Mapping quantitative trait loci with dominant markers in four-way crosses

 A common problem in mapping quantitative trait loci (QTLs) is that marker data are often incomplete. This includes missing data, dominant markers, and partially informative markers, arising in outbred populations. Here we briefly present an iteratively re-weighted least square method (IRWLS) to incorporate dominant and missing markers for mapping QTLs in four-way crosses under a heterogeneous variance model. The algorithm uses information from all markers in a linkage group to infer the QTL genotype. Monte Carlo simulations indicate that with half dominant markers, QTL detection is almost as efficient as with all co-dominant markers. However, the precision of the estimated QTL parameters generally decreases as more markers become missing or dominant. Notable differences are observed on the standard deviation of the estimated QTL position for varying levels of marker information content. The method is relatively simple so that more complex models including multiple QTLs or fixed effects can be fitted. Finally, the method can be readily extended to QTL mapping in full-sib families. Received: 16 June 1998 / Accepted: 29 September 1998     

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.     

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.     

Prevalence of segregation distortion in diploid alfalfa and its implications for genetics and breeding applications

Segregation distortion (SD) is often observed in plant populations; its presence can affect mapping and breeding applications. To investigate the prevalence of SD in diploid alfalfa (Medicago sativa L.), we developed two unrelated segregating F₁ populations and one F₂ population. We genotyped all populations with SSR markers and assessed SD at each locus in each population. The three maps were syntenic and largely colinear with the Medicago truncatula genome sequence. We found genotypic SD for 24 and 34% of markers in the F₁ populations and 68% of markers in the F₂ population; distorted markers were identified on every linkage group. The smaller percentage of genotypic SD in the F₁ populations could be because they were non-inbred and/or due to non-fully informative markers. For the F₂ population, 60 of 90 mapped markers were distorted, and they clustered into eight segregation distortion regions (SDR). Most SDR identified in the F₁ populations were also identified in the F₂ population. Genotypic SD was primarily due to zygotic rather than allelic distortion, suggesting zygotic not gametic selection is the main cause of SD. On the F₂ linkage map, distorted markers in all SDR except two showed heterozygote excess. The severe SD in the F₂ population likely biased genetic distances among markers and possibly also marker ordering and could affect QTL mapping of agronomic traits. To reduce the effects of SD and non-fully informative markers, we suggest constructing linkage maps and conducting QTL mapping in advanced generation populations.     

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).     

Quantitative trait locus mapping can benefit from segregation distortion

Segregation distortion is a phenomenon that has been observed in many experimental systems. How segregation distortion among markers arises and its impact on mapping studies are the focus of this work. Segregation distortion of markers can be considered to arise from segregation distortion loci (SDL). I develop a theory of segregation distortion and show that the presence of only a few SDL can cause the entire chromosome to distort from Mendelian segregation. Segregation distortion is detrimental to the power of detecting quantitative trait loci (QTL) with dominance effects, but it is not always a detriment to QTL mapping for additive effects. When segregation distortion of a locus is a random event, the SDL is beneficial to QTL mapping ~44% of the time. If SDL are present and ignored, power loss can be substantial. A dense marker map can be used to ameliorate the situation, and if dense marker information is incorporated, power loss is minimal. However, other situations are less benign. A method that can simultaneously map QTL and SDL is discussed, maximizing both use of mapping resources and use by agricultural and evolutionary biologists.     

Methodologies for segregation analysis and QTL mapping in plants

Most characters of biological interest and economic importance are quantitative traits. To uncover the genetic architecture of quantitative traits, two approaches have become popular in China. One is the establishment of an analytical model for mixed major-gene plus polygenes inheritance and the other the discovery of quantitative trait locus (QTL). Here we review our progress employing these two approaches. First, we proposed joint segregation analysis of multiple generations for mixed major-gene plus polygenes inheritance. Second, we extended the multilocus method of Lander and Green (1987), Jiang and Zeng (1997) to a more generalized approach. Our methodology handles distorted, dominant and missing markers, including the effect of linked segregation distortion loci on the estimation of map distance. Finally, we developed several QTL mapping methods. In the Bayesian shrinkage estimation (BSE) method, we suggested a method to test the significance of QTL effects and studied the effect of the prior distribution of the variance of QTL effect on QTL mapping. To reduce running time, a penalized maximum likelihood method was adopted. To mine novel genes in crop inbred lines generated in the course of normal crop breeding work, three methods were introduced. If a well-documented genealogical history of the lines is available, two-stage variance component analysis and multi-QTL Haseman-Elston regression were suggested; if unavailable, multiple loci in silico mapping was proposed.     

Quantitative trait locus mapping with background control in genetic populations of clonal F1 and double cross

In this study, we considered five categories of molecular markers in clonal F₁ and double cross populations, based on the number of distinguishable alleles and the number of distinguishable genotypes at the marker locus. Using the completed linkage maps, incomplete and missing markers were imputed as fully informative markers in order to simplify the linkage mapping approaches of quantitative trait genes. Under the condition of fully informative markers, we demonstrated that dominance effect between the female and male parents in clonal F₁ and double cross populations can cause the interactions between markers. We then developed an inclusive linear model that includes marker variables and marker interactions so as to completely control additive effects of the female and male parents, as well as the dominance effect between the female and male parents. The linear model was finally used for background control in inclusive composite interval mapping (ICIM) of quantitative trait locus (QTL). The efficiency of ICIM was demonstrated by extensive simulations and by comparisons with simple interval mapping, multiple‐QTL models and composite interval mapping. Finally, ICIM was applied in one actual double cross population to identify QTL on days to silking in maize.     

Linkage analysis of anther-derived monoploids showing distorted segregation of molecular markers

Monoploids can be obtained from several diploid plant species by anther culture. Mapping of molecular markers using monoploids is greatly facilitated by the simple 1:1 segregation ratio expected from all heterozygous loci in the genome. Distorted segregation of molecular markers, however, appears to be a common phenomenon in many crop species and hinders the use of monoploids for mapping purposes. This report examines the segregation pattern of two marker genes linked together with one locus or separately with two independent loci which are responsible for the observed distortion. Each of the loci exhibiting distorted segregation has one of the two alleles which inhibits regeneration of the gametic cells in vitro and disrupts the expected segregation ratio of the linked markers. All possible situations in which linkage occurs between markers and distortion-causing genes are considered. Theoretical results outlining the segregation pattern among these linkage types indicate that the distinguishable distorted ratios can be used for mapping purposes. A protocol is given for the mapping of distorted gene markers based on existing gene mapping software. An example is presented of the mapping of distorted RAPD markers of monoploids obtained from a diploid potato genotype. Received: 18 October 1999 / Accepted: 24 November 1999<@head-com-p1a.lf>Communicated by G. Wenzel     

Exploring the Genetic Characteristics of Two Recombinant Inbred Line Populations via High-Density SNP Markers in Maize

Understanding genetic characteristics can reveal the genetic diversity in maize and be used to explore evolutionary mechanisms and gene cloning. A high-density linkage map was constructed to determine recombination rates (RRs), segregation distortion regions (SDRs), and recombinant blocks (RBs) in two recombinant inbred line populations (RILs) (B73/By804 and Zong3/87-1) generated by the single seed descent method. Population B73/By804 containing 174 lines were genotyped with 198 simple sequence repeats (SSRs) markers while population Zong3/87-1 comprised of 175 lines, were genotyped with 210 SSR markers along with 1536 single nucleotide polymorphism (SNP) markers for each population, spanning 1526.7 cM and 1996.2 cM in the B73/By804 and Zong3/87-1 populations, respectively. The total variance of the RR in the whole genome was nearly 100 fold, and the maximum average was 10.43–11.50 cM/Mb while the minimum was 0.08–0.10 cM/Mb in the two populations. The average number of RB was 44 and 37 in the Zong3/87-1 and B73/By804 populations, respectively, whereas 28 SDRs were observed in both populations. We investigated 11 traits in Zong3/87-1 and 10 traits in B73/By804. Quantitative trait locus (QTLs) mapping of SNP+SSR with SNP and SSR marker sets were compared to showed the impact of different density markers on QTL mapping and resolution. The confidence interval of QTL Pa19 (FatB gene controlling palmitic acid content) was reduced from 3.5 Mb to 1.72 Mb, and the QTL Oil6 (DGAT1-2 gene controlling oil concentration) was significantly reduced from 10.8 Mb to 1.62 Mb. Thus, the use of high-density markers considerably improved QTL mapping resolution. The genetic information resulting from this study will support forthcoming efforts to understand recombination events, SDRs, and variations among different germplasm. Furthermore, this study will facilitate gene cloning and understanding of the fundamental sources of total variation and RR in maize, which is the most widely cultivated cereal crop.     

Genetic Map Construction and Detection of Genetic Loci Underlying Segregation Distortion in an Intraspecific Cross of Populus deltoides

Based on a two-way pseudo-testcross strategy, high density and complete coverage linkage maps were constructed for the maternal and paternal parents of an intraspecific F2 pedigree of Populus deltoides. A total of 1,107 testcross markers were obtained, and the mapping population consisted of 376 progeny. Among these markers, 597 were from the mother, and were assigned into 19 linkage groups, spanning a total genetic distance of 1,940.3 cM. The remaining 519 markers were from the father, and were also were mapped into 19 linkage groups, covering 2,496.3 cM. The genome coverage of both maps was estimated as greater than 99.9% at 20 cM per marker, and the numbers of linkage groups of both maps were in accordance with the 19 haploid chromosomes in Populus. Marker segregation distortion was observed in large contiguous blocks on some of the linkage groups. Subsequently, we mapped the segregation distortion loci in this mapping pedigree. Altogether, eight segregation distortion loci with significant logarithm of odds supports were detected. Segregation distortion indicated the uneven transmission of the alternate alleles from the mapping parents. The corresponding genome regions might contain deleterious genes or be associated with hybridization incompatibility. In addition to the detection of segregation distortion loci, the established genetic maps will serve as a basic resource for mapping genetic loci controlling traits of interest in future studies.     

The efficiency of designs for fine-mapping of quantitative trait loci using combined linkage disequilibrium and linkage

In a simulation study, different designs were compared for efficiency of fine-mapping of QTL. The variance component method for fine-mapping of QTL was used to estimate QTL position and variance components. The design of many families with small size gave a higher mapping resolution than a design with few families of large size. However, the difference is small in half sib designs. The proportion of replicates with the QTL positioned within 3 cM of the true position is 0.71 in the best design, and 0.68 in the worst design applied to 128 animals with a phenotypic record and a QTL explaining 25% of the phenotypic variance. The design of two half sib families each of size 64 was further investigated for a hypothetical population with effective size of 1000 simulated for 6000 generations with a marker density of 0.25 cM and with marker mutation rate 4 × 10^-4 per generation. In mapping using bi-allelic markers, 42~55% of replicated simulations could position QTL within 0.75 cM of the true position whereas this was higher for multi allelic markers (48~76%). The accuracy was lowest (48%) when mutation age was 100 generations and increased to 68% and 76% for mutation ages of 200 and 500 generations, respectively, after which it was about 70% for mutation ages of 1000 generations and older. When effective size was linearly decreasing in the last 50 generations, the accuracy was decreased (56 to 70%). We show that half sib designs that have often been used for linkage mapping can have sufficient information for fine-mapping of QTL. It is suggested that the same design with the same animals for linkage mapping should be used for fine-mapping so gene mapping can be cost effective in livestock populations.     

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.     

SAMPLE SIZE ESTIMATION FOR GENE ACTION ANALYSIS BY USING ORTHOGONAL CONTRAST

IIntroductionTheuseofrestrlctlonfragmentlengthpolymorphism（RFLP）markershasgreatlyslmpllfledthegeneticanalysisofquantitativetraits,providingareliableandextensiveframeworkofquantltatlvemarkerstowhichquantltatlyetyaitIOCI（QTL）clnhilinked［‘］．TodetectthelinkagebetwwenRFLPmarkersandPhenotyPlcvariationsoh－served,generallinearmodelofanalysisofvariance（ANOVA）hasbeenextensivelyusedL‘zJ．ByusingF、populations,thecompletegeneticInformation,thatIs,thethreegenotypesofageneticfact…     

A highly recombined,high‐density,eight‐founder wheat MAGIC map reveals extensive segregation distortion and genomic locations of introgression segments

Multiparent Advanced Generation Intercross (MAGIC) mapping populations offer unique opportunities and challenges for marker and QTL mapping in crop species. We have constructed the first eight‐parent MAGIC genetic map for wheat, comprising 18 601 SNP markers. We validated the accuracy of our map against the wheat genome sequence and found an improvement in accuracy compared to published genetic maps. Our map shows a notable increase in precision resulting from the three generations of intercrossing required to create the population. This is most pronounced in the pericentromeric regions of the chromosomes. Sixteen percent of mapped markers exhibited segregation distortion (SD) with many occurring in long (>20 cM) blocks. Some of the longest and most distorted blocks were collinear with noncentromeric high‐marker‐density regions of the genome, suggesting they were candidates for introgression fragments introduced into the bread wheat gene pool from other grass species. We investigated two of these linkage blocks in detail and found strong evidence that one on chromosome 4AL, showing SD against the founder Robigus, is an interspecific introgression fragment. The completed map is available from http://www.niab.com/pages/id/326/Resources .     

Improving QTL Mapping Resolution Based on Genotypic Sampling—a Case Using a RIL Population

The QTL mapping results were compared with the genotypically selected and random samples of the same size on the base of a RIL population. The results demonstrated that there were no obvious differences in the trait distribution and marker segregation distortion between the genotypically selected and random samples with the same population size. However, a significant increase in QTL detection power, sensitivity, specificity, and QTL resolution in the genotypically selected samples were observed. Moreover, the highly significant effect was detected in small size of genotypically selected samples. In QTL mapping, phenotyping is a more sensitive limiting factor than genotyping so that the selection of samples could be an attractive strategy for increasing genome-wide QTL mapping resolution. The efficient selection of samples should be more helpful for QTL maker assistant selection, fine mapping, and QTL cloning.     

基于基因型选择提高QTL作图的精度——以一个RIL群体为例

以PCR为基础的分子标记以及其他检测技术的发展,使得大规模的标记分析成为现实。这也为通过大群体标记分析,然后基于基因型选择挑选合适的小群体,从而提高QTL定位准确性和精度提供了可能。以一个包含294个家系的重组自交系（RIL）群体为例,通过基因型选择和随机选择的办法产生了一系列大小不等的亚群体,比较了两类群体QTL定位的结果。分析表明：相同大小的基因型选择群体与随机群体相比性状的表型分布都符合正态分布;标记的偏分离情况也没有明显的差别,都随着群体大小的增大,偏分离的比例也逐渐增大。但同等大小的基因型选择群体比随机群体的交换富集率（CE）要大,且随着选择强度的增大不断增大,如群体大小为270时,CE=1．04,群体大小为30时,CE=1．45。总体上,随着群体大小的增加,不管是随机群体还是选择群体,其QTL检测能力、灵敏性和特异性也随之增加,但选择群体的检测能力、灵敏性和特异性总体上要好于随机群体。当群体大于或等于240时,其QTL检测能力基本没有差别;群体大小大于或等于210时,其QTL检测的灵敏性和特异性也没有什么差别。这也说明：选择强度越大,效果越明显。以QTLI—LOD区间作为衡量QTL精度的一个指标,结果显示所有基因型选择群体都比相同大小随机群体的QTL定位精度高。目前QTL定位研究中,基因型数据较表型数据而言更容易准确获得,因此通过基因型选择可以更好的优化群体结构,减少田间实验的工作量,提高全基因组水平QTL作图的精度,为随后的QTL辅助选择和精细定位以及克隆提供帮助。     

Mapping quantitative trait loci with dominant and missing markers in various crosses from two inbred lines

Dominant phenotype of a genetic marker provides incomplete information about the marker genotype of an individual. A consequence of using this incomplete information for mapping quantitative trait loci (QTL) is that the inference of the genotype of a putative QTL flanked by a marker with dominant phenotype will depend on the genotype or phenotype of the next marker. This dependence can be extended further until a marker genotype is fully observed. A general algorithm is derived to calculate the probability distribution of the genotype of a putative QTL at a given genomic position, conditional on all observed marker phenotypes in the region with dominant and missing marker information for an individual. The algorithm is implemented for various populations stemming from two inbred lines in the context of mapping QTL. Simulation results show that if only a proportion of markers contain missing or dominant phenotypes, QTL mapping can be almost as efficient as if there were no missing information in the data. The efficiency of the analysis, however, may decrease substantially when a very large proportion of markers contain missing or dominant phenotypes and a genetic map has to be reconstructed first on the same data as well. So it is important to combine dominant markers with codominant markers in a QTL mapping study. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effects of genotyping errors,missing values and segregation distortion in molecular marker data on the construction of linkage maps

A simulation study was performed to investigate the effects of missing values, typing errors and distorted segregation ratios in molecular marker data on the construction of genetic linkage maps, and to compare the performance of three locus-ordering criteria (weighted least squares, maximum likelihood and minimum sum of adjacent recombination fractions criteria) in the presence of such effects. The study was based upon three linkage groups of 10 loci at 2, 6, and 10 cM spacings simulated from a doubled-haploid population of size 150. Criteria performance were assessed using the number of replicates with correctly estimated orders, the mean rank correlation between the estimated and the true order and the mean total map length. Bootstrap samples from replicates in the maximum likelihood analysis produced a measure of confidence in the estimated locus order. The effects of missing values and/or typing errors in the data are to reduce the proportion of correctly ordered maps, and this problem worsens as the distances between loci decreases. The maximum likelihood criterion is most successful at ordering loci correctly, but gives estimated map lengths, which are substantially inflated when typing errors are present. The presence of missing values in the data produces shorter map lengths for more widely spaced markers, especially under the weighted least-squares criterion. Overall, the presence of segregation distortion has little effect on this population.     

三点自交法和两点最大似然法构建水稻F2群体分子标记连锁图谱的比较

根据连锁遗传的原理,列出了三点自交法和两点自交最大似然(ML)法估算显性标记遗传距离的具体步骤和算法,将水稻F2群体含香味基因Aro及其连锁的RFLP数据转变为显性标记数据后,用上述两种方法构建的连锁图谱与用MAPMAKER软件计算共显性数据得到的图谱排序相同、标记间距离相近．但是标记数据存在较大程度偏分离时,由三点自交法构建的图谱中标记间图距有增大趋势．作者为提高作图精确性,简化计算过程,讨论了三点自交法对估算重组值的影响及其在分子标记作图中的应用价值,并建议将共显性标记转变为显性标记时进行两次自交ML法估算。