Mixed model formulations for multi-environment trials

When studying genotype X environment interaction in multi-environment trials, plant breeders and geneticists often consider one of the effects, environments or genotypes, to be fixed and the other to be random. However, there are two main formulations for variance component estimation for the mixed model situation, referred to as the unconstrained-parameters (UP) and constrained-parameters (CP) formulations. These formulations give different estimates of genetic correlation and heritability as well as different tests of significance for the random effects factor. The definition of main effects and interactions and the consequences of such definitions should be clearly understood, and the selected formulation should be consistent for both fixed and random effects. A discussion of the practical outcomes of using the two formulations in the analysis of balanced data from multi-environment trials is presented. It is recommended that the CP formulation be used because of the meaning of its parameters and the corresponding variance components. When managed (fixed) environments are considered, users will have more confidence in prediction for them but will not be overconfident in prediction in the target (random) environments. Genetic gain (predicted response to selection in the target environments from the managed environments) is independent of formulation.

Application of the cross-entropy method to the buffer allocation problem in a simulation-based environment

The buffer allocation problem (BAP) is a well-known difficult problem in the design of production lines. We present a stochastic algorithm for solving the BAP, based on the cross-entropy method, a new paradigm for stochastic optimization. The algorithm involves the following iterative steps: (a) the generation of buffer allocations according to a certain random mechanism, followed by (b) the modification of this mechanism on the basis of cross-entropy minimization. Through various numerical experiments we demonstrate the efficiency of the proposed algorithm and show that the method can quickly generate (near-)optimal buffer allocations for fairly large production lines.

Measurement and management of genotype-environment interaction (GxE) for the improvement of rainfed lowland rice yield in Cambodia

The magnitude and nature of genotype-by-environment interactions (G×E) for grain yield (GY) and days to flower (DTF) in Cambodia were examined using a random population of 34 genotypes taken from the Cambodian rice improvement program. These genotypes were evaluated in multi-environment trials (MET) conducted across three years (2000 to 2002) and eight locations in the rainfed lowlands. The G×E interaction was partitioned into components attributed to genotype-by-location (G×L), genotype-by-year (G×Y) and genotype-by-location-by-year (G×L×Y) interactions. The G×L×Y interaction was the largest component of variance for GY. The G×L interaction was also significant and comparable in size to the genotypic component (G). The G×Y interaction was small and non significant. A major factor contributing to the large G×L×Y interactions for GY was the genotypic variation for DTF in combination with environmental variation for the timing and intensity of drought. Some of the interactions for GY associated with timing of plant development and exposure to drought were repeatable across the environments enabling the identification of three-target populations of environments (TPE) for consideration in the breeding program. Four genotypes were selected for wide adaptation in the rainfed lowlands in Cambodia.