# Linear Mixed Model for Genotype Selection of Sorghum Yield
## 1 Introduction  
Sorghum (_Sorghum bicolor_ ([PERSON]) is a flowering plant found in arid and semi-arid regions of the world. It serves as a primary source of food [1, 2]. It accounts for 43% of all major food staples available for consumption in Sub-Saharan Africa [3]. The production of sorghum is the fourth in Ethiopia following maize, wheat, and teff. In Ethiopia, farmers consumed 70.43% of sorghum production for their household food consumption, and the rest of the sorghum production used for animal feed and in-kind utility to farmers [4].  
Sorghum production is mainly measured through phenotypic characteristics, of which grain yield is the main component of the characteristics. The phenotypic characteristics of cereal crops are affected by genotype effects, environmental conditions (stress), and the interactions between the genotype and the environment [5]. The studies found that there was a significant difference among genotypes on yield and yield-related traits andalso indicated the effect of drought stress on sorghum production. The analysis of these studies was performed using ANOVA, which considers all the factors as fixed effects, and multivariate analysis techniques, particularly cluster analysis and principal component analysis [6; 7]  
The investigator who compared the analysis of variance (ANOVA) and the mixed model used the Best Linear Unbiased Predictor (BLUP) to evaluate location-specific genotypic effects for rape cultivars with random locations, and the result indicated that the mixed model provided both high prediction and more efficiency in the prediction of the location specific genotype effects for rape traits with random locations [8; 9].  
In ANOVA, the performance of the genotypes that have a higher grain yield of sorghum is obtained using the arithmetic mean of the grain yield of the genotypes within the replications, which depends on the Best Linear Unbiased Estimator (BLUE) of the general linear model. However, when the number of genotypes is large, considering the genotype effects as random may be preferable, instead of being considered as fixed effects using various classical analyses such as ANOVA and additive main effect multiplicative interaction. The partition of the outcome of the genotype is based on the BLUP, which helps to select the best genotype by ranking the estimates of the grain yield in a mixed model, which incorporates both the fixed and random effects [7; 9; 10]  
The selection of genotypes, having the higher genetic gain of the genotypes for future sorghum production and breeding through BLUP, has an advantage in identifying the ranks of the genotypes by the prediction of the sorghum, as BLUP has a property of shrinkage towards the mean, which increases the accuracy by reducing the mean square error. Thus, it maximizes the association of the true and predicted genotypic values [9].  
The purpose of this study is to select the best genotypes that have high yield performance using a mixed model, compare the yield performance of genotypes through arithmetic mean and BLUP selection techniques of sorghum by considering genotypes as random effects, and determine the impact of drought on sorghum production in Ethiopia.  
The paper is organized into four sections that include the methodology, result, discussion, and conclusion of the study. Section 2 contains the methodology that explains the design of experiment and variables in the study as well as the statistical model description of the paper. Section 3 contains the results of the study that explores the descriptive summary of the data and the result of the analysis of genotype selection through the linear mixed model. Sections 4 and 5 present the study's discussion and conclusion, respectively.