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CROP BREEDING & GENETICS

Comparison of Weighting in Two-Stage Analysis of Plant Breeding Trials

Bioinformatics Unit, Institute for Crop Production and Grassland Research, Universität Hohenheim, 70593 Stuttgart, Germany

^* Corresponding author (piepho{at}uni-hohenheim.de).

Series of plant breeding trials are often unbalanced and have a complex genetic structure. To reduce computing cost, it is common practice to employ a two-stage approach, where adjusted means per location are estimated and then a mixed model analysis of these adjusted means is performed. An important question is how means from the first step should be weighted in the second step. Our objective therefore was the comparison of different weighting methods in the analysis of four typical series of plant breeding trials using mixed models with fixed or random genetic effects. We used four published weighting methods and proposed three new methods. Four evaluation criteria were computed to compare methods, using one-stage analysis as benchmark. We found that the two-stage analysis gave acceptable results with fixed genetic effects. When genetic effects were taken as random in stage two, in three of four datasets the two-stage analysis gave acceptable results. In both cases differences between weighting methods were small and the best weighting method depended on the dataset but not on the evaluation criteria. A two-stage analysis without weighting also produced acceptable results, but weighting mostly performed better. In the fourth dataset the missing data pattern was informative, resulting in violation of the missing-at-random (MAR) assumption in one- and two-stage analysis. In this case both analyses were not strictly valid.

Abbreviations: BLUE, best linear unbiased estimation • BLUP, best linear unbiased prediction • DH, doubled haploids • g.c.a., general combining ability • GLSE, generalized least squares estimates • g.v.a., general variety ability • LSD, least significant difference • MAR, missing at random • MET, multi-environmental trials • MME, mixed model equations • MSE, mean squared error • RCBD, randomized complete block design • REML, restricted maximum likelihood • s.c.a., specific combining ability • s.e.m., standard error of a mean • s.e.d., standard error of a difference • v.d., variance of a difference