Epistasis-aware genome-wide association studies provide insights into the efficient breeding of high-yield and high-quality rice

Marker-assisted selection(MAS)and genomic selection(GS)breeding have greatly improved the efficiency of rice breeding.Due to the influences of epistasis and gene pleiotropy,ensuring the actual breeding effect of MAS and GS is still a difficult challenge to overcome.In this study,113 indica rice varieties(V)and their 565 testcross hybrids(TC)were used as the materials to investigate the genetic basis of 12 quality traits and nine agronomic traits.The original traits and general combining ability of the parents,as well as the original traits and midparent heterosis of TC,were subjected to genome-wide association analysis.In total,381 primary significantly associated loci(SAL)and 1,759 secondary SALs that had epistatic interactions with these primary SALs were detected.Among these loci,322 candidate genes located within or nearby the SALs were screened,204 of which were cloned genes.A total of 39 MAS molecular modules that are beneficial for trait improvement were identified by pyramiding the superior haplotypes of candidate genes and desirable epistatic alleles of the secondary SALs.All the SALs were used to construct genetic networks,in which 91 pleiotropic loci were investigated.Additionally,we estimated the accuracy of genomic prediction in the parent V and TC by incorporating either no SALs,primary SALs,secondary SALs or epistatic effect SALs as covariates.Although the prediction accuracies of the four models were generally not significantly different in the TC dataset,the incorporation of primary SALs,secondary SALs,and epistatic effect SALs significantly improved the prediction accuracies of 5(26%),3(16%),and 11(58%)traits in the V dataset,respectively.These results suggested that SALs and epistatic effect SALs identified based on an additive genotype can provide considerable predictive power for the parental lines.They also provide insights into the genetic basis of complex traits and valuable information for molecular breeding in rice.

Influence of Epistasis and QTL×Environment Interaction on Heading Date of Rice(Oryza sativa L.)

QTLs for heading date of rice （Oryza sativa L.） with additive, epistatic, and QTL × environment （QE） interaction effects were studied using a mixed-model-based composite interval mapping （MCIM） method and a double haploid （DH） population derived from IR64/Azucena in two crop seasons. Fourteen QTLs conferring heading date in rice, which were distributed on ten chromosomes except for chromosomes 5 and 9, were detected. Among these QTLs, eight had single-locus effects, five pairs had double-locus interaction effects, and two single-loci and one pair of double-loci showed QTL × environment interaction effects. All predicted values of QTL effects varied from 1.179 days to 2.549 days, with corresponding contribution ratios of 1.04%-4.84%. On the basis of the effects of the QTLs, the total genetic effects on rice heading date for the two parents and the two superior lines were predicted, and the putative reasons for discrepancies between predicted values and observed values, and the genetic potentiality in the DH population for improvement of heading date were discussed. These results are in agreement with previous results for heading date in rice, and the results provide further information, which indicate that both epistasis and QE interaction are important genetic basis for determining heading date in rice.

Mapping epistasis and environment × QTX interaction based on four-omics genotypes for the detected QTX loci controlling complex traits in tobacco

Using newly developed methods and software, association mapping was conducted for chromium content and total sugar in tobacco leaf, based on four-omics datasets. Our objective was to collect data on genotype and phenotype for 60 leaf samples at four developmental stages, from three plant architectural positions and for three cultivars that were grown in two locations. Association mapping was conducted to detect genetic variants at quantitative trait SNP(QTS) loci, quantitative trait transcript(QTT) differences,quantitative trait protein(QTP) variability, and quantitative trait metabolite(QTM) changes,which can be summarized as QTX locus variation. The total heritabilities of the four-omics loci for both traits tested were 23.60% for epistasis and 15.26% for treatment interaction.Epistasis and environment × treatment interaction had important impacts on complex traits at all-omics levels. For decreasing chromium content and increasing total sugar in tobacco leaf, six methylated loci can be directly used for marker-assisted selection, and expression of ten QTTs, seven QTPs and six QTMs can be modified by selection or cultivation.

Analyzing the Interdependence Between Some Certain Gene Loci by Epistasis Measures in Fitness Landscapes of Schemata

GA hardness and interdependence between genes in the chromosome are important questions in the study of genetic algorithms(GA). Traditional methods, which are used to measure the interaction between genes, can only reflect the extent of epistasis between all genes in the chromosome. Therefore, the definition of the fitness landscape of schemata is proposed in this paper, and epistasis measures on this landscape of schemata are used to analyze the degree of interdependence between some certain gene loci in study. Some information between these sites can be reflected by some characters of the fitness landscape of schemata which are composed of these fixed sites. The stronger the interaction between these sites, the larger the variation of the fitness of schemata whose fixed sites correspond to those sites in study, and the more rugged the fitness landscape of these schemata. According to the degree of interaction between these given gene loci, building blocks of GA can be analyzed and determined, and further genetic operators and the structure of GA can be designed and adjusted to improve the performance of GA. At last, a lot of experiments including NK models are done, and results of empirical analysis show that this method is effective.

Epistasis and Maternal Effect in Resistance to Puccinia coronata Cda.f.sp. avenae Eriks in Oats(Avena sp.)

The objective of this paper was to investigate the mode of heredity for resistance in oats （Avena sp.） to crown rust caused by Puccinia coronata Cda. f. sp. avenae Eriks, Eight generations of 2 crosses were used to estimate genetic effects and narrow-sense heritability （NSH）. Separate generation means analysis （GMA） indicated a complex gene action controlling this trait with additive, dominance, epistatic and maternal effects （ME）. The genetic model which assumed no epistasis and no ME did not accurately describe the resistance to P. coronata. In both crosses, the digenic epistatic model with ME was sufficient to explain variation in generation means for isolate CRec58 and isolate CRec46. Additive dominance and epistatic components were negative in most cases, suggesting that gene effects contributed more to the resistance than to the susceptibility. The estimated values of NSH were 15-99% depending upon the cross and isolates. The results indicated that appropriate choice of maternal parent and recurrent selection would increase resistance to crown rust in oats.

QTL Mapping and Epistasis Analysis for Yield Traits in an RIL Population of Rice(Oryza sativa L.)

A genetic linkage map consisting of 168 DNA markers was constructed based on a recombinant inbred line(RID population derived from a cross between a high yielding indica variety, Zhong156, and a low yielding indica variety, Gumeil. The markers on the linkage map were distributed on all 12 chromosomes and covered 1 447. 9 cM of the genome. The parents and 304 RILs were grown in China National Rice Research Institute(CNRRI), Hangzhou, China, in 2001, over two seasons in a randomized block design. The statistic software of QTL Mapper 1.01 was applied to detect quantitative trait loci(QTLs)and additive by environment(AE)interactions for yield traits, including panicle length, number of panicles per plant, number of spikelets per panicle, number of filled grains per panicle, fertility and kilo-grain weight. A total of 30 QTLs with significant additive effects located on all chromosomes, except chromosomes 5 and 9, and two QTLs with significant AE interactions, were detected. Thirty-one interactions of QTLs showing significant additive by additive epistatic effects for yield traits were also detected. Genetic contributions were generally lower for QTLs showing epistatic effects compared with QTLs showing additive effects. No significant interactions between epistasis and environment were detected.

QTL Detection and Epistasis Analysis for Heading Date Using Single Segment Substitution Lines in Rice(Oryza sativa L.)

Heading date of rice is a key agronomic trait determining cultivated areas and seasons and affecting yield. In the present study, ifve primary single segment substitution lines with the same genetic background were used to detect quantitative trait loci （QTLs） for heading date in rice. Two QTLs, qHD3 and qHD6 on the short arm of chromosome 3 and the short arm of chromosome 6, respectively, were identiifed under natural long-day （NLD）. Nineteen secondary single segment substitution lines （SSSLs） and seven double segments pyramiding lines were designed to map the two QTLs and to evaluate their epistatic interaction between them. By overlapping mapping, qHD3 was mapped in a 791-kb interval between SSR markers RM3894 and RM569 and qHD6 in a 1 125-kb interval between RM587 and RM225. Results revealed the existence of epistatic interaction between qHD3 and qHD6 under natural long-day （NLD）. It was also found that qHD3 and qHD6 had signiifcant effects on plant height and yield traits, indicating that both of the QTLs have pleiotropic effects.

Identification of quantitative trait loci and epistasis for root characteristics and root exudations in maize (Zea mays L.) under deficient phosphorus

The phosphorus uptake （PU） in above-ground parts of plant, root characteristics and root exudations as well as the quantitative trait loci （QTLs） associated with these characteristics were determined for a F2：3 population derived from the cross of two contrasting maize （Zea mays L.） genotypes, 082 and Yel07. A total of 241 F2：3 families were evaluated in replicated trials under deficient phosphorus conditions in 2007 at two sites （Kaixian County and Southwest University, Chongqing, P. R. China）. The results show pleiotropy and close linkage among QTLs. Four common regions in different environments were in bnlg100- bnlg1268b （bins 1.02） for QTL of H＋, bnlg1268a-umc1290a （bins 1.09） for QTL of AP （acid phospbatase activity）, dupssrl5- P 1MT/a （bins 6.06） for QTLs of PU （phosphorus uptake） and RW （root weight）, and P IM3/d-P1M3/g （bins9.04） for QTLs of PU and AP. These QTLs are non-environment or minor QTLs x environment. By epistatic analysis, three main QTLs and eighteen QTLs x QTLs interactions were detected for the seven measured characteristics. These QTLs may affect trait expression by epistatic interaction with the other loci, and make a substantial contribution to phosphorus utilization efficiency, which should be considered when breeding maize varieties with high P efficiency. Two regions were detected in dupssrl 5- P1MT/a （bins 6.06） for QTL of RW and P1M3/d- P 1M3/g （bins 9.04） for QTL of PU and AP. They were detected in two different environments and by two methods of QTL analysis, which were useful for marker-assisted selection.

Epistasis in Predator-Prey Relationships

Epistasis is the interaction between two or more genes to control a single phenotype. We model epistasis of the prey in a two-locus two-allele problem in a basic predator-prey relationship. The resulting model allows us to examine both population sizes as well as genotypic and phenotypic frequencies. In the context of several numerical examples, we show that if epistasis results in an undesirable or desirable phenotype in the prey by making the particular genotype more or less susceptible to the predator or dangerous to the predator, elimination of undesirable phenotypes and then genotypes occurs.

SimHOEPI:A resampling simulator for generating single nucleotide polymorphism data with a high-order epistasis model

Epistasis is a ubiquitous phenomenon in genetics,and is considered to be one of main factors in current efforts to unveil missing heritability of complex diseases.Simulation data is crucial for evaluating epistasis detection tools in genome-wide association studies(GWAS).Existing simulators normally suffer from two limitations:absence of support for high-order epistasis models containing multiple single nucleotide polymorphisms(SNPs),and inability to generate simulation SNP data independently.In this study,we proposed a simulator SimHOEPI,which is capable of calculating penetrance tables of high-order epistasis models depending on either prevalence or heritability,and uses a resampling strategy to generate simulation data independently.Highlights of SimHOEPI are the preservation of realistic minor allele frequencies in sampling data,the accurate calculation and embedding of high-order epistasis models,and acceptable simulation time.A series of experiments were carried out to verify these properties from different aspects.Experimental results show that SimHOEPI can generate simulation SNP data independently with high-order epistasis models,implying that it might be an alternative simulator for GWAS.

The Statistical Power of Inclusive Composite Interval Mapping in Detecting Digenic Epistasis Showing Common F_2 Segregation Ratios

Epistasis is a commonly observed genetic phenomenon and an important source of variation of complex traits, which could maintain additive variance and therefore assure the long-term genetic gain in breeding. Inclusive composite interval mapping （ICIM） is able to identify epistatic quantitative trait loci （QTLs） no matter whether the two interacting QTLs have any additive effects. In this article, we conducted a simulation study to evaluate detection power and false discovery rate （FDR） of ICIM epistatic mapping, by considering F2 and doubled haploid （DH） populations, different F2 segregation ratios and population sizes. Results indicated that estimations of QTL locations and effects were unbiased, and the detection power of epistatic mapping was largely affected by population size, heritability of epistasis, and the amount and distribution of genetic effects. When the same likelihood of odd （LOD） threshold was used, detection power of QTL was higher in F2 population than power in DH population; meanwhile FDR in F2 was also higher than that in DH. The increase of marker density from 10 cM to 5 cM led to similar detection power but higher FDR. In simulated populations, ICIM achieved better mapping results than multiple interval mapping （MIM） in estimation of QTL positions and effect. At the end, we gave epistatic mapping results of ICIM in one actual population in rice （Oryza sativa L.）.

Privacy-preserving decision tree for epistasis detection

The interaction between gene loci,namely epistasis,is a widespread biological genetic phenomenon.In genome-wide association studies(GWAS),epistasis detection of complex diseases is a major challenge.Although many approaches using statistics,machine learning,and information entropy were proposed for epistasis detection,the privacy preserving for single nucleotide polymorphism(SNP)data has been largely ignored.Thus,this paper proposes a novel two-stage approach.A fusion strategy assists in combining and sorting the SNPs importance scores obtained by the relief and mutual information,thereby obtaining a candidate set of SNPs.This avoids missing some SNPs with strong interaction.Furthermore,differentially private decision tree is applied to search for SNPs.This achieves the efficient epistasis detection of complex diseases on the basis of privacy preserving compared with heuristic methods.The recognition rate on simulation data set is more than 90%.Also,several susceptible loci including rs380390 and rs1329428 are found in the real data set for Age-related Macular Degeneration(AMD).This demonstrates that our method is promising in epistasis detection.

Privacy-preserving decision tree for epistasis detection

The interaction between gene loci,namely epistasis,is a widespread biological genetic phenomenon.In genome-wide association studies(GWAS),epistasis detection of complex diseases is a major challenge.Although many approaches using statistics,machine learning,and information entropy were proposed for epistasis detection,the privacy preserving for single nucleotide polymorphism(SNP)data has been largely ignored.Thus,this paper proposes a novel two-stage approach.A fusion strategy assists in combining and sorting the SNPs importance scores obtained by the relief and mutual information,thereby obtaining a candidate set of SNPs.This avoids missing some SNPs with strong interaction.Furthermore,differentially private decision tree is applied to search for SNPs.This achieves the efficient epistasis detection of complex diseases on the basis of privacy preserving compared with heuristic methods.The recognition rate on simulation data set is more than 90%.Also,several susceptible loci including rs380390 and rs1329428 are found in the real data set for Age-related Macular Degeneration(AMD).This demonstrates that our method is promising in epistasis detection.

The R2R3-MYB transcription factor GaPC controls petal coloration in cotton

Although a few cases of genetic epistasis in plants have been reported, the combined analysis of genetically phenotypic segregation and the related molecular mechanism remains rarely studied. Here, we have identified a gene(named GaPC) controlling petal coloration in Gossypium arboreum and following a heritable recessive epistatic genetic model. Petal coloration is controlled by a single dominant gene,GaPC. A loss-of-function mutation of GaPC leads to a recessive gene Gapc that masks the phenotype of other color genes and shows recessive epistatic interactions. Map-based cloning showed that GaPC encodes an R2R3-MYB transcription factor. A 4814-bp long terminal repeat retrotransposon insertion at the second exon led to GaPC loss of function and disabled petal coloration. GaPC controlled petal coloration by regulating the anthocyanin and flavone biosynthesis pathways. Expression of core genes in the phenylpropanoid and anthocyanin pathways was higher in colored than in white petals. Petal color was conferred by flavonoids and anthocyanins, with red and yellow petals rich in anthocyanin and flavonol glycosides, respectively. This study provides new insight on molecular mechanism of recessive epistasis,also has potential breeding value by engineering GaPC to develop colored petals or fibers for multifunctional utilization of cotton.

A stable and major QTL region on chromosome 2 conditions pod shape in cultivated peanut(Arachis hyopgaea L.)

Peanut pod shape is a heritable trait which affects the market acceptance of in-shell peanut products.In order to determine the genetic control of pod shape,six component traits of pod shape(pod length,pod width,pod length/width ratio,pod roundness,beak degree and constriction degree)were measured using an image-based phenotyping method.A recombinant inbred line(RIL)population consisting of 181 lines was phenotyped across three environments.Continuous distributions and transgressive segregations were demonstrated in all measured traits and environments.Significant correlations were found among most component traits with broad-sense heritability ranging from 0.87 to 0.95.Quantitative trait locus(QTL)analysis yielded 26 additive QTLs explaining 3.79 to 52.37%phenotypic variations.A novel,stable and major QTL region conditioning multiple shape features was detected on chromosome 2,which spans a 10.81-Mb genomic region with 543 putative genes.Bioinformatics analysis revealed several candidate genes in this region.In addition,73 pairs of epistatic interactions involving 92 loci were identified for six component traits explaining 0.94–6.45%phenotypic variations.These results provide new genetic loci to facilitate genomics-assisted breeding of peanut pod shape.

Genetic Analysis of Root Growth in Rice Seedlings Under Different Water Supply Conditions

To understand the genetic background of root growth of rice ( Oryza sativa L.) seedlings under different water supply conditions, quantitative trait loci (QTLs) and epistatic effect on seminal root length, maximum adventitious root length, adventitious root number, total root dry weight and ratio of root to shoot were detected using molecular map including 103 restriction fragment length polymorphism (RFLP) markers and 104 amplified fragment length polymorphism (AFLP) markers mapped on a recombinant inbred line (RIL) population with 150 lines derived from a cross between an lowland rice IR1552 and an upland rice Azucena in both solution culture (lowland condition) and paper culture (upland condition). Six QTLs and twenty-two pairs of epistatic loci for the four parameters were detected. Three QTLs detected for maximum adventitious root length in solution culture (MARLS), total root dry weight in both solution culture and paper culture (TRDWS and TRDWP) accounted for about 20%, 23% and 13% of the total variations, respectively. Only epistatic loci were found for maximum adventitious root length and adventitious root number in paper culture (MARLP and ARNP), and for ratio of root to shoot in both paper and solution culture (R/SP and R/SS), which accounted for about 12%-61% of the total variations in the parameters, respectively. No identical QTL or epistatic loci were found for the parameters in both solution and paper culture. The results indicate that there is a different genetic system responsible to root growth of rice seedlings under lowland and upland conditions and epistasis might be the major genetic basis for MARLP, ARNP, R/SP and R/SS.

Analysis of digenic epistatic effects and QE interaction effects QTL controlling grain weight in rice

Immortalized F2 population of rice (Oryza sativa L.) was developed by randomly mating F1 among recombinant inbred (RI) lines derived from (Zhenshan 97B×Minghui 63),which allowed replications within and across environments.QTL (quantitative trait loci) mapping analysis on kilo-grain weight of immortalized F2 population was performed by using newly developed software for QTL mapping,QTL Mapper 2.0. Eleven distinctly digenic epistatic loci included a total of 15 QTL were located on eight chromosomes.QTL main effects of additive,dominance,and additive×additive,additive×dominance,and dominance×dominance interactions were estimated.Interaction effects between QTL main effects and environments (QE) were predicted.Less than 40% of single effects,most of which were additive effects,for identified QTL were significant at 5% level.The directional difference for QTL main effects suggested that these QTL were distributed in parents in the repulsion phase.This should make it feasible to improve kilo-grain weight of both parents by selecting appropriate new recombinants. Only few of the QE interaction effects were significant.Application prospect for QTL mapping achievements in genetic breeding was discussed.

Advanced Backcross QTL Analysis for the Whole Plant Growth Duration Salt Tolerance in Rice(Oryza sativa L.)

Salinity is a major factor limiting rice yield in coastal areas of Asia. To facilitate breeding salt tolerant rice varieties, the wholeplant growth duration salt tolerance（ST） was genetically dissected by phenotyping two sets of BC2F5 introgression lines（ILs） for four yield traits under severe natural salt stress and non-stress filed conditions using SSR markers and the methods of advanced backcross QTL（AB-QTL） analysis and selective introgression. Many QTLs affecting four yield traits under salt stress and nonstress conditions were identified, most（〉90%） of which were clustered in 13 genomic regions of the rice genome and involved in complex epistasis. Most QTLs affecting yield traits were differentially expressed under salt stress and non-stress conditions. Our results suggested that genetics complementarily provides an adequate explanation for the hidden genetic diversity for ST observed in both IL populations. Some promising Huanghuazhan（HHZ） ILs with favorable donor alleles at multiple QTLs and significantly improved yield traits under salt stress and non-stress conditions were identified, providing excellent materials and relevant genetic information for improving rice ST by marker-assisted selection（MAS） or genome selection.

Characterization of the Main Effects, Epistatic Effects and Their Environmental Interactions of QTL on the Genetic Basis of Plant Height and Heading Date in Rice

Main-effect QTL, epistatic effects and their interactions with environment are important genetic components of quantitativetraits. In this study, we analyzed the QTL, epistatic effects and QTL by environment interactions (QE) underlying plantheight and heading date, using a doubled-haploid ( DH) population consisting of 190 lines from the cross between anindica parent Zhenshan 97 and a japonica parent Wuyujing 2, and tested in two-year replicated field trials. A geneticlinkage map with 179 SSR (simple sequence repeat) marker loci was constructed. A mixed linear model approach wasapplied to detect QTL, digenic interactions and QEs for the two traits. In total, 20 main-effect QTLs, 9 digenic interactionsinvolving 18 loci, and 5 QTL by environment interactions were found to be responsible for the two traits. No interactionswere detected between the digenic interaction and environment. The amounts of variations explained by QTLs of maineffect were 53.9% for plant height and 57.8% for heading date, larger than that explained by epistasis and QEs. However,the epistasis and QE interactions sometimes accounted for a significant part of phenotypic variation and should not bedisregarded.

Genetic mapping of QTL for agronomic traits and grain mineral elements in rice

Malnutrition is one of the prevailing health problems worldwide, affecting a large proportion of the populations in rice-consuming countries. Breeding rice varieties with increased concentrations of elements in the grain is considered the most cost-effective approach to alleviate malnutrition. Development of molecular markers for high grain concentrations of essential elements, particularly Zn, for use in marker-assisted selection (MAS) can hasten breeding efforts to develop rice varieties with nutrient-dense grain. We performed QTL mapping for four agronomic traits: days to 50% flowering, plant height, number of tillers, grain yield, and 13 grain elements: As, B, Ca, Co, Cu, Fe, K, Mg, Mn, Mo, Na, P, and Zn, in two doubled-haploid populations derived from the crosses IR64 × IR69428 and BR29 × IR75862. These populations were phenotyped during 2015DS and 2015WS at IRRI, Los Ba os, The Philippines, and genotyped them with a 6 K SNP chip. Inclusive composite interval mapping revealed 15 QTL for agronomic traits and 50 QTL for grain element concentration. Of these, eight QTL showed phenotypic variance of >25% and 11 QTL were consistent across seasons. There were seven QTL co-localization regions containing QTL for more than two traits. Twenty five epistatic interactions were detected for two agronomic traits and seven mineral elements. Several DH lines with high Fe and Zn in polished rice were identified. These lines can be used as donors for breeding high-Zn rice varieties. Some of the major QTL can be further validated and used in MAS to improve the concentrations of nutritive elements in rice grain.