Classical response surface designs for fertilizer trials in sesame (Sesamum indicum L.)

Abstract

The research work entitled “Classical response surface designs for fertilizer trials in sesame (Sesamum indicum L.)” was carried out at Onattukara Regional Agricultural Research Station, Kayamkulam and College of Agriculture, Vellayani during 2020-2022. The study's objectives were to identify classical response surface designs suitable for obtaining optimum fertilizer dose for sesame, identify the limitations and advantages of the designs and provide suitable modifications, and develop open-source software for response surface methodology in agriculture. Response surface methodology will be used to find the optimal fertilizer dose of sesame under Central Composite Circumscribed (CCC), Central Composite Inscribed (CCI) and Box- Behnken Design (BBD). And the designs will be compared based on the best-fit model. The CCC and CCI design consists of 20 experimental runs and under the BBD design there were 15 experimental runs. The dosage of N, P and K taken for central points were 48, 35 and 25 respectively. The levels were selected based on the package of practice recommendations (KAU, 2016) and on the basis of preliminary soil tests. Since three factors were chosen for the experiment, the α value was ± 1.682. The experiment was conducted and observations were recorded. The average seed yield obtained under CCC, CCI and BBD were 480.75 kg ha1 , 463 kg ha-1 and 475.13 kg ha-1 respectively. From analysis, it was observed that all the eigenvalues were negative so the stationary point maximized the response. The three models (CCC, CCI, BBD) created in this study were a good fit with an insignificant lack of fit (p >0.05) at the 95% confidence level. Statistically, the better models are influenced by the multiple R2 and adjusted R2 values. Both R2 values are essential for model fitting. A higher value of R2 showed that the model could explain the result successfully. Multiple R2 values of 0.94, 0.92, and 0.97 were found for the quadratic models created using CCC, CCI, and BBD, respectively. The quadratic models' adjusted R2 scores were 0.89, 0.84, and 0.92. In all three models, R 2 values were found to be greater than 0.8 indicating a good fit of the models. Among the three models, BBD had higher R2 values than CCC and CCI, so the quadratic model developed through BBD had good predictability compared to other models. The response models were estimated using R for seed yield. The best model was obtained under the design BBD. The equational form of the Response model was given, Y= 537.333 (17.871) + 53.625 N* (10.944) + 80.125 P* (10.944) + 90.750 K* (10.944) - 49.750 N* P* (15.476) + 14.0 N* K* (15.476) +38.0 P* K* (15.476) – 14.792 N*2 (16.108) – 47.292 P*2 (16.108) – 54.542 K*2 (16.108) Where the Seed yield (Y) was the dependent variable and coded N* , P* and K* as the independent variable. The optimum levels of N, P and K for the Thilak variety obtained under CCC were 65.06 kg ha-1 , 40.88 kg ha-1 and 34.40 kg ha-1 respectively. The optimum N, P and K levels obtained under CCI were 69.58 kg ha-1 , 46.35 kg ha-1 and 36.15 kg ha-1 . Under BBD the optimum levels of N, P and K obtained were 67.17 kg ha-1 , 45.69 kg ha-1 and 36.11 kg ha-1 . The results show that the model developed under BBD was best-fit, so the optimum N, P and K doses for the Thilak variety of sesame were 67.17, 45.69, and 36.11 kg ha-1 . In the Onattukara region, the recommended dose of N, P and K as per the package of practice recommendations for sesame is 30:15:30 kg/ha (KAU, 2016). The obtained N, P and K ratio was higher compared to the recommended levels, this may be because of the fact that the initial soil nutrient levels were low. Since the soil in Onattukara is sandy, there will be more nutrient leaching. This could also contribute to greater N, P, and K levels obtained. An open-source user-friendly RSM package aimed for benefiting agricultural researchers in optimizing the response of interest was developed. This RSM package was based on Central composite design and Box-Behnken design (BBD) in Response surface methodology. The software consists of two types of Central composite design (i.e., circumscribed CCD and inscribed CCD) and Box-Behnken design. The package has 3 sections. The first section is for design generation where one can generate CCD and BBD designs without any code. In the second section, one can do the analysis of the CCD and BBD. The third section consists of graphs and plots, here the users can generate the 2D contour plots and the 3D surface plots for further analysis. The results of RSM analysis using CCC, CCI and BBD concluded that BBD was the good fit model with higher multiple and adjusted R2 values. The optimum dose of N, P and K for Thilak variety of sesame obtained under BBD was 67.17, 45.69 and 36.11 kg ha1 . A web application for RSM in agriculture with CCD and BBD for 2 and 3 factors was also developed using R.