Best Linear Unbiased Prediction and Family Selection in Crop Species

Abstract

Best linear unbiased prediction (BLUP) is the method primarily used for genetic evaluation in animal and forest species breeding. The objective was to present theory and application of BLUP in family selection. Statistical models aim to predict the breeding values of parents of half-sib and inbred families and the individual or average additive values of parents of full-sib families. We analyzed the expansion volume (EV) and grain yield of half-and full-sib families and of inbred progeny from the Viçosa popcorn {Zea mays L. subsp. mays [syn. Zea mays L. subsp. everts (Sturtev.) Zhuk.]} population in two selection cycles. The noninbred families were evaluated in a 14 by 14 simple lattice, and the inbred progeny were assessed in the incomplete block design. The additive-dominant model was fitted for yield of full-sib families of the second cycle and across generations for yield of full-sib families and EV of inbred progeny. Additive x additive epistasis was not significant for EV and yield of half-sib families. Although the predictions of breeding values in the additive and additive-dominant models are positively correlated, different sets of parents were included in the top 10% of breeding values from the two models. Therefore, the additive-dominant model should be fitted wherever possible. J.M.S. Viana and V.RAbbreviations: BLUP, best linear unbiased prediction; EV, expansion volume; MME, mixed model equations; REML, restricted maximum likelihood; UFV, Federal University of Viçosa.I NTRAPOPULATION recurrent selection aims to identify parents that have the hest additive genetic values. Several statistical methods can be used for the estimation or prediction of breeding values, assuming fixed, random, or mixed models, and hased on least squares, maximum likelihood, or Bayesian inference. A flexible and powerful methodology was developed from the combination of the hest linear unbiased prediction (BLUP) method proposed hy Henderson (1974) and the restricted maximum likelihood (REML) method proposed hy Patterson and Thompson (1971). The BLUP method is renowned and is widely used in animal and forestry breeding programs (Piepho et al., 2008). This methodology has only recently become important for genetic evaluation in annual crops breeding. In their review of the application of BLUP in plant breeding, Piepho et al. (2008) described relevant studies with and without inclusion of pedigree information, related to prediction of genotypic or additive genetic values in experiments with or without replications, analysis of genotype X environment interaction, quantitative trait loci mapping, and genetic assessment of pure and inbred lines.

Multigeneration Index in the Within‐Progenies Bulk Method for Breeding of Self‐pollinated Plants

“…The BLUP method has already been advocated for use in several crop plants (Piepho and Möhring, 2006;Oakey et al, 2006;Viana et al, 2011;Ramalho et al, 2013;Resende et al, 2013). The BLUP method has already been advocated for use in several crop plants (Piepho and Möhring, 2006;Oakey et al, 2006;Viana et al, 2011;Ramalho et al, 2013;Resende et al, 2013).…”

Parentesco na seleção para produtividade e teores de óleo e proteína em soja via modelos mistos

“…O procedimento Mixed foi utilizado para análises em modelos mistos. As rotinas utilizadas nas análises de modelos mistos estão apresentadas em Viana et al (2011). Os dados da safra 2010/2011 foram analisados com base no modelo em látice quadrado.…”

“…A matriz de parentesco A foi obtida por meio do procedimento Proc Inbred, conforme Viana et al (2011). No cenário sem informação de parentesco, considerou-se a matriz de parentesco como uma matriz identidade, o que faz com que a matriz de covariâncias seja dada por Iσ .…”

“…Entretanto, no melhoramento de espécies anuais, seu uso não é tão frequente, embora haja um número crescente de relatos, em diferentes espécies, como milho (Viana et al, 2010a(Viana et al, , 2011(Viana et al, , 2012, feijão (Baldissera et al, 2012), arroz (Borges et al, 2012) e trigo .…”

Research Article Indices estimated using REML/BLUP and introduction of a super-trait for the selection of progenies in popcorn.

“…The BLUP procedure (Henderson, 1973) minimizes the variance of the prediction error and maximizing precision. BLUP is a linear function of the observations and does not account for patterns; therefore, it maximizes the accuracy of non-biased predictors and predicts random variables (Viana et al, 2011;Resende et al, 2012). Resende (2007a) reported that the simultaneous analysis of various traits could be efficiently performed using the multivariate REML/BLUP approach.…”