Statistical approaches in QTL mapping and molecular breeding for complex traits

Most of the important agronomic traits in crops,such as yield and quality,are complex traits affected by multiple genes with gene × gene interaction as well as gene × environment interaction.Understanding the genetic architecture of complex traits is a long-term task for quantitative geneticists and plant breeders who wish to design efficient breeding programs.Conventionally,the genetic properties of traits can be revealed by partitioning the total variation into variation components caused by specific genetic effects.With recent advances in molecular genotyping and high-throughput technology,the unraveling of the genetic architecture of complex traits by analyzing quantitative trait locus (QTL) has become possible.The improvement of complex traits has also been achieved by pyramiding individual QTL.In this review,we describe some statistical methods for QTL mapping that can be used to analyze QTL × QTL interaction and QTL × environment interaction,and discuss their applications in crop breeding for complex traits.     

A statistical method for genetic mapping of sterility genes that exhibit epistasis in remote hybridization of plants using molecular markers in an F2 population

Estimation of the position and effect of sterility genes is an important problem to be solved to understand the sterility mechanism in remote hybridization in plants.In this study,a maximum likelihood (ML) method was used for estimation of the position and effect of sterility genes that exhibit epistasis in an F 2 population using the distorted segregation of markers.The ML solutions for recombination fraction and viability were obtained via an expectation-maximization algorithm.The results of Monte Carlo simulations showed that the estimates of recombination fraction and viability were consistent with their true values.The bias and standard deviation of parameters indicated that a larger sample size,closer linkage and lower viability of sterile genes led to better estimates of the parameters involved.A subset of marker data of the F 2 population derived from a single cross between the rice japonica cultivar Nipponbare and the indica cultivar Kasalath was analyzed using this method.Eight sterility genes were identified on chromosomes 1,3,6,8 and 10,and significant epistasis was detected among four pairs of sterility genes.     

Gene conversion in the chicken immunoglobulin locus: A paradigm of homologous recombination in higher eukaryotes

Gene conversion was first defined in yeast as a type of homologous recombination in which the donor sequence does not change. In chicken B cells, gene conversion builds the antigen receptor repertoire by introducing sequence diversity into the immunoglobulin genes. Immunoglobulin gene conversion continues at high frequency in an avian leukosis virus induced chicken B cell line. This cell line can be modified by homologous integration of transfected DNA constructs offering a model system for studying gene conversion in higher eukaryotes. In search for genes which might participate in chicken immunoglobulin gene conversion, we have identified chicken counterparts of the yeastRAD51, RAD52, andRAD54 genes. Disruption and overexpression of these genes in the chicken B cell line may clarify their role in gene conversion and gene targeting.     

Fitness Landscape Analysis for Optimum Multiuser Detection Problem

Optimum multiuser detection （OMD） for CDMA systems is an NP-complete combinatorial optimization problem. Fitness landscape has been proven to be very useful for understanding the behavior of combinatorial optimization algorithms and can help in predicting their performance. This paper analyzes the statistic properties of the fitness landscape of the OMD problem by performing autocorrelation analysis, fitness distance correlation test and epistasis measure. The analysis results explain why some random search algorithms are effective methods for OMD problem and give hints how to design more efficient randomized search heuristic algorithms for OMD.     

Genome-Wide Interaction-Based Association of Human Diseases—A Survey

Genome-Wide Association Studies（GWASs） aim to identify genetic variants that are associated with disease by assaying and analyzing hundreds of thousands of Single Nucleotide Polymorphisms（SNPs）. Although traditional single-locus statistical approaches have been standardized and led to many interesting findings, a substantial number of recent GWASs indicate that for most disorders, the individual SNPs explain only a small fraction of the genetic causes. Consequently, exploring multi-SNPs interactions in the hope of discovering more significant associations has attracted more attentions. Due to the huge search space for complicated multilocus interactions, many fast and effective methods have recently been proposed for detecting disease-associated epistatic interactions using GWAS data. In this paper, we provide a critical review and comparison of eight popular methods, i.e., BOOST, TEAM, epi Forest, EDCF, SNPHarvester, epi MODE, MECPM, and MIC, which are used for detecting gene-gene interactions among genetic loci. In views of the assumption model on the data and searching strategies, we divide the methods into seven categories. Moreover, the evaluation methodologies,including detecting powers, disease models for simulation, resources of real GWAS data, and the control of false discover rate, are elaborated as references for new approach developers. At the end of the paper, we summarize the methods and discuss the future directions in genome-wide association studies for detecting epistatic interactions.     

Statistical method for mapping QTLs for complex traits based on two backcross populations

Most important agronomic and quality traits of crops are quantitative in nature.The genetic variations in such traits are usually controlled by sets of genes called quantitative trait loci (QTLs),and the interactions between QTLs and the environment.It is crucial to understand the genetic architecture of complex traits to design efficient strategies for plant breeding.In the present study,a new experimental design and the corresponding statistical method are presented for QTL mapping.The proposed mapping population is composed of double backcross populations derived from backcrossing both homozygous parents to DH (double haploid) or RI (recombinant inbreeding) lines separately.Such an immortal mapping population allows for across-environment replications,and can be used to estimate dominance effects,epistatic effects,and QTL-environment interactions,remedying the drawbacks of a single backcross population.In this method,the mixed linear model approach is used to estimate the positions of QTLs and their various effects including the QTL additive,dominance,and epistatic effects,and QTL-environment interaction effects (QE).Monte Carlo simulations were conducted to investigate the performance of the proposed method and to assess the accuracy and efficiency of its estimations.The results showed that the proposed method could estimate the positions and the genetic effects of QTLs with high efficiency.     

Bin-based model construction and analytical strategies for dissecting complex traits with chromosome segment substitution lines

Chromosome segment substitution lines have been created in several experimental models,including many plant and animal species,and are useful tools for the genetic analysis and mapping of complex traits.The traditional t-test is usually applied to identify a quantitative trait locus (QTL) that is contained within a chromosome segment to estimate the QTL’s effect.However,current methods cannot uncover the entire genetic structure of complex traits.For example,current methods cannot distinguish between main effects and epistatic effects.In this paper,a linear epistatic model was constructed to dissect complex traits.First,all the long substituted segments were divided into overlapping small bins,and each small bin was considered a unique independent variable.The genetic model for complex traits was then constructed.When considering all the possible main effects and epistatic effects,the dimensions of the linear model can become extremely high.Therefore,variable selection via stepwise regression (Bin-REG) was proposed for the epistatic QTL analysis in the present study.Furthermore,we tested the feasibility of using the LASSO (least absolute shrinkage and selection operator) algorithm to estimate epistatic effects,examined the fully Bayesian SSVS (stochastic search variable selection) approach,tested the empirical Bayes (E-BAYES) method,and evaluated the penalized likelihood (PENAL) method for mapping epistatic QTLs.Simulation studies suggested that all of the above methods,excluding the LASSO and PENAL approaches,performed satisfactorily.The Bin-REG method appears to outperform all other methods in terms of estimating positions and effects.     

Primary analysis of QTG contribution to heterosis in upland cotton

In this paper, we analyzed the contribution of pure DNA factors to heterosis using quantitative trait genes (QTG) in two randomly selected strains from a recombinant inbred line of Gossypium hirsutum. According to a set of QTL mapping results, combined with analysis of DNA recombinant fragment sources in the two strains and QTL association analysis with their field traits, we hypothesize a view of “dominance + overdominance + epistasis”. That is, additive and additive epistasis may be the genetic basis of heterosis, and dominance, overdominance and epistasis may be the modes of heterosis action. Based on the heterosis results of this study, we also suggest a molecular mechanism for heterosis, and explain, in detail, with two randomly selected strains as examples. The male and female parent-derived additive epistatic QTLs of upper half mean length in LG01 and LG03 produced a trait variance of 2.99–3.52 compared with the female parent-derived loci. The trait of bolls per plant was controlled by two pairs of additive epistatic QTLs in LG02 and LG07, which were derived from both female and male parents. The QTLs were reciprocally interacted and produced a trait variance of 0.86. An initial concept of “super-hybrid cotton” was raised according to the nature of additive effect, that is genetic stability.     

A correlation method of detecting and estimating interactions of QTLs

More and more studies demonstrate that a great deal of interactions among the quantitative trait loci (QTLs) are far more than those detected by single markers. A correlation method was proposed for estimating the interactions of multiple QTLs detected by multi-markers in several mapping populations. Genetic implication of this method and usage were discussed.     

Correlation analysis and QTL identification for canopy temperature, leaf water potential and spikelet fertility in rice under contrasting moisture regimes

Canopy temperature (CT), leaf water potential(LWP) and spikelet fertility (SF) of a set of RILs (F9) from the cross between Zhenshan97B and IRAT109 were investigated under two soil moisture regimes in a drought screen facility. In water stress condition, CT was negatively correlated with SF (r = -0.2867) and LWP (r = -0.2740), and LWP was positively associated with SF (r = 0.1696). These results indicated that the plant with high drought tolerant ability could maintain higher LWP and lower CT, leading to highe rSF. A total of 44 main effect QTLs were associated with CT,LWP and SF. The accumulated contributions of QTLs for CT,LWP and SF were 87.85%, 15.06%, 79.46% under well water condition and 72.61%, 87.68%, 33.29% under stress condition, respectively. Totally 45 pairs of digenic interactions were detected. The accumulated contribution of digenic epistasis on CT, LWP and SF were 55.69%, 47.15%, 48.15% under well water condition and 53.44%, 57.94%, 54.62% under water stress condition. Compared with other drought tolerance QTL mapping researches in rice, 19 main effect QTLs were found to be located at the same or closely conjoint regions.