The genetical basis of hybrid vigour in a highly heterotic cross of Nicotiana tabacum

The genetical control of F₁ heterosis, observed in a cross of desirable Nicotiana tabacum varieties, was investigated by analysing the data of the basic generations, triple test cross-families and random samples of doubled haploids (DH) and single-seed descent (SSD) lines. Analyses of the first-degree statistics revealed a complex control underlying the genetic variation, including the presence of epistasis, linkage, maternal effects and their interactions, in addition to the additive and dominance effects of the genes segregating in the cross. These analyses identified gene dispersion, directional dominance, and duplicate epistasis, as the main causes of heterosis. The triple test-cross analysis also confirmed the presence of non-allelic interactions and indicated that the dominance ratio, although inflated by epistasis, is consistently partial for all the traits. The extent of transgression in the recombinant inbred lines finally established unequivocally that, as in numerous other crosses, gene dispersion and unidirectional, but partial, dominance are the true causes of heterosis in this cross too.     

Detection and estimation of components of genetic variation for some metric traits in tomato (Lycopersicon esculentum Mill)

Summary Sixty families from two tomato triple test crosses (S120 x EC61747 and EC31513 x Tusa Ruby) were raised in complete randomized blocks in two replications and two environments (two fertilizer levels). Jinks and Perkins' (1970) analysis was used to detect and estimate the additive, dominance and epistatic components of genetic variation for flowering time, maturity period, number of branches per plant, final height, shape index of fruit, locule number, number of fruits per plant, yield per plant and weight per fruit. The j & 1 type epistasis was more important than the i type epistasis in the first cross, while in the second cross the two components of epistasis played almost equal roles in the control of characters studied. Both the D (additive) and H (dominance) components were significant for most of the characters in both crosses and in both the environments. The D component was relatively more important than the H component in the first cross, while the situation was just the reverse in the second cross. Dominance was directional in 8 out of 36 cases. Ambidirectional dominance was observed in 27 cases. A real absence of dominance was observed in one case only.     

Triple test cross analysis in F2 populations of four barley crosses

Summary The triple test cross analysis of Jinks and Perkins (1970) was used to study different components of genetic variation in four barley F₂ populations, C 164x IB 226, C 164xJyoti, IB 226xP 113 and DL 3xP 113, for final plant height, spike length, 100-kernel weight, grain yield per plant and harvest index. The overall epistasis (i type) was, in general, a minor component but the j & 1 type epistasis was an important element for all five characters in cross 3 (IB 226xP 113). Both the additive (D) and dominance (H) components were highly significant for all the five characters in all four crosses. The dominance was directional in all cases except for 100-grain weight in crosses 1 (C 164xIB 226), 2 (C 164xJyoti) and 4(DL 3xP 113).     

The consequences of using inadequate testers in the simplified triple test-cross.

The genetical consequences of common alleles in the L1 and L2 testers of a simplified version of the triple test-cross which is applicable to populations of inbred lines are examined. The test for epistasis under these circumstances becomes ambiguous and can spuriously detect non-allelic interactions when they may not exist although it still provides a test for epistasis and the adequacy of the testers simultaneously. The tests of significance and the estimates of additive variation are biased to an extent related to the dominance and dominance x additive effects of the common loci while the significance and estimates of dominance variation are deflated because they reflect the dominance effects at the non-common loci only. The covariance of sums and differences is also underestimated for the same reasons. These expectations are illustrated by analysing the 190 simplified triple test-crosses that could be extracted from a 20 x 20 diallel set of crosses between pure-breeding lines of Nicotiana rustica.     

Cross prediction studies on spring barley

Summary The genetical and environmental control of three height characters, two maturity characters and neck length in five barley pair crosses was studied using both F₂ triple test cross and model fitting analysis.Significant additive and dominance effects were found for all six characters with some evidence of epistasis for each character. Generally, dominance was incomplete for the height characters but was significantly directional for increased height in those crosses where dwarfing genes were segregating. Variable dominance effects were found for both the maturity characters. Complete dominance was found in three cases, otherwise incomplete dominance was found. Significant directional dominance for earliness was found for both maturity characters in one cross but this was attributed to the presence of a daylength insensitivity factor in one of the parents. Most of the genetic variation for neck length was additive, though some evidence of dominance was found.Broad sense and narrow sense heritability estimates generally were found to be high for the height and maturity characters but low for neck length. It was concluded that early generation selection for height at ear emergence, for final height and for awn emergence was worthwhile. Early generation selection for neck length was not recommended from the results of this study.     

Statistical power for detecting epistasis QTL effects under the F-2 design

Epistasis refers to gene interaction effect involving two or more genes. Statistical methods for mapping quantitative trait loci (QTL) with epistasis effects have become available recently. However, little is known about the statistical power and sample size requirements for mapping epistatic QTL using genetic markers. In this study, we developed analytical formulae to calculate the statistical power and sample requirement for detecting each epistasis effect under the F-2 design based on crossing inbred lines. Assuming two unlinked interactive QTL and the same absolute value for all epistasis effects, the heritability of additive × additive (a × a) effect is twice as large as that of additive × dominance (a × d) or dominance × additive (d × a) effect, and is four times as large as that of dominance × dominance (d × d) effect. Consequently, among the four types of epistasis effects involving two loci, ''a × a'' effect is the easiest to detect whereas ''d × d'' effect is the most difficult to detect. The statistical power for detecting ''a × a'' effect is similar to that for detecting dominance effect of a single QTL. The sample size requirements for detecting ''a × d'', ''d × a'' and ''d × d'' are highly sensitive to increased distance between the markers and the interacting QTLs. Therefore, using dense marker coverage is critical to detecting those effects.     

A modified triple test-cross analysis to test and allow for inadequate testers.

When the population under investigation consists of highly inbred lines the full triple test-cross of Kearsey and Jinks (1968) supplemented by the selfed progenies of the population allows unambiguous and independent tests for epistasis and the adequacy of the pure-breeding testers, L1 and L2. This can also be achieved by supplementing the simplified triple test-cross of Jinks, Perkins and Breese (1969) with the selfed progenies of the L1i and L2i families. If the L1 and L2 testers prove to be inadequate due to the presence of common loci, modifications of the analyses are proposed which correct the resulting biases in the genetical components of variation.     

云南香型软米水稻资源农艺性状遗传效应研究

选取5份云南地方香型软米水稻种质资源和6份自育香型软米保持系按5×6不完全双列杂交设计(NCⅡ)配制成30个组合,采用加性-显性-上位性遗传模型,分析云南香型软米11个农艺性状的遗传效应。结果表明,云南香型软米多数农艺性状的遗传主要受加×加上位性效应、加性×环境效应、显性×环境效应的影响,还存在不同程度的加性效应和显性效应,单株产量受基因加性效应、显性效应、加×加上位性效应、加性×环境效应、显性×环境效应的影响;株高、有效穗的遗传率以普通狭义遗传率为主,其他性状的普通狭义遗传率和互作狭义遗传率均达极显著水平;产量构成性状之间存在不同类型和不同程度的遗传相关,多数性状之间以加×加上位性、加性×环境和显性×环境互作效应显著。     

Efficiency of triple test cross for detecting epistasis with marker information

The triple test cross (TTC) is an experimental design for detecting epistasis and estimating the components of genetic variance for quantitative traits. In this paper, we extend the analysis to include molecular information. The statistical power of the mating design was assessed under a model assuming that a finite number of loci affect the trait in question. Formulae are developed for the analysis with or without marker information relating to the recombination fraction between loci, the genetical properties of quantitative trait controlled by the quantitative trait loci (QTL), the linkage phases of the parents and population size. Application of these formulae showed that the recombination fraction between genes and the magnitude and the types of epistasis have important interactions in their effects on power. The results demonstrate that the TTC may have increased power to detect epistasis when marker information is present. However, the simulation experiments show that the standard deviation of the estimated expected mean square was higher with one marker than that with two, whereas the corresponding value without marker information was the lowest. In addition, we demonstrate that the relative position of QTL and markers and the number of markers can both affect the power of epistatic detection.     

Genetics of quantitative traits in Arabidopsis thaliana

The genetic control of 22 quantitative traits, including developmental rates and sizes, was examined in generations of Arabidopsis thaliana derived from the cross between the ecotypes, Columbia (Col) and Landsberg erecta (Ler). The data were obtained from three sets of families raised in the same trial: the 16 basic generations, that is, parents, F(1)'s, F(2)'s, backcrosses, recombinant inbred lines (RILs) and a triple test cross (TTC), the latter produced by crossing the RILs to Col, Ler and their F(1). The data were analysed by two approaches. The first (approach A) involved traditional generation mean and variance component analysis and the second (B), based around the RILs and TTC families, involved marker-based QTL analysis.From (A), genetic differences between Col and Ler were detected for all traits with moderate heritabilities. Height at flowering was the only trait to show heterosis. Dominance was partial to complete for all height traits, and there was no overdominance but there was strong evidence for directional dominance. For most other traits, dominance was ambidirectional and incomplete, with average dominance ratios of around 80%. Epistasis, particularly of the duplicate type that opposes dominance, was a common feature of all traits. The presence of epistasis must imply multiple QTL for all traits.The QTL analysis located 38 significant effects in four regions of chromosomes I, II, IV and V, but not III. QTL affecting rosette size and leaf number were identified in all four regions, with days to maturity on chromosomes IV and V. The only QTL for height was located at the expected position of the erecta gene (chromosome II; 50 cM), but the additive and dominance effects of this single QTL did not adequately explain the generation means. The possible involvement of other interacting height QTL is discussed.     

The decline in fitness with inbreeding: evidence for negative dominance‐by‐dominance epistasis in Drosophila melanogaster

Genetic interactions can play an important role in the evolution of reproductive strategies. In particular, negative dominance‐by‐dominance epistasis for fitness can theoretically favour sex and recombination. This form of epistasis can be detected statistically because it generates nonlinearity in the relationship between fitness and inbreeding coefficient. Measures of fitness in progressively inbred lines tend to show limited evidence for epistasis. However, tests of this kind can be biased against detecting an accelerating decline due to line losses at higher inbreeding levels. We tested for dominance‐by‐dominance epistasis in Drosophila melanogaster by examining viability at five inbreeding levels that were generated simultaneously, avoiding the bias against detecting nonlinearity that has affected previous studies. We find an accelerating rate of fitness decline with inbreeding, indicating that dominance‐by‐dominance epistasis is negative on average, which should favour sex and recombination.     

Genetic basis of heterosis for growth-related traits in Arabidopsis investigated by testcross progenies of near-isogenic lines reveals a significant role of epistasis

Epistasis seems to play a significant role in the manifestation of heterosis. However, the power of detecting epistatic interactions among quantitative trait loci (QTL) in segregating populations is low. We studied heterosis in Arabidopsis thaliana hybrid C24 x Col-0 by testing near-isogenic lines (NILs) and their triple testcross (TTC) progenies. Our objectives were to (i) provide the theoretical basis for estimating different types of genetic effects with this experimental design, (ii) determine the extent of heterosis for seven growth-related traits, (iii) map the underlying QTL, and (iv) determine their gene action. Two substitution libraries, each consisting of 28 NILs and covering approximately 61 and 39% of the Arabidopsis genome, were assayed by 110 single-nucleotide polymorphism (SNP) markers. With our novel generation means approach 38 QTL were detected, many of which confirmed heterotic QTL detected previously in the same cross with TTC progenies of recombinant inbred lines. Furthermore, many of the QTL were common for different traits and in common with the 58 QTL detected by a method that compares triplets consisting of a NIL, its recurrent parent, and their F(1) cross. While the latter approach revealed mostly (75%) overdominant QTL, the former approach allowed separation of dominance and epistasis by analyzing all materials simultaneously and yielded substantial positive additive x additive effects besides directional dominance. Positive epistatic effects reduced heterosis for growth-related traits in our materials.     

Estimation of Epistatic Variance Components and Heritability in Founder Populations and Crosses

Genetic association studies have explained only a small proportion of the estimated heritability of complex traits, leaving the remaining heritability “missing.” Genetic interactions have been proposed as an explanation for this, because they lead to overestimates of the heritability and are hard to detect. Whether this explanation is true depends on the proportion of variance attributable to genetic interactions, which is difficult to measure in outbred populations. Founder populations exhibit a greater range of kinship than outbred populations, which helps in fitting the epistatic variance. We extend classic theory to founder populations, giving the covariance between individuals due to epistasis of any order. We recover the classic theory as a limit, and we derive a recently proposed estimator of the narrow sense heritability as a corollary. We extend the variance decomposition to include dominance. We show in simulations that it would be possible to estimate the variance from pairwise interactions with samples of a few thousand from strongly bottlenecked human founder populations, and we provide an analytical approximation of the standard error. Applying these methods to 46 traits measured in a yeast (Saccharomyces cerevisiae) cross, we estimate that pairwise interactions explain 10% of the phenotypic variance on average and that third- and higher-order interactions explain 14% of the phenotypic variance on average. We search for third-order interactions, discovering an interaction that is shared between two traits. Our methods will be relevant to future studies of epistatic variance in founder populations and crosses.     

Probability of Obtaning Negative Estimates of Heritability from Full-Sib Analysis under a General Model of Gene Action

Formulae are derived for the probability of obtaining negative estimates of heritability (h²) in full-sib analysis under the additive-dominance-epistasis model of gene action. Evaluation of the probabilities was undertaken for several combinations of sire/dam number, h² and proportions of dominance and additive X additive epistatic variances, assuming two full-sibs per mating and that the dominance related epistasis is absent. In the light of the results, minimum sample sizes for obtaining admissible estimates from sire, dam components and their combination have been prescribed.     

Genetic basis of variation of yield, and yield components in mungbean (Vigna radiata (L.) Wilczek)

Additive, dominance, and epistasis genetic basis of seed yield per plant, number of pods per plant, number of seeds per pod, and 1000 seed weight in mungbean (Vigna radiata (L.) Wilczek) have been examined, using Triple Test Cross (TTC) analysis. The material for TTC test was evaluated in two seasons i.e., kharif (July-October) and spring/summer (March-June), at the research station of the Nuclear Institute for Agriculture and Biology (NIAB), Faisalabad, Pakistan. Epistasis was present significantly for number of pods per plant and number of seeds per pod when grown in the spring/summer season (March to June). Partition of epistasis showed that additive x additive ('i' type) interaction was an important component of number of pods per plant, and number of seeds per pod was found to be of both types 'i' type, and additive x dominance, and dominance x dominance ('j' and 'l' type) interactions. This indicated that epistasis might be a non-trivial factor in the inheritance of pods per plant, and seeds per pod in mungbean. The expression of epistasis was influenced differentially by particular genotypes, indicating that a limited number of genotypes may not be sufficient to detect non-allelic interactions for a trait in mungbean. Additive and dominance genetic components were significant for all four traits in kharif season (July to October) but only for seed yield and 1000 seed weight in spring/summer season. This suggests that the genes controlling seed yield per plant, and 1000 seed weight are equally sensitive to the environment. The predominance additive gene action in those traits is not significantly influenced by epistasis, suggesting that improvement of the traits can be achieved through standard selection procedures.     

Overview of QTL detection in plants and tests for synergistic epistatic interactions

Improvements in the usefulness of QTL analysis arise from better statistical methods applied to the problem, ability to analyze more complex mating designs, and the fitting of less simplified genetic models. Here we review the advantages of different plant mating designs in QTL analysis and conclude that diallel designs have several favorable properties. We then turn to the detection of systematic genome-wide synergistic epistasis. This form of epistasis has important implications from evolutionary (maintenance of sexual reproduction and concealment of cryptic genetic variation) and practical perspectives (response to pyramided favorable alleles). We develop two methods for detecting systematic synergistic epistasis, one based on analyzing interactions between locus effects and predicted individual genotypic values and one based on analyzing pairwise locus interactions. Using the first method we detect synergistic epistasis in a barley and a wheat dataset but not in a maize dataset. We fail to detect synergistic epistasis with the second method. We discuss our results in the light of theoretical questions concerning the mechanisms of synergistic epistasis.     

A triple test cross analysis to detect epistatic gene effects in cabbage (Brassica oleracea var. capitata L.): An updated methodology

The cross-pollinated crop Brassica oleracea var. capitata L. shows good heterotic heterosis at high output; better standing of the plants; early maturity; larger and more homogeneous heads; consistency of head compactness; and disease-tolerance in F1 hybrids. There is very limited information documented on the epistasis of essential cabbage characters. We expand the research in this study to include an upgraded test to cross-design for enrolling and estimating epistasis and other genetic variance components controlling head yield and component traits in cabbage. The data was obtained from 45 families produced by crossing 15 lines with three testers; SC 2008–09, E-1-3-1&2, and their single cross F1, was subjected to triple test cross analysis. The current study results confirmed “j + 1” form of epistasis which is a major component for all traits. The plant spread, non-wrapper leaves, nethead/grossweight, polar/equatorial diameter, marketable head yield per plot, iron content and dry matter lugged both “j + 1” and 'i' type with the predominance of the 'i' type of interaction. Except for head shape index, equatorial diameter, head compactness was more noticeable when observed in dominance component. The degree of dominance is in the partial range, but both the head shape index/compactness and equatorial diameter showed over dominance. For maximum part, superiority was shown in both the directions. Appropriate breeding procedures are proposed to exploit the different forms of gene effects discovered for genetic improvement of head yield and quality traits.     

The nature of gene action in a Nicotiana rustica cross revealed by the recombinant inbred and second-cycle hybrid analysis

 A unique set of data recorded on 60 randomly extracted single-seed-descent (F_∞) lines of a highly heterotic cross between two varieties of Nicotiana rustica and their 870 reciprocally produced pairwise crosses, the second-cycle hybrids (SCH), are analysed to investigate the true nature of genetical control in the cross and the results are compared with those in earlier publications. The analysis revealed that epistasis, genotype-by-micro-environmental interaction, maternal effects and linkage are significant for several characters and the additive and non-additive components of variation take large values for all of the traits. Epistasis is predominantly duplicate and not complementary. Dominance is high but partial, all estimates of dominance ratio lying between 0.5 and 0.9. Dominance is predominantly unidirectional for leaf length, leaf width and final height, while for the remaining traits, some genes show ambidirectional dominance, although the incidence of unidirectional dominance is much higher throughout. The direction of dominance is predominantly for the increased score, except for flowering time where alleles conferring earliness are up to five times more frequently dominant. The present study has also confirmed that the F₂ and SCH_i distributions are very similar and that the former can be used to predict the transgression in the latter with confidence. The reduced range of the SCH _i families compared to the recombinant inbreds, further indicated that heterosis among many of the SCH_i is due to gene dispersion and there is little evidence for the presence of over-dominance. Received: 8 July 1996 / Accepted: 8 November 1996     

THE OCCURRENCE AND SIGNIFICANCE OF EPISTATIC VARIANCE FOR QUANTITATIVE CHARACTERS AND ITS MEASUREMENT IN HAPLOIDS

Epistatic genetic variance for quantitative traits may play an important role in evolution, but detecting epistasis in diploid organisms is difficult and requires complex breeding programs and very large sample sizes. We develop a model for detecting epistasis in organisms with a free-living haploid stage in their life cycles. We show that epistasis is indicated by greater variance among families of haploid progeny derived from individual diploids than among clonally replicated haploid sibs from the same sporophyte. Simulations show that the power to detect epistasis is linearly related to the number of sporophytes and the number of haploids per sporophyte in the dataset. We illustrate the model with data from growth variation among gametophytes of the moss, Ceratodon purpureus. The experiment failed to detect epistatic variance for biomass production, although there was evidence of additive variance.     

Single tester triple test cross analysis in spring wheat

Summary Two experiments, each including the same 30 homozygous varieties of spring wheat plus one separate tester variety, were conducted in order to detect epistasis and to test and estimate the additive and dominance components of genetic variation for five quantitative traits: final plant height, spike length, number of spikelets per spike, 100-kernel weight and grain yield per plant. Epistasis played a significant role in the control of 100-kernel weight and yield per plant. There was a gratifyingly good agreement between the two independent methods (2¯B₁i — ¯f_1i — ¯P_i and 2¯B_ci — ¯F_1i) used to test the presence of epistasis. In both experiments, there was a remarkably uniform high dominance ratio for most of the traits studied indicating that this test cross design is equally sensitive to both additive and dominance genetic variation.