Components of variation of polygenic systems with digenic epistasis

Abstract

In this paper an extension of the biometric model of Mather and Jinks for the analysis of variation with digenic epistasis is presented. Epistatic effects can contribute favorably to the determination of the genotypic values of selected individuals or families and of superior hybrids. Selection will be inefficient, however, if there is a large number of interacting genes because the epistatic components of the between-family and within-family genotypic variances are very high compared to the portion attributable to the average effects of genes. Selection tends to be efficient when the number of interacting genes is reduced, but this depends on the magnitude of due to dominance and environmental variances. The dominance component (H) and the epistatic component due to interactions between homozygous and heterozygous genic combinations (J) can only be estimated when one or more quadratic statistics from the S3 generation, obtained by randomly mating F2 individuals, are used.<br>Neste artigo é apresentada uma extensão do modelo biométrico de Mather e Jinks para análise de variação, considerando epistasia entre genes de dois locos. Apesar dos efeitos epistáticos poderem contribuir de modo positivo para a determinação dos valores genotípicos de indivíduos ou famílias selecionados e de híbridos superiores, a seleção será ineficiente se é elevado o número de genes que interagem, pois neste caso as variâncias genotípicas total, entre progênies e dentro de famílias são devidas praticamente a efeitos de interação entre genes não alélicos. Dependendo dos valores das variâncias devida à dominância e de ambiente, quando é reduzido o número de genes que interagem a seleção tende a ser eficiente. O componente de dominância (H) e o componente epistático devido às interações entre combinação gênica homozigota e combinação heterozigota (J) são individualmente estimáveis apenas quando se usa uma ou mais estatísticas quadráticas associadas à geração S3, obtida por acasalamentos ao acaso entre indivíduos F2

Inheritance of root traits and phosphorus uptake in common bean (Phaseolus vulgaris L.) under limited soil phosphorus supply

“…A part of such negative variances can be due to the non-allelic interactions, which introduce some uncertainty into the estimates of variances in segregating populations (Mather & Jinks, 1974). If the number of interacting genes is relatively high, the differences between epistatic genetic values of the individuals account for almost the entire genotypic variance, causing low estimates of heritability and biased estimates of the additive and dominance components (Viana, 2000). The magnitude of the additive × additive components should be assessed towards developing superior pure lines (Viana, 2000), but a more accurate evaluation of the epistatic components of variation requires the analysis of specific crosses built for this purpose (Khattak et al, 2001).…”

Genetic adaptability of inheritance of resistance to biotic and abiotic stress level on crop: Role of epistasis

“…Genetics quantitative is largely influenced by the additive theory (Wagner et al, 1998). Epistatic effects are not involved in genetic studies for the theoretical complexity of the statistical studies by introducing the epistatic component (Viana, 2000). Until recently, empirical work on this fundamental issue has been limited partly because of the absence of reliable quantitative genetic approaches for quantifying epistasis (Whitlock et al, 1995;Fenster et al, 1997).…”

“…In contrast, epistasis is common in gene systems that determine quantitative traits, it is also a major problem in studies of these traits because it complicates the interpretation of genetic experiments and makes predictions difficult (Viana, 2000). The importance of epistasis is not well understood, and its contribution to quantitative variation was once considered to be small (Crow, 1987).…”

Impact of Epistasis in Inheritance of Quantitative Traits in Crops

“…Because of the complexity of theoretical genetics studies on epistasis, there is a lack of information about the contribution of the epistatic components of genotypic variance when predicting gains from selection. The estimation of epistatic components of genotypic variance is unusual in genetic studies because the limitation of the methodology, as in the case of the triple test cross, the high number of generations to be produced and assessed (Viana, 2000), and mainly because only one type of progeny, Half-Sib, Full-Sib or inbred families, is commonly included in the experiments (Viana, 2005). If there is no epistasis, generally it is satisfactory to assess the selection efficiency and to predict gain based on the broad-sense heritability.…”