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.     

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.     

Linkage group correction using epistatic distorted markers in F2 and backcross populations

Epistasis has been frequently observed in all types of mapping populations. However, relatively little is known about the effect of epistatic distorted markers on linkage group construction. In this study, a new approach was proposed to correct the recombination fraction between epistatic distorted markers in backcross and F₂ populations under the framework of fitness and liability models. The information for three or four markers flanking with an epistatic segregation distortion locus was used to estimate the recombination fraction by the maximum likelihood method, implemented via an expectation–maximisation algorithm. A set of Monte Carlo simulation experiments along with a real data analysis in rice was performed to validate the new method. The results showed that the estimates from the new method are unbiased. In addition, five statistical properties for the new method in a backcross were summarised and confirmed by theoretical, simulated and real data analyses.     

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.     

Inclusive composite interval mapping (ICIM) for digenic epistasis of quantitative traits in biparental populations

It has long been recognized that epistasis or interactions between non-allelic genes plays an important role in the genetic control and evolution of quantitative traits. However, the detection of epistasis and estimation of epistatic effects are difficult due to the complexity of epistatic patterns, insufficient sample size of mapping populations and lack of efficient statistical methods. Under the assumption of additivity of QTL effects on the phenotype of a trait in interest, the additive effect of a QTL can be completely absorbed by the flanking marker variables, and the epistatic effect between two QTL can be completely absorbed by the four marker-pair multiplication variables between the two pairs of flanking markers. Based on this property, we proposed an inclusive composite interval mapping (ICIM) by simultaneously considering marker variables and marker-pair multiplications in a linear model. Stepwise regression was applied to identify the most significant markers and marker-pair multiplications. Then a two-dimensional scanning (or interval mapping) was conducted to identify QTL with significant digenic epistasis using adjusted phenotypic values based on the best multiple regression model. The adjusted values retain the information of QTL on the two current mapping intervals but exclude the influence of QTL on other intervals and chromosomes. Epistatic QTL can be identified by ICIM, no matter whether the two interacting QTL have any additive effects. Simulated populations and one barley doubled haploids (DH) population were used to demonstrate the efficiency of ICIM in mapping both additive QTL and digenic interactions.     

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。     

Effects of missing marker and segregation distortion on QTL mapping in F2 populations

Missing marker and segregation distortion are commonly encountered in actual quantitative trait locus (QTL) mapping populations. Our objective in this study was to investigate the impact of the two factors on QTL mapping through computer simulations. Results indicate that detection power decreases with increasing levels of missing markers, and the false discovery rate increases. Missing markers have greater effects on smaller effect QTL and smaller size populations. The effect of missing markers can be quantified by a population with a reduced size similar to the marker missing rate. As for segregation distortion, if the distorted marker is not closely linked with any QTL, it will not have significant impact on QTL mapping; otherwise, the impact of the distortion will depend on the degree of dominance of QTL, frequencies of the three marker types, the linkage distance between the distorted marker and QTL, and the mapping population size. Sometimes, the distortion can result in a higher genetic variance than that of non-distortion, and therefore benefits the detection of linked QTL. A formula of the ratio of genetic variance explained by QTL under distortion and non-distortion was given in this study, so as to easily determine whether the segregation distortion marker (SDM) increases or decreases the QTL detection power. The effect of SDM decreases rapidly as its linkage relationship with QTL becomes looser. In general, distorted markers will not have a great effect on the position and effect estimations of QTL, and their effects can be ignored in large-size mapping populations.     

Multipoint mapping of viability and segregation distorting loci using molecular markers

In line-crossing experiments, deviations from Mendelian segregation ratios are usually observed for some markers. We hypothesize that these deviations are caused by one or more segregation-distorting loci (SDL) linked to the markers. We develop both a maximum-likelihood (ML) method and a Bayesian method to map SDL using molecular markers. The ML mapping is implemented via an EM algorithm and the Bayesian method is performed via the Markov chain Monte Carlo (MCMC). The Bayesian mapping is computationally more intensive than the ML mapping but can handle more complicated models such as multiple SDL and variable number of SDL. Both methods are applied to a set of simulated data and real data from a cross of two Scots pine trees.     

Quantitative trait loci mapping and the genetic basis of heterosis in maize and rice

Despite its importance to agriculture, the genetic basis of heterosis is still not well understood. The main competing hypotheses include dominance, overdominance, and epistasis. NC design III is an experimental design that has been used for estimating the average degree of dominance of quantitative trait loci (QTL) and also for studying heterosis. In this study, we first develop a multiple-interval mapping (MIM) model for design III that provides a platform to estimate the number, genomic positions, augmented additive and dominance effects, and epistatic interactions of QTL. The model can be used for parents with any generation of selfing. We apply the method to two data sets, one for maize and one for rice. Our results show that heterosis in maize is mainly due to dominant gene action, although overdominance of individual QTL could not completely be ruled out due to the mapping resolution and limitations of NC design III. For rice, the estimated QTL dominant effects could not explain the observed heterosis. There is evidence that additive × additive epistatic effects of QTL could be the main cause for the heterosis in rice. The difference in the genetic basis of heterosis seems to be related to open or self pollination of the two species. The MIM model for NC design III is implemented in Windows QTL Cartographer, a freely distributed software.     

Quantitative trait loci for life span in Drosophila melanogaster: interactions with genetic background and larval density

The genetic architecture of variation in adult life span was examined for a population of recombinant inbred lines, each of which had been crossed to both inbred parental strains from which the lines were derived, after emergence from both high and low larval density. QTL affecting life span were mapped within each sex and larval density treatment by linkage to highly polymorphic roo-transposable element markers, using a composite interval mapping method. We detected a total of six QTL affecting life span; the additive effects and degrees of dominance for all were highly sex- and larval environment-specific. There were significant epistatic interactions between five of the life span QTL, the effects of which also differed according to genetic background, sex, and larval density. Five additional QTL were identified that contributed to differences among lines in their sensitivity to variation in larval density. Further fine-scale mapping is necessary to determine whether candidate genes within the regions to which the QTL map are actually responsible for the observed variation in life span.     

A haplotype-based algorithm for multilocus linkage disequilibrium mapping of quantitative trait loci with epistasis

For tightly linked loci, cosegregation may lead to nonrandom associations between alleles in a population. Because of its evolutionary relationship with linkage, this phenomenon is called linkage disequilibrium. Today, linkage disequilibrium-based mapping has become a major focus of recent genome research into mapping complex traits. In this article, we present a new statistical method for mapping quantitative trait loci (QTL) of additive, dominant, and epistatic effects in equilibrium natural populations. Our method is based on haplotype analysis of multilocus linkage disequilibrium and exhibits two significant advantages over current disequilibrium mapping methods. First, we have derived closed-form solutions for estimating the marker-QTL haplotype frequencies within the maximum-likelihood framework implemented by the EM algorithm. The allele frequencies of putative QTL and their linkage disequilibria with the markers are estimated by solving a system of regular equations. This procedure has significantly improved the computational efficiency and the precision of parameter estimation. Second, our method can detect marker-QTL disequilibria of different orders and QTL epistatic interactions of various kinds on the basis of a multilocus analysis. This can not only enhance the precision of parameter estimation, but also make it possible to perform whole-genome association studies. We carried out extensive simulation studies to examine the robustness and statistical performance of our method. The application of the new method was validated using a case study from humans, in which we successfully detected significant QTL affecting human body heights. Finally, we discuss the implications of our method for genome projects and its extension to a broader circumstance. The computer program for the method proposed in this article is available at the webpage http://www.ifasstat.ufl.edu/genome/~LD.     

QTL Mapping in New Arabidopsis thaliana Advanced Intercross-Recombinant Inbred Lines

Background

Even when phenotypic differences are large between natural or domesticated strains, the underlying genetic basis is often complex, and causal genomic regions need to be identified by quantitative trait locus (QTL) mapping. Unfortunately, QTL positions typically have large confidence intervals, which can, for example, lead to one QTL being masked by another, when two closely linked loci are detected as a single QTL. One strategy to increase the power of precisely localizing small effect QTL, is the use of an intercross approach before inbreeding to produce Advanced Intercross RILs (AI-RILs).

Methodology/Principal Findings

We present two new AI-RIL populations of Arabidopsis thaliana genotyped with an average intermarker distance of 600 kb. The advanced intercrossing design led to expansion of the genetic map in the two populations, which contain recombination events corresponding to 50 kb/cM in an F₂ population. We used the AI-RILs to map QTL for light response and flowering time, and to identify segregation distortion in one of the AI-RIL populations due to a negative epistatic interaction between two genomic regions.

Conclusions/Significance

The two new AI-RIL populations, EstC and KendC, derived from crosses of Columbia (Col) to Estland (Est-1) and Kendallville (Kend-L) provide an excellent resource for high precision QTL mapping. Moreover, because they have been genotyped with over 100 common markers, they are also excellent material for comparative QTL mapping.     

Conditional QTL mapping of oil content in rapeseed with respect to protein content and traits related to plant development and grain yield

Oil content in rapeseed (Brassica napus L.) is generally regarded as a character with high heritability that is negatively correlated with protein content and influenced by plant developmental and yield related traits. To evaluate possible genetic interrelationships between these traits and oil content, QTL for oil content were mapped using data on oil content and on oil content conditioned on the putatively interrelated traits. Phenotypic data were evaluated in a segregating doubled haploid population of 282 lines derived from the F₁ of a cross between the old German cultivar Sollux and the Chinese cultivar Gaoyou. The material was tested at four locations, two each in Germany and in China. QTLMapper version 1.0 was used for mapping unconditional and conditional QTL with additive (a) and locus pairs with additive × additive epistatic (aa) effects. Clear evidence was found for a strong genetic relationship between oil and protein content. Six QTL and nine epistatic locus pairs were found, which had pleiotropic effects on both traits. Nevertheless, two QTL were also identified, which control oil content independent from protein content and which could be used in practical breeding programs to increase oil content without affecting seed protein content. In addition, six additional QTL with small effects were only identified in the conditional mapping. Some evidence was apparent for a genetic interrelationship between oil content and the number of seeds per silique but no evidence was found for a genetic relationship between oil content and flowering time, grain filling period or single seed weight. The results indicate that for closely correlated traits conditional QTL mapping can be used to dissect the genetic interrelationship between two traits at the level of individual QTL. Furthermore, conditional QTL mapping can reveal additional QTL with small effects that are undetectable in unconditional mapping.     

High-resolution quantitative trait locus mapping reveals sign epistasis controlling ovariole number between two Drosophila species

Identifying the genes underlying genetically complex traits is of fundamental importance for medicine, agriculture, and evolutionary biology. However, the level of resolution offered by traditional quantitative trait locus (QTL) mapping is usually coarse. We analyze here a trait closely related to fitness, ovariole number. Our initial interspecific mapping between Drosophila sechellia (8 ovarioles/ovary) and D. simulans (15 ovarioles/ovary) identified a major QTL on chromosome 3 and a minor QTL on chromosome 2. To refine the position of the major QTL, we selected 1038 additional recombinants in the region of interest using flanking morphological markers (selective phenotyping). This effort generated approximately one recombination event per gene and increased the mapping resolution by approximately seven times. Our study thus shows that using visible markers to select for recombinants can efficiently increase the resolution of QTL mapping. We resolved the major QTL into two epistatic QTL, QTL3a and QTL3b. QTL3a shows sign epistasis: it has opposite effects in two different genetic backgrounds, the presence vs. the absence of the QTL3b D. sechellia allele. This property of QTL3a allows us to reconstruct the probable order of fixation of the QTL alleles during evolution.     

Simultaneous mapping of epistatic QTL in DU6i × DBA/2 mice

We have mapped epistatic quantitative trait loci (QTL) in an F₂ cross between DU6i × DBA/2 mice. By including these epistatic QTL and their interaction parameters in the genetic model, we were able to increase the genetic variance explained substantially (8.8%–128.3%) for several growth and body composition traits. We used an analysis method based on a simultaneous search for epistatic QTL pairs without assuming that the QTL had any effect individually. We were able to detect several QTL that could not be detected in a search for marginal QTL effects because the epistasis cancelled out the individual effects of the QTL. In total, 23 genomic regions were found to contain QTL affecting one or several of the traits and eight of these QTL did not have significant individual effects. We identified 44 QTL pairs with significant effects on the traits, and, for 28 of the pairs, an epistatic QTL model fit the data significantly better than a model without interactions. The epistatic pairs were classified by the significance of the epistatic parameters in the genetic model, and visual inspection of the two-locus genotype means identified six types of related genotype–phenotype patterns among the pairs. Five of these patterns resembled previously published patterns of QTL interactions.     

QTL mapping of resistance to Fusarium ear rot using a RIL population in maize

Fusarium ear rot is a prevalent disease in maize, reducing grain yields and quality. Resistance breeding is an efficient way to minimize losses caused by the disease. In this study, 187 lines from a RIL population along with the resistant (87-1) and susceptible (Zong 3) parents were planted in Zhengzhou and Beijing with three replications in years 2004 and 2006. Each line was artificially inoculated using the nail-punch method. Significant genotypic variation in response to Fusarium ear rot was detected in both years. Based on a genetic map containing 246 polymorphic SSR markers with average genetic distances of 9.1 cM, the ear-rot resistance QTL were firstly analyzed by composite interval mapping (CIM). Three QTL were detected in both Zhengzhou and Beijing in 2004; and three and four QTL, respectively, were identified in 2006. The resistant parent contributed all resistance QTL. By using composite interval mapping and a mixed model (MCIM), significant epistatic effects on Fusarium ear rot as well as interactions between mapped loci and environments were observed across environments. Two QTL on chromosome 3 (3.04 bin) were consistently identified across all environments by the two methods. The major resistant QTL with the largest effect was flanked by markers umc1025 and umc1742 on chromosome 3 (3.04 bin), explaining 13–22% of the phenotypic variation. The SSR markers closely flanking the major resistance QTL will facilitate marker-assisted selection (MAS) of resistance to Fusarium ear rot in maize breeding programs.     

Dissecting the genetic architecture of agronomic traits in multiple segregating populations in rapeseed (<Emphasis Type="Italic">Brassica napus</Emphasis> L.)

Detection of QTL in multiple segregating populations is of high interest as it includes more alleles than mapping in a single biparental population. In addition, such populations are routinely generated in applied plant breeding programs and can thus be used to identify QTL which are of direct relevance for a marker-assisted improvement of elite germplasm. Multiple-line cross QTL mapping and joint linkage association mapping were used for QTL detection. We empirically compared these two different biometrical approaches with regard to QTL detection for important agronomic traits in nine segregating populations of elite rapeseed lines. The plants were intensively phenotyped in multi-location field trials and genotyped with 253 SNP markers. Both approaches detected several additive QTL for diverse traits, including flowering time, plant height, protein content, oil content, glucosinolate content, and grain yield. In addition, we identified one epistatic QTL for flowering time. Consequently, both approaches appear suited for QTL detection in multiple segregating populations.     

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.     

An empirical Bayes method for estimating epistatic effects of quantitative trait loci

Summary .   The genetic variance of a quantitative trait is often controlled by the segregation of multiple interacting loci. Linear model regression analysis is usually applied to estimating and testing effects of these quantitative trait loci (QTL). Including all the main effects and the effects of interaction (epistatic effects), the dimension of the linear model can be extremely high. Variable selection via stepwise regression or stochastic search variable selection (SSVS) is the common procedure for epistatic effect QTL analysis. These methods are computationally intensive, yet they may not be optimal. The LASSO (least absolute shrinkage and selection operator) method is computationally more efficient than the above methods. As a result, it has been widely used in regression analysis for large models. However, LASSO has never been applied to genetic mapping for epistatic QTL, where the number of model effects is typically many times larger than the sample size. In this study, we developed an empirical Bayes method (E-BAYES) to map epistatic QTL under the mixed model framework. We also tested the feasibility of using LASSO to estimate epistatic effects, examined the fully Bayesian SSVS, and reevaluated the penalized likelihood (PENAL) methods in mapping epistatic QTL. Simulation studies showed that all the above methods performed satisfactorily well. However, E-BAYES appears to outperform all other methods in terms of minimizing the mean-squared error (MSE) with relatively short computing time. Application of the new method to real data was demonstrated using a barley dataset.     

Substitution mapping of Pup1: a major QTL increasing phosphorus uptake of rice from a phosphorus-deficient soil

A major QTL for P uptake had previously been mapped to a 13-cM marker interval on the long arm of chromosome 12. To map that major QTL with higher precision and certainty, a secondary mapping population was developed by backcrossing a near-isogenic line containing the QTL from the donor parent to the recurrent parent of low P uptake. Two different mapping strategies have been followed in this study. A conventional QTL mapping approach was based on individual F(2) RFLP data and the phenotypic evaluation of family means in the F(3). The second strategy employed a substitution-mapping approach. Phenotypic and marker data were obtained for 160 F(3) individuals of six highly informative families that differed in the size of donor chromosomal segments in the region of the putative QTL. QTL mapping showed that close to 80% of the variation between families was due to a single QTL, hereafter referred to as Pup1 (Phosphorus uptake 1). Pup1 was placed in a 3-cM interval flanked by markers S14025 and S13126, which is within 1 cM of the position identified in the original QTL mapping experiment. Other chromosomal regions and epistatic effects were not significant. Substitution mapping revealed that Pup1 co-segregated with marker S13126 and that the flanking markers, S14025 and S13752, were outside the interval containing Pup1. The two mapping strategies therefore yielded almost identical results and, in combining the advantages of both, Pup1 could be mapped with high certainty. The QTL mapping appoach showed that the phenotypic variation between families was due to only one QTL without any additional epistacic interactions, whereas the advantage of substitution mapping was to place clearly defined borders around the QTL.