Epistasis in the multiple locus symmetric viability model

The n-locus two-allele symmetric viability model is considered in terms of the parameters measuring the additive epistasis in fitness. The dynamics is analysed using a simple linear transformation of the gametic frequencies, and then the recurrence equations depend on the epistatic parameters and Geiringer's recombination distribution only. The model exhibits an equilibrium, the central equilibrium, where the 2 ⁿ gametes are equally frequent. The transformation simplifies the stability analysis of the central point, and provides the stability conditions in terms of the existence conditions of other equilibria. For total negative epistasis (all epistatic parameters are negative) the central point is stable for all recombination distributions. For free recombination either a central point (segregating one, two, ... or n loci) or the n-locus fixation states are stable. For no recombination and some epistatic parameters positive the central point is unstable and several boundary equilibria may be locally stable. The sign structure of the additive epistasis is therefore an important determinant of the dynamics of the n-locus symmetric viability model. The non-symmetric multiple locus models previously analysed are dynamically related, and they all have an epistatic sign structure that resembles that of the multiplicative viability model. A non-symmetric model with total negative epistasis which share dynamical properties with the similar symmetric model is suggested.Supported in part by NIH grant GM 28016, and by grant 81-5458 from the Danish Natural Science Research Council     

Epistatic models and pre-selection of markers improve prediction of performance in corn

In our previous papers, we demonstrated that the inclusion of epistatic interactions in marker models improved prediction for corn (Zea mays L.) grain quality traits. The utility of pre-selecting markers for epistatic models was not reported. In papers by other researchers, including epistatic effects in a model did not improve prediction efficacy for whole genome selection. The objectives of this study were therefore to evaluate the value of: (1) pre-selecting markers and interactions at different type 1 error levels to predict performance; (2) adding epistatic interactions to models including all markers, and (3) using marker-based models to predict performance of kernel weight (KWT), flowering date (FDT), and plant height (PHT). Data for KWT, FDT, PHT, and oil and protein concentrations were obtained for 500 S₂ lines and their testcrosses from the crosses of Illinois high oil × Illinois low oil and Illinois high protein × Illinois low protein corn strains. Pre-selection using an epistatic model including both single-locus and two-locus interaction effects significant at the P = 0.05 level significantly increased prediction efficacy over selection including all markers and epistatic interactions. Adding all epistatic interactions to a model including all markers did not improve prediction. For most traits, prediction based on the P = 0.05 epistatic pre-selection model was nearly as effective as prediction based on phenotype, suggesting subsequent marker-based selection would be effective.     

Epistasis for fitness-related quantitative traits in Arabidopsis thaliana grown in the field and in the greenhouse

The extent to which epistasis contributes to adaptation, population differentiation, and speciation is a long-standing and important problem in evolutionary genetics. Using recombinant inbred (RI) lines of Arabidopsis thaliana grown under natural field conditions, we have examined the genetic architecture of fitness-correlated traits with respect to epistasis; we identified both single-locus additive and two-locus epistatic QTL for natural variation in fruit number, germination, and seed length and width. For fruit number, we found seven significant epistatic interactions, but only two additive QTL. For seed germination, length, and width, there were from two to four additive QTL and from five to eight epistatic interactions. The epistatic interactions were both positive and negative. In each case, the magnitude of the epistatic effects was roughly double that of the effects of the additive QTL, varying from -41% to +29% for fruit number and from -5% to +4% for seed germination, length, and width. A number of the QTL that we describe participate in more than one epistatic interaction, and some loci identified as additive also may participate in an epistatic interaction; the genetic architecture for fitness traits may be a network of additive and epistatic effects. We compared the map positions of the additive and epistatic QTL for germination, seed width, and seed length from plants grown in both the field and the greenhouse. While the total number of significant additive and epistatic QTL was similar under the two growth conditions, the map locations were largely different. We found a small number of significant epistatic QTL x environment effects when we tested directly for them. Our results support the idea that epistatic interactions are an important part of natural genetic variation and reinforce the need for caution in comparing results from greenhouse-grown and field-grown plants.     

Epistatic interaction is an important genetic basis of grain yield and its components in maize

A population of 294 recombinant inbred lines (RIL) derived from Yuyu22, an elite maize hybrid extending broadly in China, has been constructed to investigate the genetic basis of grain yield, and associated yield components in maize. The main-effect quantitative trait loci (QTL), digenic epistatic interactions, and their interactions with the environment for grain yield and its three components were identified by using the mixed linear model approach. Thirty-two main-effect QTL and forty-four pairs of digenic epistatic interactions were detected for the four measured traits in four environments. Our results suggest that both additive effects and epistasis (additive × additive) effects are important genetic bases of grain yield and its components in the RIL population. Only 30.4% of main-effect QTL for ear length were involved in epistatic interactions. This implies that many loci in epistatic interactions may not have significant effects for traits alone but may affect trait expression by epistatic interaction with the other loci.     

Epistasis interaction of QTL effects as a genetic parameter influencing estimation of the genetic additive effect

Epistasis, an additive-by-additive interaction between quantitative trait loci, has been defined as a deviation from the sum of independent effects of individual genes. Epistasis between QTLs assayed in populations segregating for an entire genome has been found at a frequency close to that expected by chance alone. Recently, epistatic effects have been considered by many researchers as important for complex traits. In order to understand the genetic control of complex traits, it is necessary to clarify additive-by-additive interactions among genes. Herein we compare estimates of a parameter connected with the additive gene action calculated on the basis of two models: a model excluding epistasis and a model with additive-by-additive interaction effects. In this paper two data sets were analysed: 1) 150 barley doubled haploid lines derived from the Steptoe × Morex cross, and 2) 145 DH lines of barley obtained from the Harrington × TR306 cross. The results showed that in cases when the effect of epistasis was different from zero, the coefficient of determination was larger for the model with epistasis than for the one excluding epistasis. These results indicate that epistatic interaction plays an important role in controlling the expression of complex traits.     

Mapping QTL for Biomass Yield and Its Components in Rice (Oryza sativa L.)

Addicive effects, additive by additive epistatic effects, and their environmental interactions of QTLs are important genetic components of quantitative traits. Genetic architecture underlying rice biomass yield and its two component traits (straw yield and grain yield) were analyzed for a population of 125 DH lines from an inter-subspecific cross of IR64/Azucena. The mixed-model based composite interval mapping approach (MCIM) was used to detect QTLs, There were 12 QTLs detected with additive main effects, 27 QTLs involved in digenic interaction with aa and/or aae effects, and 18 QTLs affected by environments with ae and/or aae effects. It was revealed that epistatic effects and QE interaction effects existed on biomass yield and its component traits in rice. In addition, the genetic basis of relationships among these traits were investigated. Four QTLs and one pair of epistatic QTLs were detected to be responsible for the positive correlation between biomass yield and straw yield. Three QTLs might be responsible for the negative correlation between straw yield and grain yield. This result could partially explain the genetic basis of correlation among the three traits, and provide useful information for genetic improvement of these traits by marker-assisted selection.     

Mapping QTLs with epistatic effects and QTL×environment interactions by mixed linear model approaches

A new methodology based on mixed linear models was developed for mapping QTLs with digenic epistasis and QTL×environment (QE) interactions. Reliable estimates of QTL main effects (additive and epistasis effects) can be obtained by the maximum-likelihood estimation method, while QE interaction effects (additive×environment interaction and epistasis×environment interaction) can be predicted by the-best-linear-unbiased-prediction (BLUP) method. Likelihood ratio and t statistics were combined for testing hypotheses about QTL effects and QE interactions. Monte Carlo simulations were conducted for evaluating the unbiasedness, accuracy, and power for parameter estimation in QTL mapping. The results indicated that the mixed-model approaches could provide unbiased estimates for both positions and effects of QTLs, as well as unbiased predicted values for QE interactions. Additionally, the mixed-model approaches also showed high accuracy and power in mapping QTLs with epistatic effects and QE interactions. Based on the models and the methodology, a computer software program (QTLMapper version 1.0) was developed, which is suitable for interval mapping of QTLs with additive, additive×additive epistasis, and their environment interactions. Received: 23 October 1998 / Accepted: 11 May 1999     

Genetic investigation of contributions of embryo and endosperm genes to malt Kolbach index, alpha-amylase activity and wort nitrogen content in barley

 A genetic model is proposed for the analysis of embryo and endosperm effects as well as GE interaction effects. An investigation of three malting quality traits in grains of seven parents and their F₂s was undertaken in a half-diallel cross of barley (Hordeum distichum L.) over 2 years. The results indicated that the malt Kolbach index (KI), alpha-amylase activity (αAA) and wort soluble nitrogen (Wort-N) are controlled by both embryo genetic effects and endosperm genetic effects. Variance of the endosperm additive effects was obviously larger than that of the embryo additive effects. In the contribution of the embryo genetic effects to variation in malt αAA and Wort-N, the dominance effects were considerably larger than the additive effects. The endosperm dominance effects constituted a major part of the total genetic effect on the KI. Significant endosperm GE interactions were also detected in the malt traits concerned. Endosperm general heritability (h ² _e ) tended to be larger than interaction heritability (h ² _oE or h ² _eE ) for all the traits. Endosperm heterosis was observed to be significantly positive for αAA but negative for Wort-N in the F₂ seed generation. Prediction of main gene effects for seven parents showed that ‘Ganmu 2’ and ‘Supi1’ were suitable parental varieties for malt αAA and Wort-N improvement. Our genetic model for malting quality traits and its application in breeding are discussed. Received: 5 August 1997 / Accepted: 11 September 1997     

Host genetic architecture in single and multiple infections

Hosts are often target to multiple simultaneous infections by genetically diverse parasite strains. The interaction among these strains and the interaction of each strain with the host was shown to have profound effects on the evolution of parasite traits. Host factors like genetic architecture of resistance have so far been largely neglected. To see whether genetic architecture differs between different kinds of infections we used joint scaling analysis to compare the genetic components of resistance in the red flour beetle Tribolium castaneum exposed to single and multiple strains of the microsporidian Nosema whitei. Our results indicate that additive, dominance and epistatic components were more important in single infections whereas maternal components play a decisive role in multiple infections. In detail, parameter estimates of additive, dominance and epistatic components correlated positively between single and multiple infections, whereas maternal components correlated negatively. These findings may suggest that specificity of host–parasite interactions are mediated by genetic and especially epistatic components whereas maternal effects constitute a more general form of resistance.     

Asymptotic distribution for epistatic tests in case-control studies

We propose a statistical model for dissecting a multilocus genotypic value into its main (additive and dominant) effects and epistatic effects between different loci in a case-control association study. The model can discern four different kinds of epistasis, additive × additive, additive × dominant, dominant × additive, and dominant × dominant interactions. To test each kind of epistasis, a χ² test statistic was computed for a two by two contingency table derived from combined genotypes in both case and control groups. We derived an analytical approach for estimating the asymptotic distribution of the χ² test statistic for epistatic tests under the null hypothesis, with the result being consistent with that from Monte Carlo simulations. The new model was used to analyze a case-control data set for candidate gene studies of stroke, leading to the identification of several significant interactions between causal SNPs on this disease.     

Epistasis plays an important role as genetic basis of heterosis in rice

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Analysis on additive effects and additive-by-additive epistatic effects of QTLs for yield traits in a recombinant inbred line population of rice

A linkage map consisting of 158 DNA markers were constructed by using a recombinant inbred line (RIL) population derived from the indica-indica rice cross Zhenshan 97B 2 Milyang 46. Quantitative trait loci (QTLs) conditioning grain yield and five yield component traits were determined at the one-locus and two-locus levels, and genotype-by-environment (GE) interactions were analyzed. Thirty-one QTLs were detected to have significant additive effects for yield traits, of which 12 also exhibited significant epistatic effects. Sixteen significant additive-by-additive (AA) interactions were detected, of which nine occurred between QTLs with own additive effects (M_epQTLs), four occurred between QTLs showing epistatic effects only (epQTLs), and three occurred between M_epQTLs and epQTLs. Significant GE interactions were found for six QTLs with additive effects and one AA interaction. Generally, the contributions to the phenotypic variation were higher due to QTL main effects than to epistatic effects. The detection of additive effects and AA effects of a QTL interfered with each other, indicating that the detection of QTLs with main effects, as well as the magnitude and directions of the additive effects, might vary depending on their interactions with other loci.     

Probability of Inadmissible Estimates of Heritability from Full-Sib Analysis Under a General Model of Gene Action

Evaluation of probabilities of the heritability (h²) estimates in full-sib analysis falling outside the permissible limits [0,1] was undertaken for several combinations of sire/dam numbers, h² and proportions of dominance and additive × additive epistatic variances, assuming two full-sibs per mating and the dominance related epistasis as negligible. In the light of the results use of sire component and sire-dam combination has been recommended in the estimation of heritability of lowly and highly heritable traits respectively.     

Genetic analysis of single-locus and epistatic QTLs for seed traits in an adapted × nuña RIL population of common bean (Phaseolus vulgaris L.)

Key message

The QTLs analyses here reported demonstrate the significant role of both individual additive and epistatic effects in the genetic control of seed quality traits in the Andean common bean.

Abstract

Common bean shows considerable variability in seed size and coat color, which are important agronomic traits determining farmer and consumer acceptability. Therefore, strategies must be devised to improve the genetic base of cultivated germplasm with new alleles that would contribute positively to breeding programs. For that purpose, a population of 185 recombinant inbred lines derived from an Andean intra-gene pool cross, involving an adapted common bean (PMB0225 parent) and an exotic nuña bean (PHA1037 parent), was evaluated under six different—short and long-day—environmental conditions for seed dimension, weight, color, and brightness traits, as well as the number of seed per pod. A multi-environment Quantitative Trait Loci (QTL) analysis was carried out and 59 QTLs were mapped on all linkage groups, 18 of which had only individual additive effects, while 27 showed only epistatic effects and 14 had both individual additive and epistatic effects. Multivariate models that included significant QTL explained from 8 to 68  % and 2 to 15 % of the additive and epistatic effects, respectively. Most of these QTLs were consistent over environment, though interactions between QTLs and environments were also detected. Despite this, QTLs with differential effect on long-day and short-day environments were not found. QTLs identified were positioned in cluster, suggesting that either pleiotropic QTLs control several traits or tightly linked QTLs for different traits map together in the same genomic regions. Overall, our results show that digenic epistatic interactions clearly play an important role in the genetic control of seed quality traits in the Andean common bean.     

籼粳杂交稻穗部性状的遗传效应及其与环境互作

采用包括基因型与环境互作效应的加性显性加性×加性上位性遗传模型,分析了不同环境下籼粳杂交稻穗部性状的遗传特点.结果表明,除了主穗粒数的加性与环境互作和二次枝梗数的显性与环境互作不显著外,其他性状均存在显著和极显著的加性、显性、加性×加性上位性遗传效应及其与环境的互作效应,其中均以显性效应为主,显性与环境互作效应对枝梗性状的影响较为明显.遗传率分析表明,各性状的普通广义遗传率最大,互作遗传率也有一定作用.杂种优势预测表明,除了一次、二次枝梗数外,其他性状均表现正向的杂种优势,基因型与环境互作只影响杂种优势表达的程度,而不改变其方向.遗传效应预测值结果表明,IR6615837、IR6560085、明恢63和R6694个亲本可以明显改良杂交后代多数穗部性状,且环境影响程度较小,可作为优良亲本列于育种计划中.     

Genetic variants and underlying mechanisms influencing variance heterogeneity in maize

Traditional genetic studies focus on identifying genetic variants associated with the mean difference in a quantitative trait. Because genetic variants also influence phenotypic variation via heterogeneity, we conducted a variance‐heterogeneity genome‐wide association study to examine the contribution of variance heterogeneity to oil‐related quantitative traits. We identified 79 unique variance‐controlling single nucleotide polymorphisms (vSNPs) from the sequences of 77 candidate variance‐heterogeneity genes for 21 oil‐related traits using the Levene test (P < 1.0 × 10^?5). About 30% of the candidate genes encode enzymes that work in lipid metabolic pathways, most of which define clear expression variance quantitative trait loci. Of the vSNPs specifically associated with the genetic variance heterogeneity of oil concentration, 89% can be explained by additional linked mean‐effects genetic variants. Furthermore, we demonstrated that gene × gene interactions play important roles in the formation of variance heterogeneity for fatty acid compositional traits. The interaction pattern was validated for one gene pair (GRMZM2G035341 and GRMZM2G152328) using yeast two‐hybrid and bimolecular fluorescent complementation analyses. Our findings have implications for uncovering the genetic basis of hidden additive genetic effects and epistatic interaction effects, and we indicate opportunities to stabilize efficient breeding and selection of high‐oil maize (Zea mays L.).     

Mapping single-locus and epistatic quantitative trait loci for plant architectural traits in chrysanthemum

Plant architecture is important for chrysanthemum cultivation and breeding. To determine the genetic basis of plant architectural traits in chrysanthemum, a population of 142 F1 plants derived from a cross between the creeping ground-cover chrysanthemum cultivar Yuhualuoying and the erect potted cultivar Aoyunhanxiao was used to detect quantitative trait loci (QTL) associated with plant height, plant width, inter-node length and flower neck length. The broad-sense heritability h _B ² for the four plant architectural traits ranged from 0.33 to 0.83, and transgressive segregation was observed. Single-locus QTL analysis revealed a total of five QTL, accounting for 6.0?C16.1% of the phenotypic variation. Additionally, 11 pairs of epistatic QTL were identified, explaining 3.5?C14.5% of the phenotypic variations. The majority of the interactions detected occurred between background loci. These results indicate that both additive and epistatic effects contribute to phenotypic variation in the plant architecture of chrysanthemum. It is expected that the identified markers associated with the additive QTL and epistatic QTL detected in this study will be of importance in future breeding programs to develop chrysanthemum cultivars exhibiting desirable plant architecture.     

Learning genetic epistasis using Bayesian network scoring criteria

Background  

Gene-gene epistatic interactions likely play an important role in the genetic basis of many common diseases. Recently, machine-learning and data mining methods have been developed for learning epistatic relationships from data. A well-known combinatorial method that has been successfully applied for detecting epistasis is Multifactor Dimensionality Reduction (MDR). Jiang et al. created a combinatorial epistasis learning method called BNMBL to learn Bayesian network (BN) epistatic models. They compared BNMBL to MDR using simulated data sets. Each of these data sets was generated from a model that associates two SNPs with a disease and includes 18 unrelated SNPs. For each data set, BNMBL and MDR were used to score all 2-SNP models, and BNMBL learned significantly more correct models. In real data sets, we ordinarily do not know the number of SNPs that influence phenotype. BNMBL may not perform as well if we also scored models containing more than two SNPs. Furthermore, a number of other BN scoring criteria have been developed. They may detect epistatic interactions even better than BNMBL.     

Identification and characterization of QTL underlying whole-plant physiology in Arabidopsis thaliana: δ13C, stomatal conductance and transpiration efficiency

Water limitation is one of the most important factors limiting crop productivity world-wide and has likely been an important selective regime influencing the evolution of plant physiology. Understanding the genetic and physiological basis of drought adaptation is therefore important for improving crops as well as for understanding the evolution of wild species. Here, results are presented from quantitative trait loci (QTL) mapping of flowering time (a drought escape mechanism) and carbon stable isotope ratio (δ¹³C) (a drought-avoidance mechanism) in Arabidopsis thaliana. Whole-genome scans were performed using multiple-QTL models for both additive and epistatic QTL effects. We mapped five QTL affecting flowering time and five QTL affecting δ¹³C, but two genomic regions contained QTL with effects on both traits, suggesting a potential pleiotropic relationship. In addition, we observed QTL–QTL interaction for both traits. Two δ¹³C QTL were captured in near-isogenic lines to further characterize their physiological basis. These experiments revealed allelic effects on δ¹³C through the upstream trait of stomatal conductance with subsequent consequences for whole plant transpiration efficiency and water loss. Our findings document considerable natural genetic variation in whole-plant, drought resistance physiology of Arabidopsis and highlight the value of quantitative genetic approaches for exploring functional relationships regulating physiology.