# Prediction of hybrid means from a partial circulant diallel table using the ordinary least square and the mixed model methods

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## Data

2005

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## Resumo

By definition, the genetic effects obtained from a circulant diallel table are random. However, because of the methods
of analysis, those effects have been considered as fixed. Two different statistical approaches were applied. One
assumed the model to be fixed and obtained solutions through the ordinary least square (OLS) method. The other
assumed a mixed model and estimated the fixed effects (BLUE) by generalized least squares (GLS) and the best
linear unbiased predictor (BLUP) of the random effects. The goal of this study was to evaluate the consequences
when considering these effects as fixed or random, using the coefficient of correlation between the responses of
observed and non-observed hybrids. Crossings were made between S1 inbred lines from two maize populations
developed at Universidade Federal de Goiás, the UFG-Samambaia “Dent” and UFG-Samambaia “Flint”. A circulant
inter-group design was applied, and there were five (s = 5) crossings for each parent. The predictions were made
using a reduced model. Diallels with different sizes of s (from 2 to 5) were simulated, and the coefficients of
correlation were obtained using two different approaches for each size of s. In the first approach, the observed
hybrids were included in both the estimation of the genetic parameters and the coefficient of correlation, while in the
second a cross-validation process was employed. In this process, the set of hybrids was divided in two groups: one
group, comprising 75% of the original group, to estimate the genetic parameters, and a second one, consisting of the
remaining 25%, to validate the predictions. In all cases, a bootstrap process with 200 resamplings was used to
generate the empirical distribution of the correlation coefficient. This coefficient showed a decrease as the value of s
decreased. The cross-validation method allowed to estimate the bias magnitude in evaluating the correlation
coefficient using the same hybrids, to predict the genetic parameters and the correlation evaluation. The bias was
shown to be greater when the OLS method was used. When the correlation coefficients of the observed and
estimated hybrid means were obtained through the mixed instead of the fixed model, this decrease was less marked.
The selection of hybrids superior to the checks, in terms of grain weight, also differed in the two different approaches.
Nineteen percent of the hybrids were shown to be superior to the checks in the fixed models, while only 1.8% of them
were superior in the mixed model.

## Descrição

## Palavras-chave

Diallel analysis, Cross-validation, BLUP, Prediction

## Citação

REIS, Américo José dos Santos et al. Prediction of hybrid means from a parial circulant diallel table using the ordinary least square and the mixed model methods. Genetics and Molecular Biology, Ribeirão Preto, v. 28, n. 2, p. 314-320, 2005.