Simulation of mixed models in augmented block design


  • Aladir Horacio Santos FUOM; Faculdade de Filosofia; Departamento de Ciências Exatas
  • Eduardo Bearzoti UFLA; Departamento de Ciências Exatas
  • Daniel Furtado Ferreira UFLA; Departamento de Ciências Exatas
  • João Luís da Silva Filho UFLA; Departamento de Biologia



augmented design, mixed model, molecular marker


The augmented block design is widely used in breeding programs, with non-replicated treatments generally being selection units, and replicated treatments being standard cultivars. Originally, an intrablock analysis (fixed model) was proposed. Although non-replicated treatments and/or blocks can be considered of random nature, mixed linear models could be used instead. This work evaluated such an approach, using computer simulation. Populations consisted of sets of randomly generated inbred lines. Molecular marker data were also simulated to allow the estimation of the genetic covariance matrix. Different conditions were considered, varying heritability and the coefficient b of Smith of soil heterogeneity. For each condition 100 simulations were performed, considering four linear models, varying respectively the nature of the effects of blocks and non-replicated treatments (fixed - F, or random - R): FF, FR, RF and RR. In relation to FF, the mixed models were more efficient under low to intermediate heritability and high b. Mixed models could improve inference in breeding programs using the augmented block design and the choice of the model should rely on the kind of selection. If this is truncated, the RF model should be preferred; if it is not, then the RR model would be more suitable.


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How to Cite

Simulation of mixed models in augmented block design . (2002). Scientia Agricola, 59(3), 483-489.