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

Abstract

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 S 1 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.

Potential of maize single-cross hybrids for extraction of inbred lines using the mean components and mixed models with microsatellite marker information

“…All analyses were performed using the SAS ® PROC IML program. The program to calculate BLUPs was adapted from Reis et al (2005).…”

Prediction of genotypic values and estimation of genetic parameters in common bean

“…In the literature, the studies that use mixed linear models in annual plants are rare, being more common for the perennial plants. An example of the use of mixed models in the annual plants is the study of Reis et al (2005) and that of Bernardo et al (1996a;1996b) The data were analyzed by the methods REML and BLUP, according to Resende and Dias (2000) and Resende et al (2001). The analyses were obtained using model 23 of the software SELEGEN REML/BLUP (Resende 2002).…”

Prediction of genotypic values of maize hybrids in unbalanced experiments

“…The ranking of the best hybrid remained unchanged, regardless of the statistical method, trait or degree of data imbalance. Reis et al (2005), in a study with similar objectives, but using diallel analysis, also found small differences in the ranking of the best hybrids, causing no difficulties for their identification.…”

“…According to Bernardo (1996), there is a tendency to obtain higher R 2 estimates between the observed and predicted values with an increase in the number of hybrids. Reis et al (2005) investigated the causes of this correlation and identified a bias in these estimates when the sample size is small and in the absence of a cross-validation procedure. This is relevant not only to assess the ability of the model to describe the set of observed data, but, above all, its predictive reliability.…”