Bias in the prediction of genetic gain due to mass and half-sib selection in random mating populations

The prediction of gains from selection allows the comparison of breeding methods and selection strategies, although these estimates may be biased. The objective of this study was to investigate the extent of such bias in predicting genetic gain. For this, we simulated 10 cycles of a hypothetical breeding program that involved seven traits, three population classes, three experimental conditions and two breeding methods (mass and half-sib selection). Each combination of trait, population, heritability, method and cycle was repeated 10 times. The predicted gains were biased, even when the genetic parameters were estimated without error. Gain from selection in both genders is twice the gain from selection in a single gender only in the absence of dominance. The use of genotypic variance or broad sense heritability in the predictions represented an additional source of bias. Predictions based on additive variance and narrow sense heritability were equivalent, as were predictions based on genotypic variance and broad sense heritability. The predictions based on mass and family selection were suitable for comparing selection strategies, whereas those based on selection within progenies showed the largest bias and lower association with the realized gain.

Dominance, epistasis, heritabilities and expected genetic gains

Although epistasis is common in gene systems that determine quantitative traits, it is usually not possible to estimate the epistatic components of genotypic variance because experiments in breeding programs include only one type of progeny. As the study of this phenomenon is complex, there is a lack of theoretical knowledge on the contribution of the epistatic variances when predicting gains from selection and on the bias in estimating genetic parameters when fitting the additive-dominant model. The objective of this paper is to discuss these aspects. Regarding a non-inbred population, the genetic value due to dominance and the epistatic components of the genotypic value are not indicators of the number of favorable genes present in an individual. Thus, the efficiency of a selection process should be based on the narrow-sense heritability, a function only of additive variance. If there is no epistasis, generally it is satisfactory to assess the selection efficiency and to predict gain based on the broad-sense heritability. Regardless of the selection unit or type of epistasis, the bias in the estimate of the additive variance when assuming the additive-dominant model is considerable. This implies overestimation of the heritabilities at half sib family mean, plant within family and plant levels, and underestimation if the selection units are full sib progenies. The predicted gains will have a bias proportional to that of the heritability.

Quantitative genetics theory for non-inbred populations in linkage disequilibrium

Although linkage disequilibrium, epistasis and inbreeding are common phenomena in genetic systems that control quantitative traits, theory development and analysis are very complex, especially when they are considered together. The objective of this study is to offer additional quantitative genetics theory to define and analyze, in relation to non-inbred cross pollinating populations, components of genotypic variance, heritabilities and predicted gains, assuming linkage disequilibrium and absence of epistasis. The genotypic variance and its components, additive and due to dominance genetic variances, are invariant over the generations only in regard to completely linked genes and to those in equilibrium. When the population is structured in half-sib families, the additive variance in the parents' generation and the genotypic variance in the population can be estimated. When the population is structured in full-sib families, none of the components of genotypic variance can be estimated. The narrow sense heritability level at plant level can be estimated from the parent-offspring or mid parent-offspring regression. When there is dominance, the narrow sense heritability estimate in the in F2 is biased due to linkage disequilibrium when estimated by the Warner method, but not when estimated by means of the plant F2-family F3 regression. The bias is proportional to the number of pairs of linked genes, without independent assortment, and to the degree of dominance, and tends to be positive when genes in the coupling phase predominate or negative and of higher value when genes in the repulsion phase predominate. Linkage disequilibrium is also cause of bias in estimates of the narrow sense heritabilities at full-sib family mean and at plant within half-sib and full-sib families levels. Generally, the magnitude of the bias is proportional to the number of pairs of genes in disequilibrium and to the frequency of recombining gametes.

Analysis of general and specific combining abilities of popcorn populations, including selfed parents

Estimation of general and specific combining ability effects in a diallel analysis of cross-pollinating populations, including the selfed parents, is presented in this work. The restrictions considered satisfy the parametric values of the GCA and SCA effects. The method is extended to self-pollinating populations (suitable for other species, without the selfed parents). The analysis of changes in population means due to inbreeding (sensitivity to inbreeding) also permits to assess the predominant direction of dominance deviations and the relative genetic variability in each parent population. The methodology was used to select popcorn populations for intra- and inter-population breeding programs and for hybrid production, developed at the Federal University of Viçosa, MG, Brazil. Two yellow pearl grain popcorn populations were selected.

Biometrical analyses of linolenic acid content of soybean seeds

The genetic reduction of linolenic acid levels increases the quality and stability of soybean oil. The objective of this study was to determine the inheritance and evaluate the nature and magnitude of gene effects on soybean seed linolenic acid level. Means and variances of F-1, F-2, and F-3 generations were made from the cross between accession BARC-12 (low linolenic acid content) and the commercial Brazilian cultivar CAC-1 (normal linolenic acid content). The results demonstrated that linolenic acid content in soybean is under the genetic control of a small number of genes. The additive model explained the means for the three generations and for the parents. Non-allelic gene interactions had little effect on the determination of genotypic values for the individuals. The generation means and population variation analyses demonstrated that the dominance deviations contribute little to the trait. These results showed that backcross breeding programs can be used to introduce the low linolenic acid content trait into soybean seeds, since it is possible to identify with very high accuracy the desired genotypes in segregating populations