An expectation and maximization algorithm for estimating Q X E interaction effects.

A Markov chain Monte Carlo (MCMC) implemented Bayesian method has been developed to detect quantitative trait loci (QTL) effects and Q x E interaction effects. However, the MCMC algorithm is time consuming due to repeated samplings of QTL parameters. We developed an expectation and maximization (EM) algorithm as an alternative method for detecting QTL and Q x E interaction. Simulation studies and real data analysis showed that the EM algorithm produced comparable result as the Bayesian method, but with a speed many magnitudes faster than the MCMC algorithm. We used the EM algorithm to analyze a well known barley dataset produced by the North American Barley Genome Mapping Project. The dataset contained eight quantitative traits collected from 150 doubled-haploid (DH) lines evaluated in multiple environments. Each line was genotyped for 495 polymorphic markers. The result showed that all eight traits exhibited QTL main effects and Q x E interaction effects. On average, the main effects and Q x E interaction effects contributed 34.56 and 16.23% of the total phenotypic variance, respectively. Furthermore, we found that whether or not a locus shows Q x E interaction does not depend on the presence of main effect.