Multi-QTL Mapping for Quantitative Traits Using Epistatic Distorted Markers

The interaction between segregation distortion loci (SDL) has been often observed in all kinds of mapping populations. However, little has been known about the effect of epistatic SDL on quantitative trait locus (QTL) mapping. Here we proposed a multi-QTL mapping approach using epistatic distorted markers. Using the corrected linkage groups, epistatic SDL was identified. Then, these SDL parameters were used to correct the conditional probabilities of QTL genotypes, and these corrections were further incorporated into the new QTL mapping approach. Finally, a set of simulated datasets and a real data in 304 mouse F₂ individuals were used to validate the new method. As compared with the old method, the new one corrects genetic distance between distorted markers, and considers epistasis between two linked SDL. As a result, the power in the detection of QTL is higher for the new method than for the old one, and significant differences for estimates of QTL parameters between the two methods were observed, except for QTL position. Among two QTL for mouse weight, one significant difference for QTL additive effect between the above two methods was observed, because epistatic SDL between markers C66 and T93 exists (P = 2.94e-4).     

Genetic mapping of sterile genes with epistasis in backcross designs

The mapping of sterile genes is an essential issue, which should be solved for the investigation of sterility mechanism in wide hybridization of plants. However, the methods formerly developed cannot address the problem of mapping sterile loci with epistasis. In this study, we developed a new method to map sterile genes with epistasis in wide hybridizations of plants using a backcross design. The maximum likelihood method was used to estimate the parameters of recombination fractions and effects of sterile genes, and the convergent results of these parameters were obtained using the expectation maximization (EM) algorithm. The application and efficiency of this method were tested and demonstrated by a set of simulated data and real data analysis. Results from the simulation experiments showed that the method works well for simultaneously estimating the positions and effects of sterile genes, as well as the epistasis between sterile genes. A real data set of a backcross (BC) population from an interspecific hybrid between cultivated rice, Oryza sativa, and its wild African relative, Oryza longistaminata, was analyzed using the new method. Five sterile genes were detected on the chromosomes of 1, 3, 6, 8 and 10, and significant epistatic effects were found among the four pairs of sterile genes.     

与偏分离位点连锁的QTL作图的统计方法

提出了一种统计方法,可以估计与偏分离位点连锁的QTL的位置和效应。该方法利用回交群体中呈现偏分离的分子标记,首先用最大似然法对偏分离位点与标记位点之间的重组率和配子存活率进行估计,然后用区间作图法估计加性-显性模型下QTL的位置和效应参数。该方法可用于对常规作图研究中表现偏分离的标记进行分析,以帮助我们发现新的偏分离基因（或不育基因）和数量性状位点。     

A new strategy for estimating two-locus recombination fractions under some natural inequality restrictions

Linkage analysis is now being widely used to map markers on each chromosome in the human genome, to map genetic diseases, and to identify genetic forms of common diseases. Two-locus linkage analysis and multi-locus analysis have been investigated comprehensively, and many computer programs have been developed to perform linkage analysis. Yet there exists a shortcoming in traditional methods, i.e., the parameter space of two-locus recombination fractions has not been emphasized sufficiently in the usual analyses. In this paper, we propose a new strategy for estimating the two-locus recombination fractions based on data of backcross family in the framework of some natural and necessary parameter restrictions. The new strategy is based on a restricted projection algorithm, which can provide fast reasonable estimates of recombination fraction, and can therefore serve as a superior alternative algorithm. Results obtained from both real and simulated data indicate that the new algorithm performs well in the estimation of recombination fractions and outperforms current methods.     

Influence of epistatic segregation distortion loci on genetic marker linkages in Japanese flounder

For genetic linkage analysis of Japanese flounder, 160 doubled haploids (DH) were artificially produced using mitotic gynogenesis and were genotyped for 458 simple sequence repeat (SSR) markers, 101 of which show distortional segregation. The genetic linkage map was constructed by modifying recombination fractions between the distorted markers. Between the corrected and uncorrected genetic maps, there were considerable differences in genetic distance, but not in relative locations among markers. Using a liability model, a segregation distortion locus (SDL), with an additive genetic effect of 1.772, was mapped between markers BDHYP387 and Poli56TUF of chromosome 24 in the corrected genetic map. Additionally, six pairs of epistatic SDLs were identified on chromosomes 1, 5, 8, 9, 23, and 24. Changes in genetic distances between markers did not occur on chromosome regions with main effect SDLs. However, most chromosome regions where genetic distances changed covered the detected epistatic SDLs. This study concluded that epistatic SDLs decrease linkages between markers and lengthen genetic distances in Japanese flounder. This finding has been partially validated in other DH populations derived from three female Japanese flounders.     

单位点孢子体-配子体互作模型中不育基因的位置和效应的估计方法

水稻籼粳亚种间杂交F1通常表现为高度不育,这种不育性的一种遗传学解释称为单位点孢子体-配子体互作模型.为了研究这种不育性,提出了一种统计方法,可以估计单位点孢子体-配子体互作模型中不育基因位点的位置和效应.该方法利用回交群体中呈现异常分离的标记位点,用最大似然法对不育基因与标记位点之间的重组率和雌配子存活率进行估计.由于所依据的是非连续变异的遗传标记的分离,而不是连续分布的配子育性指标,因此可以避免由育性直接估计所带来的重组率结果的不稳定.     

Marker-assisted introgression of 4 Phytophthora capsici resistance QTL alleles into a bell pepper line: validation of additive and epistatic effects

The aim of the present study was to transfer resistance to P. capsici alleles at four quantitative trait loci (QTLs) from a small fruited pepper into a bell pepper recipient line using markers. The marker-assisted selection program was initiated from a doubled-haploid line issued from the mapping population and involved three cycles of marker-assisted backcross (MAB). Two populations, derived by selfing the plants selected after the first selection cycle, were genotyped and evaluated phenotypically for their resistance level. The additive and epistatic effects of the four resistance factors were re-detected and validated in these populations, indicating that introgression of 4 QTLs in this MAB program was successful. A decrease of the effect for the moderate-effect QTLs and of the epistatic interaction was observed. Phenotypic evaluations of horticultural traits were performed on sample of each backcross generation. The results indicated an efficient return to the recipient phenotype using this MAB strategy.     

A nearest-neighboring-end algorithm for genetic mapping

MOTIVATION: High-throughput methods are beginning to make possible the genotyping of thousands of loci in thousands of individuals, which could be useful for tightly associating phenotypes to candidate loci. Current mapping algorithms cannot handle so many data without building hierarchies of framework maps. RESULTS: A version of Kruskal's minimum spanning tree algorithm can solve any genetic mapping problem that can be stated as marker deletion from a set of linkage groups. These include backcross, recombinant inbred, haploid and double-cross recombinational populations, in addition to conventional deletion and radiation hybrid populations. The algorithm progressively joins linkage groups at increasing recombination fractions between terminal markers, and attempts to recognize and correct erroneous joins at peaks in recombination fraction. The algorithm is O (mn3) for m individuals and n markers, but the mean run time scales close to mn2. It is amenable to parallel processing and has recovered true map order in simulations of large backcross, recombinant inbred and deletion populations with up to 37,005 markers. Simulations were used to investigate map accuracy in response to population size, allelic dominance, segregation distortion, missing data and random typing errors. It produced accurate maps when marker distribution was sufficiently uniform, although segregation distortion could induce translocated marker orders. The algorithm was also used to map 1003 loci in the F7 ITMI population of bread wheat, Triticum aestivum L. emend Thell., where it shortened an existing standard map by 16%, but it failed to associate blocks of markers properly across gaps within linkage groups. This was because it depends upon the rankings of recombination fractions at individual markers, and is susceptible to sampling error, typing error and joint selection involving the terminal markers of nearly finished linkage groups. Therefore, the current form of the algorithm is useful mainly to improve local marker ordering in linkage groups obtained in other ways. AVAILABILITY: The source code and supplemental data are http://www.iubio.bio.indiana.edu/soft/molbio/qtl/flipper/ CONTACT: ccrane@purdue.edu.     

A new strategy for estimating recombination fractions between dominant markers from an F2 population

Although most high-density linkage maps have been constructed from codominant markers such as single-nucleotide polymorphisms (SNPs) and microsatellites due to their high linkage information, dominant markers can be expected to be even more significant as proteomic technique becomes widely applicable to generate protein polymorphism data from large samples. However, for dominant markers, two possible linkage phases between a pair of markers complicate the estimation of recombination fractions between markers and consequently the construction of linkage maps. The low linkage information of the repulsion phase and high linkage information of coupling phase have led geneticists to construct two separate but related linkage maps. To circumvent this problem, we proposed a new method for estimating the recombination fraction between markers, which greatly improves the accuracy of estimation through distinction between the coupling phase and the repulsion phase of the linked loci. The results obtained from both real and simulated F2 dominant marker data indicate that the recombination fractions estimated by the new method contain a large amount of linkage information for constructing a complete linkage map. In addition, the new method is also applicable to data with mixed types of markers (dominant and codominant) with unknown linkage phase.     

Reduced recombination and distorted segregation in a Solanum tuberosum (2x) x S. spegazzinii (2x) hybrid.

In this paper we describe the reduced recombination and distorted segregation in an interspecific hybrid between Solanum tuberosum and Solanum spegazzinii. To study these phenomena, a cross was made between a (di)haploid S. tuberosum, used as a female parent, and a diploid wild potato species, S. spegazzinii, used as a male parent. Next, a backcross (BC) population was made with F1 genotype 38 that was backcrossed to S. tuberosum. In the backcross, S. tuberosum was used as the male parent. RFLP linkage maps were made using the F1 and the BC populations, yielding linkage maps of the interspecific hybrid, S. spegazzinii, and S. tuberosum from which male and female linkage maps could be constructed. The computer program JOINMAP was used to construct and combine the separate linkage maps. Subsequently, the separate linkage maps were compared with each other, and reduced recombination was observed in the linkage maps of the male S. tuberosum and the interspecific hybrid. The reason for this reduced recombination is discussed. Another common feature in linkage maps is the observation of distorted segregation. The distorted segregation of alleles from the interspecific hybrid was studied in more detail in the BC population. Most of the distortion was probably caused by gamete selection, but for 3 loci, on chromosomes 2, 3, and 4, we found evidence for the presence of a strong selection force acting at the zygote level against homozygous genotypes.     

Modeling segregation distortion for viability selection I. Reconstruction of linkage maps with distorted markers

Molecular markers have been widely used to map quantitative trait loci (QTL). The QTL mapping partly relies on accurate linkage maps. The non-Mendelian segregation of markers, which affects not only the estimation of genetic distance between two markers but also the order of markers on a same linkage group, is usually observed in QTL analysis. However, these distorted markers are often ignored in the real data analysis of QTL mapping so that some important information may be lost. In this paper, we developed a multipoint approach via Hidden Markov chain model to reconstruct the linkage maps given a specified gene order while simultaneously making use of distorted, dominant and missing markers in an F₂ population. The new method was compared with the methods in the MapManager and Mapmaker programs, respectively, and verified by a series of Monte Carlo simulation experiments along with a working example. Results showed that the adjusted linkage maps can be used for further QTL or segregation distortion locus (SDL) analysis unless there are strong evidences to prove that all markers show normal Mendelian segregation.     

GENETIC ARCHITECTURE AND POSTZYGOTIC REPRODUCTIVE ISOLATION: EVOLUTION OF BATESON–DOBZHANSKY–MULLER INCOMPATIBILITIES IN A POLYGENIC MODEL

The Bateson–Dobzhansky–Muller model predicts that postzygotic isolation evolves due to the accumulation of incompatible epistatic interactions, but few studies have quantified the relationship between genetic architecture and patterns of reproductive divergence. We examined how the direction and magnitude of epistatic interactions in a polygenic trait under stabilizing selection influenced the evolution of hybrid incompatibilities. We found that populations evolving independently under stabilizing selection experienced suites of compensatory allelic changes that resulted in genetic divergence between populations despite the maintenance of a stable, high‐fitness phenotype. A small number of loci were then incompatible with multiple alleles in the genetic background of the hybrid and the identity of these incompatibility loci changed over the evolution of the populations. For F₁ hybrids, reduced fitness evolved in a window of intermediate strengths of epistatic interactions, but F₂ and backcross hybrids evolved reduced fitness across weak and moderate strengths of epistasis due to segregation variance. Strong epistatic interactions constrained the allelic divergence of parental populations and prevented the development of reproductive isolation. Because many traits with varying genetic architectures must be under stabilizing selection, our results indicate that polygenetic drift is a plausible hypothesis for the evolution of postzygotic reproductive isolation.     

Multi-QTL mapping for quantitative traits using distorted markers

Marker segregation distortion is a common natural phenomenon. However, relatively little is known about utilizing distorted markers for detecting quantitative trait loci (QTL). Therefore, in this study we proposed a multi-QTL mapping approach that uses distorted markers. First, the information from all markers, including distorted markers, was used to detect segregation distortion loci (SDL). Second, the information from the detected SDL was used to correct the conditional probabilities of the QTL genotypes conditional on marker information, and these corrected probabilities were then incorporated into a multi-QTL mapping methodology. Finally, the proposed approach was validated by both Monte Carlo simulation studies and real data analysis. The results from the simulation studies show that as long as one or two SDL are placed around the simulated QTL, there are no differences between the new method and the ordinary interval mapping method in terms of the power of QTL detection or the estimates of the position and dominant effects of the QTL. However, the power of QTL detection is higher under the dominant genetic model of SDL than under the additive genetic model, and the estimate for the additive effect of QTL using the new method is significantly different from the estimate obtained using ordinary interval mapping. The above results were further confirmed by the detection of QTL for dried soymilk in 222 F_2:4 families in soybean.     

Genetic analysis of freezing tolerance in blueberry (Vaccinium section Cyanococcus)

An understanding of the genetic control of freezing tolerance (FT) in woody perennials is important for the effective selection and development of plants with a broader climatic adaptation. This study was undertaken to examine the inheritance and gene action of FT in segregating populations of a woody perennial blueberry (Vaccinium, section Cyanococcus). Two backcross populations were derived from interspecific hybrids of the diploid species Vaccinium darrowi and Vaccinium caesariense, which are widely divergent in their FT. The bud FTs of uniformly cold acclimated plants of parental, F₁, and two backcross populations were evaluated with a laboratory controlled freeze-thaw regime, followed by a visual assessment of injury. FT (LT₅₀) was defined as the temperature causing 50% of the flower buds to be injured. Data indicate that the two parents were homozygous for genes for low or high FT. Freezing-tolerance values of the parental and F₁ populations indicate that freeze-sensitivity is a partially dominant trait. Results from reciprocal crosses revealed that there was no significant maternal influence on freezing tolerance. Parental phenotypes were fully recovered in 40–42 plants of each testcross population, suggesting that FT is determined by relatively few genes. The degree of dominance and an analysis of generation means revealed that FT in blueberry is controlled largely by additive gene effects and, to a lesser degree, by dominance gene effects. Testing of various genetic models indicated that FT inheritance can be adequately explained by a simple additive-dominance model; however, two epistatic models involving additive-additive and dominance-dominance interactions also fit the data. Received: 25 May 1999 / Accepted: 16 June 1999     

Estimation of the Recombination Fraction by the Maximum Likelihood Method in Mapping Interacting Genes Relative to Marker Loci

For mapping nonlinked interacting genes relative to marker loci, the recombination fractions can be calculated by using the log-likelihood functions were derived that permit estimation of recombinant fractions by solving the ML equations on the basis of F₂ data at various types of interaction. In some cases, the recombinant fraction estimates are obtained in the analytical form while in others they are numerically calculated from concrete experimental data. With the same type of epistasis the log-functions were shown to differ depending on the functional role (suppression or epistasis) of the mapped gene. Methods for testing the correspondence of the model and the recombination fraction estimates to the experimental data are discussed. In ambiguous cases, analysis of the linked marker behavior makes it possible to differentiate gene interaction from distorted single-locus segregation, which at some forms of interaction imitate phenotypic ratios.     

Construction of an intraspecific linkage map of lentil (<Emphasis Type="Italic">Lens culinaris</Emphasis> ssp. <Emphasis Type="Italic">culinaris</Emphasis>)

The first intraspecific linkage map of the lentil genome was constructed with 114 molecular markers (100 RAPD, 11 ISSR and three RGA) using an F₂ population developed from a cross between lentil cultivars ILL5588 and ILL7537 which differed in resistance for ascochyta blight. Linkage analysis at a LOD score of 4.0 and a maximum recombination fraction of 0.25 revealed nine linkage groups comprising between 6 and 18 markers each. The intraspecific map spanned a total length of 784.1 cM. The markers were distributed throughout the genome, however markers were clustered in the middle or near the middle of the linkage groups, suggesting the location of centromeres. Of 114 mapped markers, 16 (14.0%) were distorted, usually at the end or middle of the linkage groups. The utility of ISSR and RGA markers for mapping in lentil was explored, and the primer with an (AC) repeat motif was found to be useful.Communicated by H.C. Becker     

基于分离亚群体QTL定位的模拟研究

在数量性状QTL的精细定位中, 通过数量性状目标QTL的近等基因系可构建分离群体。在目标QTL效应较大的情况下, 数量性状表型值可反映目标QTL的基因型。若目标QTL附近的标记密度大时, 大样本才能定位该QTL。但是, 这增加了试验费用。为节约试验经费, 若只利用QTL纯合隐性基因型植株的分子标记信息, 也可比较准确地定位该QTL。利用极大似然法, 分别推导出F2、BC、DH以及RIL群体中重组率及其标准误的估计公式。Monte Carlo模拟研究表明, 基于定位群体中全部数据或隐性纯合基因型数据所获得的重组率估计值是一致的, 且在相同样本容量条件下, 二者精度相当。     

Gene actions of QTLs affecting several agronomic traits resolved in a recombinant inbred rice population and two backcross populations

To understand the types of gene action controlling seven quantitative traits in rice, we carried out quantitative trait locus (QTL) mapping in order to distinguish between the main-effect QTLs (M-QTLs) and digenic epistatic QTLs (E-QTLs) responsible for the trait performance of 254 recombinant inbred lines (RILs) from rice varieties Lemont/Teqing and two backcross hybrid (BCF₁) populations derived from these RILs. We identified 44 M-QTL and 95 E-QTL pairs in the RI and BCF₁ populations as having significant effects on the mean values and mid-parental heterosis of heading date, plant height, flag leaf length, flag leaf width, panicle length, spikelet number and spikelet fertility. The E-QTLs detected collectively explained a larger portion of the total phenotypic variation than the M-QTLs in both the RI and BCF₁ populations. In both BCF₁ populations, over-dominant (or under-dominant) loci were more important than additive and complete or partially dominant loci for M-QTLs and E-QTL pairs, thereby supporting prior findings that overdominance resulting from epistatic loci are the primary genetic basis of inbreeding depression and heterosis in rice.     

Specific Features of the Nuclear Genome Recombination in Backcross Progenies of Barley–Wheat Hybrids Hordeum vulgare L. (2n = 14) × Triticum aestivum L. (2n = 42)

The backcross progenies of the barley–wheat hybrids Hordeum vulgare L. (2n = 14) × Triticum aestivum L. (2n= 42) and two alloplasmic lines derived from them were studied using microsatellite markers of barley and wheat. The F₁ hybrids and first backcross plants BC₁ contained the genetic material of both cultivated barley and the cultivars of common wheat involved in developing of these hybrid genotypes. The genomes of BC₃, BC₄, and alloplasmic lines contained no microsatellite markers of the cultivated barley, whereas chromosomes of each homeologous group of common wheat were identified. In chromosomes of backcross progenies BC₃, BC₄, and alloplasmic lines yielded by backcrosses of hybrids and various common wheat cultivars, microsatellite markers of the parental wheat cultivars were shown to undergo recombination.     

QTL analysis reveals context-dependent loci for seed glucosinolate trait in the oilseed <Emphasis Type="Italic">Brassica juncea</Emphasis>: importance of recurrent selection backcross scheme for the identification of ‘true’ QTL

Seed glucosinolate content in Brassica juncea is a complex quantitative trait. A recurrent selection backcross (RSB) method with a doubled haploid (DH) generation interspersing backcross generations was used for the introgression of low glucosinolate alleles from an east European gene pool B. juncea line, Heera into an Indian gene pool variety, Varuna. Phenotypic comparisons among the DH populations derived from early to advanced backcrosses revealed a shift in the mean values for various glucosinolates with the advancement of backcrossing, indicating a change in the selective values of the alleles with change in the genetic background due to the existence of epistasis and context dependencies. QTL mapping for various seed glucosinolates from early (F₁DH) and advanced generation (BC₄DH) populations confirmed the presence of epistasis and context dependency. The common QTL detected in both F₁DH and BC₄DH changed their R ² values from the former to the later generation. Some of the QTL detected in the F₁DH became irrelevant in the BC₄DH population. Further, new QTL were detected in the BC₄DH population for various glucosinolates. A validation study on a population of low glucosinolate DH lines derived from all the backcross generations of the RSB breeding programme revealed that the QTL detected in BC₄DH were the ‘true’ QTL. Using glucosinolate as an example, the study provides strong evidence for the importance of the RSB method for the identification of the ‘true’ QTL which would be significant for marker assisted introgression of a complex quantitative trait whose expression is influenced by epistatic interactions. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. Authors N. Ramchiary, N. C. Bisht, V. Gupta, A. Mukhopadhyay and N. Arumugam have contributed equally to this work.