In plant breeding, multienvironment trials (MET) may include sets of related genetic strains. In self‐pollinated species the covariance matrix of the breeding values of these genetic strains is equal to the additive genetic covariance among them. This can be expressed as an additive relationship matrix, A, multiplied by the additive genetic variance. Using Mixed Model Methodology, the genetic covariance matrix can be estimated and Best Linear Unbiased Predictors (BLUPs) of the breeding values obtained. The effectiveness of exploiting relationships among strains tested in METs and usefulness of these BLUPs of breeding values for simultaneously modeling the main effects of genotypes and genotype × environment interaction (GE) have not been thoroughly studied. In this study, we obtained BLUPs of breeding values using genetic variance–covariance structures constructed as the Kroneker product (direct product) of a structured matrix of genetic variances and covariances for sites and a matrix of genetic relationships between strains, A. Results are compared with those from traditional fixed effects and random effects models for studying GE ignoring genetic relationships. A CIMMYT international wheat trial was used for illustration. Results showed that direct products of factor analytic structures with matrix A efficiently model the main effects of genotypes and GE. These models showed the lowest standard error of the BLUPs [SE(BLUP)] of breeding values. Genotypes that were related to other genotypes had small SE(BLUP). Related genotypes can clearly be visualized in biplots.

In self‐pollinated species, the variance–covariance matrix of breeding values of the genetic strains evaluated in multienvironment trials (MET) can be partitioned into additive effects, additive × additive effects, and their interaction with environments. The additive relationship matrix A can be used to derive the additive × additive genetic variance–covariance relationships among strains, Ã. This study shows how to separate total genetic effects into additive and additive × additive and how to model the additive × environment interaction and additive × additive × environment interaction by incorporating variance–covariance structures constructed as the Kronecker product of a factor‐analytic model across sites and the additive (A) and additive × additive relationships (Ã), between strains. Two CIMMYT international trials were used for illustration. Results show that partitioning the total genotypic effects into additive and additive × additive and their interactions with environments is useful for identifying wheat (Triticum aestivum L.) lines with high additive effects (to be used in crossing programs) as well as high overall production. Some lines and environments had high positive additive × environment interaction patterns, whereas other lines and environments showed a different additive × additive × environment interaction pattern.

Pongamia pinnata, commercially important tree species used to produce biofuels, is known for its multipurpose benefits and its role in agro-forestry. Present study examines the amenability of vegetative propagation and effect of maturation in candidate plus tree P. pinnata through rooting of stem cuttings treated with varying concentrations and combinations of auxins. The performance of the cuttings was evaluated using SAS GLM software and the data were analyzed as a one-way classified data with and without sub sampling for inferring auxin concentration that can be included in programmes aimed at genetic improvement of the tree species. All auxin treatments promoted sprouting and at lower concentrations triggered/enhanced rooting of cuttings. The effectiveness was in the order of IBA [ NAA [ IAA when applied singly. IBA at 4.92 mM was found to be most effective where rooting percentage and number of roots were significantly higher (P \ 0.01) than in control. However higher concentrations of auxins above 7 mM in general inhibited the rooting of cuttings. The interaction among auxins was found to be effective in root induction and differentiation and the most stimulating effects were observed in three-component mixture. The effect of other cutting characteristics such as juvenility and cutting position on rooting is also discussed.

Candidate plus trees (CPTs) of Pongamia pinnata, a potential biodiesel plant occurring across 10 locations in North Guwahati, were identified based on morphological markers (vegetative and reproductive) using combined analysis over locations. Identified CPTs were then multiplied using seed propagation technique in a nursery bed. The performance of the candidate trees with respect to seed and pod traits, the two most important characters with regard to oil, were evaluated using CROPSTAT software for inferring potential genotypes that can be included in programmes aimed at genetic improvement of the species. Total oil content from the seeds of plus trees was also analysed using solvent extraction procedure at their boiling points. Hexane extraction yielded maximum oil content from seeds (33%) compared with petroleum ether (30%). When the seed to solvent ratio varied, no significant difference was noticed on the total oil yield for an individual tree, although the recovery of solvent and the time taken for oil extraction were significantly reduced at higher ratios of solvent used.