Analysis Of Epistatic: A Genetic Model For Triploid Endosperms Traits

The concept of epistasis was introduced nearly 100 years ago and has been proved important to understand the genetic variation and genetic breeding. Many evidences have been found that the additive by additive (AA) epistasis can be inherited stably. But in classical quantitative genetics, the epistasis was always ignored in seed traits. In classical quantitative genetics, the diallel cross was always conducted to understand the genetic backgrounds of many agronomy traits and seed traits. Researchers conducted the artificial selection based on diallel cross to improve the quantity and quality of some traits, such as the quality and quantity of the rice, according to the phenotype improvement or genotype improvement.In present work, a genetic model of diploid endosperm traits was proposed for analyzing additive by additive epistasis of direct effect (AA) and maternal effect (AmAm) along with direct additive effect, dominance effect, cytoplasm effect, as well as maternal additive and dominance effects. The genetic model was constructed according to the modified diallel crosses. The analysis for the genetic model was based on the mixed linear model approach in matrix form. We used minimum norm quadratic unbiased estimation (MINQUE) methods with 1 for all prior components (MINQUE (1)) to estimate the variance components for single trait and covariance components between two traits. The statistical method, adjusted unbiased prediction (AUP), was used to predict the random effect vectors. The jackknife procedure was conducted to estimate the variance of the estimates. And one-tail /-test was used to test the zero variation of the variance components for single trait. The two-tail /-test was used to test zero correlation of the covariance components between two traits and to test the zero effect of the random effect vectors.Monte Carlo simulations were conducted to test the estimation of genetic parameters and the robust of the genetic model. Both balanced design and unbalanced design based on modified diallel crosses were constructed for simulation analysis. The simulation results indicated that both balanced design and unbalanced design had the similar efficiency for estimating the variance components for single trait and covariance components between two traits. The results also suggested that the additive by additive epistatic variation could be detected significantly. The power of the additive by additiveepistatic variance was almost equal to one. And when there was no direct additive variation, the additive by additive epistatic variation also could be detected significantly.A worked example in rice endosperm traits was used to illuminate the application of analyzing additive by additive epistatic variation. It was suggested that the epistasis could influence the genetic variation with the absence of additive effect. It also indicated that the result would be more accurate for estimating the heritability and breeding value based on the additive by additive epistatsis than only based on the additive effects.