Estimation of variance for reciprocal general and specific combining ability effects by EM-AI algorithm

Abstract

In diallel analysis, using mixed models, it is possible to estimate the variance components of general combining ability (GCA), specific combining ability (SCA), reciprocal GCA (RGCA), reciprocal SCA (RSCA), and parents, even in unbalanced datasets. These variances can be estimated by likelihood maximization via numerical algorithms (e.g., expectation maximization [EM] and average information [AI]), which have different advantages. Thus, the objective of this study was to describe and implement the EM-AI algorithm (combination of EM and AI) in R software to estimate the variance components of RGCA, RSCA, and parents effects in diallel analysis. Two real datasets and three diallel models (Griffing’s Model 1, Griffing’s Model 1 + RGCA, and Model 3, a general diallel model with the effects of GCA, SCA, RGCA, RSCA, and parents) were used to evaluate the efficiency of the algorithms AI, EM, and EM-AI. The AI algorithm failed to converge for the three diallel models in both datasets. The other algorithms (EM and EM-AI) converged normally, and the estimated variance components with these algorithms were similar for the three diallel models in both datasets. However, the EM-AI algorithm was more efficient than the EM algorithm, and the general diallel model (Model 3) provided more accurate estimates of variance parameters. Thus, the EM-AI algorithm with routine implemented in R has potential for use in diallel analyses in plant breeding.