Analytic methods for seed models with genotype x environment interactions

Genetic models with genotype effect (G) and genotype x environment interaction effect (GE) are proposed for analyzing generation means of seed quantitative traits in crops. The total genetic effect (G) is partitioned into seed direct genetic effect (G0), cytoplasm genetic of effect (C), and maternal plant genetic effect (Gm). Seed direct genetic effect (G0) can be further partitioned into direct additive (A) and direct dominance (D) genetic components. Maternal genetic effect (Gm) can also be partitioned into maternal additive (Am) and maternal dominance (Dm) genetic components. The total genotype x environment interaction effect (GE) can also be partitioned into direct genetic by environment interaction effect (G0E), cytoplasm genetic by environment interaction effect (CE), and maternal genetic by environment interaction effect (GmE). G0E can be partitioned into direct additive by environment interaction (AE) and direct dominance by environment interaction (DE) genetic components. GmE can also be partitioned into maternal additive by environment interaction (AmE) and maternal dominance by environment interaction (DmE) genetic components. Partitions of genetic components are listed for parent, F1, F2 and backcrosses. A set of parents, their reciprocal F1 and F2 seeds is applicable for efficient analysis of seed quantitative traits. MINQUE(0/1) method can be used for estimating variance and covariance components. Unbiased estimation for covariance components between two traits can also be obtained by the MINQUE(0/1) method. Random genetic effects in seed models are predictable by the Adjusted Unbiased Prediction (AUP) approach with MINQUE(0/1) method. The jackknife procedure is suggested for estimation of sampling variances of estimated variance and covariance components and of predicted genetic effects, which can be further used in a t-test for parameter. Unbiasedness and efficiency for estimating variance components and predicting genetic effects are tested by Monte Carlo simulations.