Application of Response Surface Methodology in Modelling and Optimization of The Yields of Common Bean (Phaseolus Vulgaris L.) using Animal Organic Manures

Abstract

The objective of design and analysis of experiments is to optimize a response which is influenced by several independent variables. In agriculture, many statistical studies have focused on investigating the effect of application of organic manure on the yield and yield components of crops. With most of these studies showing a clear positive effect of application of organic manures on the yield and yield components of various crops. However, many of these studies do not try to optimize the application of the manures for maximum productivity, but select the best treatment among the treatment range used. This is mainly due to design and analysis of experiments applied. Therefore, there is a need to apply a statistical method that would establish the effect of the application of organic manures on crop production and in addition optimize the levels of application of these manures for maximum productivity. This study aimed at application of response surface methodology for optimization of the yields of common bean (Phaseolus Vulgaris L.) using animal organic manure. The study was conducted at Chuka University Horticultural Demonstration Farm. An experiment laid down in a Randomized Complete Block Design was used. The treatments consisted of three organic manure sources (cattle manure, poultry manure and goat manure) each at three levels (0, 3 and 6 tonnes per ha). Data was collected from six weeks after sowing to physiological maturity. Data collected included the number of pods per plant grain yields at harvest. The data collected was subjected to analysis of variance and multiple Regression Analysis using the R-statistical software. The Central Composite Design was used to develop a second order polynomial model, with a goal of optimizing the multiple responses of common beans to animal organic manure. The findings indicated that there was a positive response of the goat and the poultry manure (p < 0.05) to common bean performance with the interaction of poultry and goat yielding the best results (p-value=1.51E-07)<0.05. Cattle manure did not significantly increase performance of common beans. This could be attributed to slow realise of nutrients and low N content in cattle manure. It was concluded that more use of poultry and goat would increase the yields of common beans in the area of study. The recommended levels of application of the manures in the area of study were 2.1608 t ha-1, 12.7213 t ha-1 and 4.1417 t ha-1 cattle manure, poultry manure and goat manure respectively. These are the optimum levels that would lead to maximum yield of common beans without an extra cost of input.