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.     

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.     

Heterosis for biomass-related traits in Arabidopsis investigated by quantitative trait loci analysis of the triple testcross design with recombinant inbred lines

Arabidopsis thaliana has emerged as a leading model species in plant genetics and functional genomics including research on the genetic causes of heterosis. We applied a triple testcross (TTC) design and a novel biometrical approach to identify and characterize quantitative trait loci (QTL) for heterosis of five biomass-related traits by (i) estimating the number, genomic positions, and genetic effects of heterotic QTL, (ii) characterizing their mode of gene action, and (iii) testing for presence of epistatic effects by a genomewide scan and marker x marker interactions. In total, 234 recombinant inbred lines (RILs) of Arabidopsis hybrid C24 x Col-0 were crossed to both parental lines and their F1 and analyzed with 110 single-nucleotide polymorphism (SNP) markers. QTL analyses were conducted using linear transformations Z1, Z2, and Z3 calculated from the adjusted entry means of TTC progenies. With Z1, we detected 12 QTL displaying augmented additive effects. With Z2, we mapped six QTL for augmented dominance effects. A one-dimensional genome scan with Z3 revealed two genomic regions with significantly negative dominance x additive epistatic effects. Two-way analyses of variance between marker pairs revealed nine digenic epistatic interactions: six reflecting dominance x dominance effects with variable sign and three reflecting additive x additive effects with positive sign. We conclude that heterosis for biomass-related traits in Arabidopsis has a polygenic basis with overdominance and/or epistasis being presumably the main types of gene action.     

Something Old and Something New: Wedding Recombinant Inbred Lines with Traditional Line Cross Analysis Increases Power to Describe Gene Interactions

In this paper we present a novel approach to quantifying genetic architecture that combines recombinant inbred lines (RIL) with line cross analysis (LCA). LCA is a method of quantifying directional genetic effects (i.e. summed effects of all loci) that differentiate two parental lines. Directional genetic effects are thought to be critical components of genetic architecture for the long term response to selection and as a cause of inbreeding depression. LCA typically begins with two inbred parental lines that are crossed to produce several generations such as F1, F2, and backcrosses to each parent. When a RIL population (founded from the same P1 and P2 as was used to found the line cross population) is added to the LCA, the sampling variance of several nonadditive genetic effect estimates is greatly reduced. Specifically, estimates of directional dominance, additive x additive, and dominance x dominance epistatic effects are reduced by 92%, 94%, and 56% respectively. The RIL population can be simultaneously used for QTL identification, thus uncovering the effects of specific loci or genomic regions as elements of genetic architecture. LCA and QTL mapping with RIL provide two qualitatively different measures of genetic architecture with the potential to overcome weaknesses of each approach alone. This approach provides cross-validation of the estimates of additive and additive x additive effects, much smaller confidence intervals on dominance, additive x additive and dominance x dominance estimates, qualitatively different measures of genetic architecture, and the potential when used together to balance the weaknesses of LCA or RIL QTL analyses when used alone.     

Effect on linkage disequilibrium of selection for a quantitative character with epistasis

Summary Selection for a character controlled by additive genes induces linkage disequilibrium which reduces the additive genetic variance usable for further selective gains. Additive x additive epistasis contributes to selection response through development of linkage disequilibrium between interacting loci. To investigate the relative importance of the two effects of linkage disequilibrium, formulae are presented and results are reported of simulations using models involving additive, additive x additive and dominance components. The results suggest that so long as epistatic effects are not large relative to additive effects, and the proportion of pairs of loci which show epistasis is not very high, the predominant effect of linkage disequilibrium will be to reduce the rate of selection response.     

Epistasis in maize (Zea mays L.)

Summary Three flint and three dent maize (Zea mays L.) inbred lines, their possible F₁ crosses, F₂ and backcross progenies, and all possible three-way crosses were evaluated in a three-year experiment for yield, ear moisture, and plant height. The purpose was to estimate genetic parameters in European breeding materials from (i) generation means analysis, (ii) diallel analysis of generation means, and (iii) analysis of F₁ and three-way cross hybrids. Method (i) was based on the F-metric model and methods (ii) and (iii) on the Eberhart-Gardner (1966) genetic model; both models extended for heterotic maternal effects.Differences among generation means for yield and plant height were mainly attributable to dominance effects. Epistatic effects were significantly different from zero in a few crosses and considerably reduced heterosis in both traits. Additive x additive and domiance x dominance effects for yield were consistently positive and negative, respectively. Significant maternal effects were established to the advantage of generations with a heterozygous seed parent. In the diallel analysis, mean squares for dominance effects were greater than for additive effects for yield and plant height but smaller for ear moisture. Though significant for yield and plant height, epistatic variation was small compared to additive and dominance variation. Estimates of additive x additive epistasis for yield were significantly negative in 11 of 15 crosses, suggesting that advantageous gene combinations in the lines had been disrupted by recombination in the segregating generations. The analysis of hybrids supported the above findings regarding the analysis of variance. However, the estimates of additive x additive epistasis for yield were considerably smaller and only minimally correlated with those from the diallel analysis. Use of noninbred materials as opposed to materials with different levels of inbreeding is considered the main reason for the discrepancies in the results.     

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.     

The genetic architecture of male colour differences between a sympatric Lake Malawi cichlid species pair

The genetic basis of traits involved in reproductive isolation is a key parameter in models of sympatric speciation by sexual selection, a potential mechanism driving the explosive radiation of East African cichlids. Analysis of hybrid crosses between two sympatric Lake Malawi cichlid species, representing the extremes of the extant colour distribution, generated Castle-Wright estimates of four to seven loci controlling colour differences. Segregation patterns deviated from a purely additive model with a significant contribution from dominance, and possibly also epistasis. Evidence was found for a strong influence of autosomal loci. As departures from simple additive variation could effect the operation of models of sympatric speciation, dominance and epistasis should not be neglected.     

Epistasis between calpain 1 and its inhibitor calpastatin within breeds of cattle

The calpain gene family and its inhibitors have diverse effects, many related to protein turnover, which appear to affect a range of phenotypes such as diabetes, exercise-induced muscle injury, and pathological events associated with degenerative neural diseases in humans, fertility, longevity, and postmortem effects on meat tenderness in livestock species. The calpains are inhibited by calpastatin, which binds directly to calpain. Here we report the direct measurement of epistatic interactions of causative mutations for quantitative trait loci (QTL) at calpain 1 (CAPN1), located on chromosome 29, with causative mutations for QTL variation at calpastatin (CAST), located on chromosome 7, in cattle. First we identified potential causative mutations at CAST and then genotyped these along with putative causative mutations at CAPN1 in >1500 cattle of seven breeds. The maximum allele substitution effect on the phenotype of the CAPN1:c.947G>C single nucleotide polymorphism (SNP) was 0.14 sigma(p) (P = 0.0003) and of the CAST:c.155C>T SNP was also 0.14 sigma(p) (P = 0.0011) when measured across breeds. We found significant epistasis between SNPs at CAPN1 and CAST in both taurine and zebu derived breeds. There were more additive x dominance components of epistasis than additive x additive and dominance x dominance components combined. A minority of breed comparisons did not show epistasis, suggesting that genetic variation at other genes may influence the degree of epistasis found in this system.     

THE GENETIC ARCHITECTURE OF WING SIZE DIVERGENCE AT VARYING SPATIAL SCALES ALONG A BODY SIZE CLINE IN DROSOPHILA MELANOGASTER

Latitudinal clines in quantitative traits are common, but surprisingly little is known about the genetic bases of these divergences and how they vary within and between clines. Here, we use line‐cross analysis to investigate the genetic architecture of wing size divergences at varying spatial scales along a body size cline in Drosophila melanogaster. Our results revealed that divergences in wing size along the cline were due to strong additive effects. Significant nonadditive genetic effects, including epistasis and maternal effects, were also detected, but they were relatively minor in comparison to the additive effects and none were common to all crosses. There was no evidence of increased epistasis in crosses between more geographically distant populations and, unlike in previous studies, we found no significant dominance effects on wing size in any cross. Our results suggest there is little variation in the genetic control of wing size along the length of the Australian cline. They also highlight marked inconsistencies in the magnitude of dominance effects across studies, which may reflect different opportunities for mutation accumulation while lines are in laboratory culture.     

Self-fertilization and the evolution of recombination

In this article, we study the effect of self-fertilization on the evolution of a modifier allele that alters the recombination rate between two selected loci. We consider two different life cycles: under gametophytic selfing, a given proportion of fertilizations involves gametes produced by the same haploid individual, while under sporophytic selfing, a proportion of fertilizations involves gametes produced by the same diploid individual. Under both life cycles, we derive approximations for the change in frequency of the recombination modifier when selection is weak relative to recombination, so that the population reaches a state of quasi-linkage equilibrium. We find that gametophytic selfing increases the range of epistasis under which increased recombination is favored; however, this effect is substantial only for high selfing rates. Moreover, gametophytic selfing affects the relative influence of different components of epistasis (additive x additive, additive x dominance, dominance x dominance) on the evolution of the modifier. Sporophytic selfing has much stronger effects: even a small selfing rate greatly increases the parameter range under which recombination is favored, when there is negative dominance x dominance epistasis. This effect is due to the fact that selfing generates a correlation in homozygosity at linked loci, which is reduced by recombination.     

Both additivity and epistasis control the genetic variation for fruit quality traits in tomato

The effect of a gene involved in the variation of a quantitative trait may change due to epistatic interactions with the overall genetic background or with other genes through digenic interactions. The classical populations used to map quantitative trait loci (QTL) are poorly efficient to detect epistasis. To assess the importance of epistasis in the genetic control of fruit quality traits, we compared 13 tomato lines having the same genetic background except for one to five chromosome fragments introgressed from a distant line. Six traits were assessed: fruit soluble solid content, sugar content and titratable acidity, fruit weight, locule number and fruit firmness. Except for firmness, a large part of the variation of the six traits was under additive control, but interactions between QTL leading to epistasis effects were common. In the lines cumulating several QTL regions, all the significant epistatic interactions had a sign opposite to the additive effects, suggesting less than additive epistasis. Finally the re-examination of the segregating population initially used to map the QTL confirmed the extent of epistasis, which frequently involved a region where main effect QTL have been detected in this progeny or in other studies.     

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.     

The separation of epistatic from additive and dominance variation in generation means. II

Summary The difficulty of specifying additive and dominance variation in the presence of epistasis is described. This difficulty can be overcome when the epistasis is at a relatively low level of intensity but when epistasis is the major source of genetic variation no measure of additive or dominance variation is possible.Heterosis in a cross between two inbred lines ofNicotiana rustica was found to be due to dominance opposed to a small extent by epistasis. The misleading nature of another method of partitioning heterosis is pointed out.     

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).     

Identification of QTL for maize resistance to common smut by using recombinant inbred lines developed from the Chinese hybrid Yuyu22

Common smut in maize, caused by Ustilago maydis, reduces grain yield greatly. Agronomic and chemical approaches to control such diseases are often impractical or ineffective. Resistance breeding could be an efficient approach to minimize the losses caused by common smut. In this study, quantitative trait loci (QTL) for resistance to common smut in maize were identified. In 2005, a recombinant inbred line (RIL) population along with the resistant (Zong 3) and susceptible (87-1) parents were planted in Beijing and Zhengzhou. Significant genotypic variation in resistance to common smut was observed at both locations after artificial inoculation by injecting inoculum into the whorl of plants with a modified hog vaccinator. Basing on a genetic map containing 246 polymorphic SSR markers with an average linkage distance of 9.11 cM, resistance QTL were analysed by composite interval mapping. Six additive-effect QTL associated with resistance to common smut were identified on chromosomes 3 (three QTL), 5 (one QTL) and 8 (two QTL), and explained 3.2% to 12.4% of the phenotypic variation. Among the 6 QTL, 4 showed significant QTL x environment (Q x E) interaction effects, which accounted for 1.2% to 2.5% of the phenotypic variation. Nine pairs of epistatic interactions were also detected, involving 18 loci distributed on all chromosomes except 2, 6 and 10, which contributed 0.8% to 3.0% of the observed phenotypic variation. However, no significant epistasis x environment interactions were detected. In total, additive QTL effects and Q x E interactions explained 38.8% and 8.0% of the phenotypic variation, respectively. Epistatic effects contributed 15% of the phenotypic variation. The results showed that besides the additive QTL, both epistasis and Q x E interactions formed an important genetic basis for the resistance to Ustilago maydis in maize.     

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.     

Genetic expectations of quantitative trait loci main and interaction effects obtained with the triple testcross design and their relevance for the analysis of heterosis

Interpretation of experimental results from quantitative trait loci (QTL) mapping studies on the predominant type of gene action can be severely affected by the choice of statistical model, experimental design, and provision of epistasis. In this study, we derive quantitative genetic expectations of (i) QTL effects obtained from one-dimensional genome scans with the triple testcross (TTC) design and (ii) pairwise interactions between marker loci using two-way analyses of variance (ANOVA) under the F(2)- and the F(infinity)-metric model. The theoretical results show that genetic expectations of QTL effects estimated with the TTC design are complex, comprising both main and epistatic effects, and that genetic expectations of two-way marker interactions are not straightforward extensions of effects estimated in one-dimensional scans. We also demonstrate that the TTC design can partially overcome the limitations of the design III in separating QTL main effects and their epistatic interactions in the analysis of heterosis and that dominance x additive epistatic interactions of individual QTL with the genetic background can be estimated with a one-dimensional genome scan. Furthermore, we present genetic expectations of variance components for the analysis of TTC progeny tested in a split-plot design, assuming digenic epistasis and arbitrary linkage.     

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.