Teoria de modelos mistos aplicada ao delineamento em blocos aumentados

Abstract

Augmented designs were proposed to deal with low availability of material to constitute replications and experimental plots, and with large amounts of treatments. Amongst them, augmented block design is largely used. In this design, there are replicated (common) and non-replicated (regular) treatments; in breeding programs the latter are often the selection units and the former standard cultivars. Inference has traditionally been made by means of an intrablock analysis (fixed models). If regular treatments and/or blocks can be considered of random nature, however, a mixed linear model could be used instead, specially if genetic covariance matrix among selection units can be assigned, from pedigree information or molecular marker data. This work aimed at the evaluation of the use of mixed models to describe augmented block designs, and their efficiency over traditional intrablock analysis, using computer simulation. Data were generated considering a fictitious plant species with200 independent genes controlling a trait of interest. Gene effects (that is, half the difference among homozygotes) were random outcomes from an exponential density with mean equal to 1. Frequencies of favorable allele of each locus ranged from 0.2 to 0.8. Populations consisted of sets of randomly generated inbred lines, with different sizes (50, 100 or 200). Molecular data were also generated, considering 100marker loci, in such a way that expected similarities between any pair of lines were the same for trait and marker loci. Such data were used in the estimation of the genetic covariance matrix. Environmental variances were established according to predetermined heritabilities h2 (0.2, 0.5 or 0.8) and split into block and residual components with weights determined by the magnitude of Smith's coefficient b of soil heterogeneity (0.1, 0.5 or 0.9). Two amounts of blocks were considered (0.2 or 0.05 the number of lines). In each combination of such parameters, 100 simulations were made, considering four linear models, varying the nature of block and regular treatment effects (fixed - F, or random - R), respectively FF, FR, RF and RR. The effects of such mixed models were estimated using best linear unbiased prediction (BLUP) and, when at least one of those factors was regarded as random, two variants were considered, assuming or not variance components as known. In the latter, components were estimating by restricted maximum likelihood, using the EM algorithm. The mixed models were evaluated through bias, mean squared error (MSE), Pearson's and Spearman's correlation, and bias on estimating the actual percentage of elite lines, that is, those superior to best common treatment ("elite bias"). Results showed that biases were negligible for all models. Considering the other criteria, for most situations the RR model with known variance components was the best, as theoretically expected. When variance components were estimated, however, correlation of Pearson and that of Spearman were highest with RF model, which is that with recovery of interblock information only. On the other hand, RR model generally showed the least elite biases. Comparing to FF, mixed models (RF or RR) were more efficient specially under lower precision, that is, low to intermediate heritability and high b (high residual variance in relation to block differences). Under such conditions, therefore, results suggested that mixed models could improve inference in breeding programs and that the choice of the model should rely on the kind of selection. If this is truncated, RF model should be preferred; if this is not, such as that based on the performance of check varieties, then RR would be more suitable, justifying the costs of generating molecular data.