 81.2% of the variability in yield (𝑅2 = 0.8123), with an adjusted 𝑅2 of 0.7854. In the second season, the model demonstrates strong explanatory power with 𝑅2 = 0.9094, adjusted 𝑅2 = 0.8965.. This indicates that approximately 90.9% of the variability in the marketable number of tubers is explained by the mixture components and their interactions.
The first-order Scheffé mixture model revealed that 𝑥3 had the largest estimated linear coefficient. The effect of 𝑥3 was, however, not statistically significant in either growing season, suggesting that its apparent importance was not statistically secure after accounting for the nonlinear blending effects. Across all trials, the results indicated that additive effects predominated with few significant quadratic interactions.

Potato yield, marketable number of tubers, Scheffé model, Fertilizer optimization, Canonical analysis

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