The EIM algorithm in the joint segregation analysis of quantitative traits

In this article, a new algorithm for obtaining the maximum likelihood estimators (MLEs) of parameters in the joint segregation analysis (JSA) of multiple generations of P1, F1, P2, F2 and F2:3 (MG5) for quantitative traits was set up. Firstly, owing to the fact that the component variance of the heterogeneous genotype in F2:3 included both the first-order genetic parameters (denoted by the means of distributions) and the second-order parameters, a simple closed form for the MLEs of the means of component distributions did not exist while the expectation and maximization (EM) algorithm was used. To simplify the estimation of parameters, the first partial derivative of the above variance on the mean in the sample log-likelihood function was omitted. However, this would be remedied by the iterated method. Then, variances of component distributions for segregating populations were partitioned into major-gene, polygenic and environmental variances so that the generally iterated formulae for estimating the means as well as polygenic and environmental variances of component distributions in the maximization step (M-step) of the EM algorithm were obtained. Therefore, the EM algorithm for estimating parameters in the JSA model for the MG5 was simplified. This is called the expectation and iterated maximization (EIM) algorithm. Finally, an example of the inheritance of the resistance of soybean to beanfly showed that the results of mixed inheritance analysis in this paper coincided with those in both Wang & Gai (2001) and Wei et al. (1989), so the EIM algorithm was appropriate.