Simulation of mixed models in augmented block design

Abstract

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.

BLUP for phenotypic selection in plant breeding and variety testing

“…Federer (1998) proposed to analyse such designs (and other incomplete block designs) assuming random genotypic values. Santos et al (2002) showed by simulation that BLUP in augmented designs may be hampered by poor estimates of genetic variance components. With known variance components, BLUP was always superior to BLUE.…”

Comparing Linear Mixed Models for Preliminary Yield Trials That Follow Augmented Experimental Designs

“…In such situations, augmented designs are commonly used (Kehel et al, 2010;Peternelli & De Resende, 2015). In unreplicated augmented design, standard or check lines are replicated for controlling experimental error (Santos et al 2002). However, spatial variation within locations might exist because of different factors like moisture gradient in the soil and variation in soil physical and chemical properties such as pH and fertility (Scharf & Alley, 1993;Adhikari et al, 1999;Wu & Dutilleul, 1999;Stroup, 2002).…”

“…The selection of an appropriate statistical model plays an important role in increasing precision in estimated results (El-Mohsen, 2013). According to Santos et al (2002), linear mixed model approach is one of the novel approaches to analyzing augmented experimental designs. Both row and column effects can be included in the model and residual variance can be reduced accordingly (Wu et al, 2013).…”

Delineamentos aumentados no melhoramento de plantas em condições de restrições de recursos

“…Várias propostas de métodos de análises a serem empregados nos delineamentos aumentados ou de experimentos incompletos estão presentes na literatura (FEDERER, 1956;DUARTE & VENCOVSKY, 2001, 2005SANTOS et al, 2002;SOUZA et al, 2006). Os principais resultados se resumem no uso de modelos mistos e na escolha do método de estimação dos componentes de variância, que deve ser apropriado para cada situação.…”

“…Os principais resultados se resumem no uso de modelos mistos e na escolha do método de estimação dos componentes de variância, que deve ser apropriado para cada situação. Em alguns trabalhos, encontra-se a proposta de se avaliar a real eficiência de seleção dos melhores genótipos entre os diferentes delineamentos de uso potencial, em que é evidenciado que o uso de repetições é favorável quando não há restrições de recursos (SANTOS et al, 2002;SOUZA et al, 2006).…”