Optimizing sweet potatoes yield: advanced modelling With augmented second-order rotatable designs using Trigonometric Functions

Abstract

Food security faces significant threats from climate change, population growth, and economic pressures. Despite efforts to improve productivity, distribution, and sustainable agriculture, many regions still remain insecure. Optimizing sweet potato yield requires carefully designed experiments to identify key yield-enhancing factors. The main objective of this study was to optimize sweet potato yield through advanced modelling with augmented second order rotatable design using trigonometric functions. The specific objectives were to: construct augmented second order rotatable designs in three dimensions; determine optimality criteria D-, A-, T- and E- for augmented second order rotatable designs; examine the relative efficiencies for augmented second order rotatable designs and apply augmented second-order rotatable designs to obtain design points that optimize sweet potato yield. The study transformed cyclic coordinates into Cartesian form to create numerical sequences used in moment conditions for developing diverse sets, which were further augmented to yield second-order rotatable designs in three- dimensional space. The evaluation of each design's performance and its relative efficiency involved the application of optimality criteria, such as D-, A-, T-, and E-criteria. The augmented second-order rotatable design was fitted to the data to obtain design points that optimize sweet potato yield. The R statistical software was used for modeling and analysis while Python was used in the construction of the design and evaluation of optimality criteria. The three augmented second order rotatable designs in three dimensions were successfully constructed. Generally, the twenty three point second order rotatable design turned out to be the most optimal and efficient design. Goat manure significantly outperformed poultry and rabbit manure, quadratic effects and interactions among poultry, rabbit, and goat manure also played a crucial role in boosting sweet potato yield. The study found that the optimal levels of poultry manure, rabbit manure, and goat manure that led to maximum yield were 35g/hole, 25g/hole and 45g/hole respectively. The application of these specific quantities resulted in the highest yield performance of 4kg/mounding. In conclusion, the study developed an optimal and efficient augmented second-order rotatable design. This advanced design was subsequently applied to effectively optimize sweet potato yield, demonstrating its practical utility in enhancing agricultural productivity. It is recommended that agricultural practitioners should consider integrating goat manure into sweet potato farming practices to optimize yield. The study underscores the importance of advanced experimental designs in agriculture for further research, promoting more efficient and sustainable farming techniques.