Prediction with measurement errors in finite populations

We address the problem of selecting the best linear unbiased predictor (BLUP) of the latent value (e.g., serum glucose fasting level) of sample subjects with heteroskedastic measurement errors. Using a simple example, we compare the usual mixed model BLUP to a similar predictor based on a mixed model framed in a finite population (FPMM) setup with two sources of variability, the first of which corresponds to simple random sampling and the second, to heteroskedastic measurement errors. Under this last approach, we show that when measurement errors are subject-specific, the BLUP shrinkage constants are based on a pooled measurement error variance as opposed to the individual ones generally considered for the usual mixed model BLUP. In contrast, when the heteroskedastic measurement errors are measurement condition-specific, the FPMM BLUP involves different shrinkage constants. We also show that in this setup, when measurement errors are subject-specific, the usual mixed model predictor is biased but has a smaller mean squared error than the FPMM BLUP which points to some difficulties in the interpretation of such predictors. (C) 2011 Elsevier By. All rights reserved.

Efeitos gênicos de caracteres associados à eficiência no uso de nitrogênio em milho

Os objetivos deste trabalho foram determinar o controle genético da eficiência no uso do nitrogênio (EUN), identificar a importância das eficiências na absorção (EAN) e na utilização (EUtN) na sua composição,  e quantificar relação entre produção de matéria seca da parte aérea (MPS) e do sistema radicular com a EUN e  com seus componentes. Foram avaliadas 41 combinações híbridas em duas disponibilidades de N: baixa (BN)  e alta (AN). Utilizou-se o delineamento de blocos ao acaso com duas repetições, em arranjo fatorial simples  (combinação híbrida x disponibilidade de N). As análises estatísticas foram realizadas por meio das equações  de modelos mistos. Correlações de elevada magnitude foram detectadas entre EAN e EUN, bem como entre  essas eficiências e a MPS, tanto em BN como em AN. Em ambas as disponibilidades de N, efeitos genéticos  aditivos apresentaram maior importância para os caracteres associados à EUN. Dessa forma, a seleção baseada  no desempenho individual de linhagens quanto à MPS pode possibilitar a obtenção de genótipos com alta  EUN. Independentemente da disponibilidade de N, a EAN é o componente mais importante da EUN.

Strategies in identifying individuals in a segregant population of common bean and implications of genotype x environment interaction in the success of selection

The objective of this study was to compare the BLUP selection method with different selection strategies in F-2:4 and assess the efficiency of this method on the early choice of the best common bean (Phaseolus vulgaris) lines. Fifty-one F-2:4 progenies were produced from a cross between the CVIII8511 x RP-26 lines. A randomized block design was used with 20 replications and one-plant field plots. Character data on plant architecture and grain yield were obtained and then the sum of the standardized variables was estimated for simultaneous selection of both traits. Analysis was carried out by mixed models (BLUP) and the least squares method to compare different selection strategies, like mass selection, stratified mass selection and between and within progeny selection. The progenies selected by BLUP were assessed in advanced generations, always selecting the greatest and smallest sum of the standardized variables. Analyses by the least squares method and BLUP procedure ranked the progenies in the same way. The coincidence of the individuals identified by BLUP and between and within progeny selection was high and of the greatest magnitude when BLUP was compared with mass selection. Although BLUP is the best estimator of genotypic value, its efficiency in the response to long term selection is not different from any of the other methods, because it is also unable to predict the future effect of the progenies x environments interaction. It was inferred that selection success will always depend on the most accurate possible progeny assessment and using alternatives to reduce the progenies x environments interaction effect.