Joint linkage and linkage disequilibrium mapping of quantitative trait loci in natural populations

Linkage analysis and allelic association (also referred to as linkage disequilibrium) studies are two major approaches for mapping genes that control simple or complex traits in plants, animals, and humans. But these two approaches have limited utility when used alone, because they use only part of the information that is available for a mapping population. More recently, a new mapping strategy has been designed to integrate the advantages of linkage analysis and linkage disequilibrium analysis for genome mapping in outcrossing populations. The new strategy makes use of a random sample from a panmictic population and the open-pollinated progeny of the sample. In this article, we extend the new strategy to map quantitative trait loci (QTL), using molecular markers within the EM-implemented maximum-likelihood framework. The most significant advantage of this extension is that both linkage and linkage disequilibrium between a marker and QTL can be estimated simultaneously, thus increasing the efficiency and effectiveness of genome mapping for recalcitrant outcrossing species. Simulation studies are performed to test the statistical properties of the MLEs of genetic and genomic parameters including QTL allele frequency, QTL effects, QTL position, and the linkage disequilibrium of the QTL and a marker. The potential utility of our mapping strategy is discussed.     

Mapping quantitative trait loci using molecular marker linkage maps

Summary High-density restriction fragment length polymorphism (RFLP) and allozyme linkage maps have been developed in several plant species. These maps make it technically feasible to map quantitative trait loci (QTL) using methods based on flanking marker genetic models. In this paper, we describe flanking marker models for doubled haploid (DH), recombinant inbred (RI), backcross (BC), F₁ testcross (F₁TC), DH testcross (DHTC), recombinant inbred testcross (RITC), F₂, and F₃ progeny. These models are functions of the means of quantitative trait locus genotypes and recombination frequencies between marker and quantitative trait loci. In addition to the genetic models, we describe maximum likelihood methods for estimating these parameters using linear, nonlinear, and univariate or multivariate normal distribution mixture models. We defined recombination frequency estimators for backcross and F₂ progeny group genetic models using the parameters of linear models. In addition, we found a genetically unbiased estimator of the QTL heterozygote mean using a linear function of marker means. In nonlinear models, recombination frequencies are estimated less efficiently than the means of quantitative trait locus genotypes. Recombination frequency estimation efficiency decreases as the distance between markers decreases, because the number of progeny in recombinant marker classes decreases. Mean estimation efficiency is nearly equal for these methods.     

QTL analysis: unreliability and bias in estimation procedures

Several statistical methods which employ multiple marker data are currently available for the analysis of quantitative trait loci (QTL) in experimental populations. Although comparable estimates of QTL location and effects have been obtained by these methods, using simulated and real data sets, their accuracy and reliability have not been extensively investigated. The present study specifically examines the merit of using F₂ and doubled haploid populations for locating QTL and estimating their effects. Factors which may affect accuracy and reliability of QTL mapping, such as the number and position of the markers available, the accuracy of the marker locations and the size of the experimental population used, are considered. These aspects are evaluated for QTL of differing heritabilities and locations along the chromosome.A population of 300 F₂ individuals and 150 doubled haploid lines gave estimates of QTL position and effect which were comparable, albeit extremely unreliable. Even for a QTL of high heritability (10%), the confidence interval was 35 cM. There was little increase in reliability to be obtained from using 300, rather than 200, F₂ individuals and 100 doubled haploid lines gave similar results to 150. QTL estimates were not significantly improved either by using the expected, rather than the observed, marker positions or by using a dense map of markers rather than a sparse map. A QTL which was asymmetrically located in the linkage group resulted in inaccurate estimates of QTL position which were seriously biassed at low heritability of the QTL. In a population of 300 F₂ individuals the bias increased from 4 cM to 20 cM, for a QTL with 10% and 2% heritability respectively.     

Using molecular markers to map multiple quantitative trait loci: models for backcross,recombinant inbred,and doubled haploid progeny

Summary To maximize parameter estimation efficiency and statistical power and to estimate epistasis, the parameters of multiple quantitative trait loci (QTLs) must be simultaneously estimated. If multiple QTL affect a trait, then estimates of means of QTL genotypes from individual locus models are statistically biased. In this paper, I describe methods for estimating means of QTL genotypes and recombination frequencies between marker and quantitative trait loci using multilocus backcross, doubled haploid, recombinant inbred, and testcross progeny models. Expected values of marker genotype means were defined using no double or multiple crossover frequencies and flanking markers for linked and unlinked quantitative trait loci. The expected values for a particular model comprise a system of nonlinear equations that can be solved using an interative algorithm, e.g., the Gauss-Newton algorithm. The solutions are maximum likelihood estimates when the errors are normally distributed. A linear model for estimating the parameters of unlinked quantitative trait loci was found by transforming the nonlinear model. Recombination frequency estimators were defined using this linear model. Certain means of linked QTLs are less efficiently estimated than means of unlinked QTLs.     

More about quantitative trait locus mapping with diallel designs

We present a general regression-based method for mapping quantitative trait loci (QTL) by combining different populations derived from diallel designs. The model expresses, at any map position, the phenotypic value of each individual as a function of the specific-mean of the population to which the individual belongs, the additive and dominance effects of the alleles carried by the parents of that population and the probabilities of QTL genotypes conditional on those of neighbouring markers. Standard linear model procedures (ordinary or iteratively reweighted least-squares) are used for estimation and test of the parameters.     

QTL mapping of internal heat necrosis in tetraploid potato

Internal heat necrosis (IHN) is a physiological disorder of potato tubers. We developed a linkage map of tetraploid potato using AFLP and SSR markers, and mapped QTL for mean severity and percent incidence of IHN. Phenotypic data indicated that the distribution of IHN is skewed toward resistance. Late foliage maturity was slightly but significantly correlated with increased IHN symptoms. The linkage map for ‘Atlantic’, the IHN-susceptible parent, covered 1034.4 cM and included 13 linkage groups, and the map for B1829-5, the IHN-resistant parent, covered 940.2 cM and contained 14 linkage groups. QTL for increased resistance to IHN were located on chromosomes IV, V, and groups VII and X of ‘Atlantic’, and on group VII of B1829-5 in at least 2 of 3 years. The QTL explained between 4.5 and 29.4% of the variation for mean severity, and from 3.7 to 14.5% of the variation for percent incidence. Most QTL detected were dominant, and associated with decreased IHN symptoms. One SSR and 13 AFLP markers that were linked to IHN were tested in a second population. One AFLP marker was associated with decreased symptoms in both populations. The SSR marker was not associated with IHN in the second population, but was closely linked in repulsion to another marker that was associated with IHN, and had the same (negative) effect on the trait as the SSR marker did in the first population. The correlation between maturity and IHN may be partially explained by the presence of markers on chromosome V that are linked to both traits. This research represents the first molecular genetic research of IHN in potato.     

High-resolution joint linkage disequilibrium and linkage mapping of quantitative trait loci based on sibship data

This paper proposes variance component models for high resolution joint linkage disequilibrium (LD) and linkage mapping of quantitative trait loci (QTL) based on sibship data; this can include population data if independent individuals are treated as single sibships. One application of these models is late onset complex disease gene mapping, when parental data are not available. The models simultaneously incorporate both LD and linkage information. The LD information is contained in mean coefficients of sibship data. The linkage information is contained in the variance-covariance matrices of trait values for sibships with at least two siblings. We derive formulas for calculating the probability of sharing two trait alleles identical by descent (IBD) for sibpairs in interval mapping of QTL; this is the coefficient of dominant variance of the trait covariance of sibpairs on major QTL. To investigate the performance of the formulas, we calculate the numerical values via the formulas and get satisfactory approximations. We compare the power and sample sizes for both LD and linkage mapping. By simulation and theoretical analysis, we compare the results with those of Fulker and Abecasis "AbAw" approach. It is well known that the resolution of linkage analysis can be low for complex disease gene mapping. LD mapping, on the other hand, can increase mapping precision and is useful in high resolution mapping. Linkage analysis is less sensitive to population subdivisions and admixtures. The level of LD is sensitive to population stratification which may easily lead to spurious association. Performing a joint analysis of LD and linkage mapping can help to overcome the limits of both approaches. Moreover, the advantages of the two complementary strategies can be utilized maximally. In practice, linkage analysis may be performed using pedigree data to identify suggestive linkage between markers and trait loci based on a sparse marker map. In the presence of linkage, joint LD and linkage mapping can be carried out to do fine gene mapping based on a dense genetic map using both pedigree and population data. Population and pedigree data of any type can be combined to perform a joint analysis of high resolution LD and linkage mapping of QTL by generalizing the method.     

The genetic basis of floral traits associated with mating system evolution in Leptosiphon (Polemoniaceae): an analysis of quantitative trait loci

Mapping of quantitative trait loci (QTL) was used to investigate the genetic architecture of divergence in floral characters associated with the mating system, an important adaptive trait in angiosperms. Two species of Leptosiphon (Polemoniaceae), one strongly self-fertilizing (L. bicolor) and the other partially outcrossing (L. jepsonii), were crossed to produce F2 and both backcross progenies. For each crossing population, a linkage map was created using amplified fragment length polymorphism markers, and QTL were identified for several dimensions of floral size. For each of the five traits examined, three to seven QTL were detected, with independent datasets yielding congruent results in some but not all cases. The phenotypic effect of individual QTL was generally moderate. We estimated that many of the QTL were additive or showed dominance toward L. bicolor, whereas comparison of mean trait values for parental and cross progenies showed apparent overall dominance of L. jepsonii traits. Colocalization of QTL for different dimensions of floral size was consistent with high phenotypic correlations between floral traits. Substantial segregation distortion was observed in marker loci, the majority favoring alleles from the large-flowered parent. A low frequency of male sterility in the F2 population is consistent with the Dobzhansky-Muller model for the evolution of reproductive isolation.     

Detecting Marker-Qtl Linkage and Estimating Qtl Gene Effect and Map Location Using a Saturated Genetic Map

A simulation study was carried out on a backcross population in order to determine the effect of marker spacing, gene effect and population size on the power of marker-quantitative trait loci (QTL) linkage experiments and on the standard error of maximum likelihood estimates (MLE) of QTL gene effect and map location. Power of detecting a QTL was virtually the same for a marker spacing of 10 cM as for an infinite number of markers and was only slightly decreased for marker spacing of 20 or even 50 cM. The advantage of using interval mapping as compared to single-marker analysis was slight. ``Resolving power' of a marker-QTL linkage experiment was defined as the 95% confidence interval for the QTL map location that would be obtained when scoring an infinite number of markers. It was found that reducing marker spacing below the resolving power did not add appreciably to narrowing the confidence interval. Thus, the 95% confidence interval with infinite markers sets the useful marker spacing for estimating QTL map location for a given population size and estimated gene effect.     

A genetic linkage map based on AFLP and SSR markers and mapping of QTL for dry-matter content in sweetpotato

We developed a genetic linkage map of sweetpotato using amplified fragment length polymorphism (AFLP) and simple sequence repeat (SSR) markers and a mapping population consisting of 202 individuals derived from a broad cross between Xushu 18 and Xu 781, and mapped quantitative trait loci (QTL) for the storage root dry-matter content. The linkage map for Xushu 18 included 90 linkage groups with 2077 markers (1936 AFLP and 141 SSR) and covered 8,184.5 cM with an average marker distance of 3.9 cM, and the map for Xu 781 contained 90 linkage groups with 1954 markers (1824 AFLP and 130 SSR) and covered 8,151.7 cM with an average marker distance of 4.2 cM. The maps described herein have the best coverage of the sweetpotato genome and the highest marker density reported to date. These are the first maps developed that have 90 complete linkage groups, which is in agreement with the actual number of chromosomes. Duplex and triplex markers were used to detect the homologous groups, and 13 and 14 homologous groups were identified in Xushu 18 and Xu 781 maps, respectively. Interval mapping was performed first and, subsequently, a multiple QTL model was used to refine the position and magnitude of the QTL. A total of 27 QTL for dry-matter content were mapped, explaining 9.0–45.1 % of the variation; 77.8 % of the QTL had a positive effect on the variation. This work represents an important step forward in genomics and marker-assisted breeding of sweetpotato.     

Spurious linkage between markers in QTL mapping

Selective genotyping of extreme progeny is a powerful method to increase the information content per individual when looking for quantitative trait loci (QTLs) using molecular markers for which a map is known. However, if marker information from the selected individuals is used to construct the map of the markers, this can lead to distorted segregation of the markers that in turn can lead to the estimation of a spurious linkage between independently inherited markers. The mistaken estimation of linkage between independently inherited markers will occur when there are two (or more) independently inherited QTLs linked to two (or more) markers and the same individuals are used to estimate the map of the markers and to do the QTL estimation. The incorrect linkage occurs because in selecting individuals from the tails of the phenotypic distribution we will also be selecting certain combinations of the markers instead of obtaining a random sample of the true distribution of the marker genotypes. Analytical results are outlined and the analyses of a simulated data set illustrate the problems that could arise when data from individuals chosen by selective genotyping are incorrectly employed to construct a marker map. A strategy is proposed to remedy this problem.     

A Bayesian approach for constructing genetic maps when markers are miscoded

The advent of molecular markers has created opportunities for a better understanding of quantitative inheritance and for developing novel strategies for genetic improvement of agricultural species, using information on quantitative trait loci (QTL). A QTL analysis relies on accurate genetic marker maps. At present, most statistical methods used for map construction ignore the fact that molecular data may be read with error. Often, however, there is ambiguity about some marker genotypes. A Bayesian MCMC approach for inferences about a genetic marker map when random miscoding of genotypes occurs is presented, and simulated and real data sets are analyzed. The results suggest that unless there is strong reason to believe that genotypes are ascertained without error, the proposed approach provides more reliable inference on the genetic map.     

Mapping of QTLs for androgenetic response based on a molecular genetic map of x Triticosecale Wittmack.

Quantitative trait loci (QTLs) for androgenetic response were mapped in a doubled haploid (DH) population derived from the F1 hybrid of 2 unrelated varieties of triticale, 'Torote' and 'Presto'. A molecular marker linkage map of this cross was previously constructed using 73 DH lines. This map contains 356 markers (18 random amplified 5 polymorphic DNA, 40 random amplified microsatellite polymorphics, 276 amplified fragment length polymorphisms, and 22 simple sequence repeats) and was used for QTL analysis. The genome was well covered, and of the markers analysed, 336 were located in 21 linkage groups (81.9%) identified using SSR markers. The map covered a total length of 2465.4 cM with an average of 1 marker for each 6.9 cM. The distribution of the markers was not homogeneous across the 3 genomes, with 50.7% detected in the R genome. Several QTLs were found for the following variables related to the androgenetic response: number of embryos/100 anthers; plants regenerated from 100 embryos; number of green plants/total number of plants; and number of green plants/1000 anthers. Two were detected on chromosome 6B and 4R, which together had a 30% total influence on the induction of embryos. Another was found on 6B and on the unidentified LG1; these influenced the production of total plants from haploid embryo cultures. One QTL on chromosome 3R determined the photosynthetic viability of the haploid plantlets regenerated from microspores. Other QTLs were found on chromosomes 1B, 1R, 4R, and 7R, which helped the control of the final androgenetic response (the number of plantlets obtained for every 1000 anthers cultured).     

Analysis of complex leaf and flower characters in Rhododendron using a molecular linkage map

 A molecular linkage map of Rhododendron has been constructed by using a segregating population from an interspecific cross. Parent-specific maps based on 239 RAPD, 38 RFLP, and two microsatellite markers were aligned using markers heterozygous in both parents. The map of the male parent ‘Cunningham’s White’ comprised 182 DNA markers in 13 linkage groups corresponding to the basic chromosome number. In the female parent ‘Rh 16’ 168 markers were located on 18 linkage groups. An assignment of putative homologous linkage groups was possible for 11 groups of each parent. QTL analyses based on the non-parametric Kruskal-Wallis rank-sum test were performed for the characters “leaf chlorosis” and “flower colour” scored as quantitative traits. For leaf chlorosis, two genomic regions bearing QTLs with significant effects on the trait were identified on two linkage groups of the chlorosis-tolerant parent. RAPD marker analysis of additional lime-stressed genotypes tested under altered environmental conditions verified the relationship between marker allele frequencies and the expression of chlorosis. Highly significant QTL effects for flower colour were found on two chromosomes indicating major genes located in these genome areas. The prospects for utilization of a linkage map in Rhododendron are discussed. Received: 28 September 1998 / Accepted: 5 November 1998     

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.     

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.     

Identification of QTL underlying somatic embryogenesis capacity of immature embryos in soybean (Glycine max (L.) Merr.)

High embryogenesis capacity of soybean (Glycine max (L.) Merr.) in vitro possessed potential for effective genetic engineering and tissue culture. The objects of this study were to identify quantitative trait loci (QTL) underlying embryogenesis traits and to identify genotypes with higher somatic embryogenesis capacity. A mapping population, consisting of 126 F_5:6 recombinant inbred lines, was advanced by single-seed-descent from cross between Peking (higher primary and secondary embryogenesis) and Keburi (lower primary and secondary embryogenesis). This population was evaluated for primary embryogenesis capacity from immature embryo cultures by measuring the frequency of somatic embryogenesis (FSE), the somatic embryo number per explant (EPE) and the efficiency of somatic embryogenesis (ESE). A total of 89 simple sequence repeat markers were used to construct a genetic linkage map. Six QTL were associated with somatic embryogenesis. Two QTL for FSE were found, QFSE-1 (Satt307) and QFSE-2 (Satt286), and both were located on linkage group C2 that explained 45.21 and 25.97% of the phenotypic variation, respectively. Four QTL for EPE (QEPE-1 on MLG H, QEPE-2 on MLG G and QEPE-3 on MLG G) were found, which explained 7.11, 7.56 and 6.12% of phenotypic variation, respectively. One QTL for ESE, QESE-1 (Satt427), was found on linkage group G that explained 6.99% of the phenotypic variation. QEPE-2 and QESE-1 were located in the similar region of MLG G. These QTL provide potential for marker assistant selection of genotypes with higher embryogenesis.     

Composite interval mapping reveals a major locus influencing embryonic development rate in rainbow trout (Oncorhynchus mykiss)

Little is known about the genetics controlling the rate of embryonic development in salmonids, despite the fact that this trait plays an important role in the life history of wild and cultured stocks. We investigated the genetics of embryonic development rate by performing an analysis of quantitative trait loci (QTL) on two families of androgenetically derived doubled haploid rainbow trout produced from a hybrid of two clonal lines with divergent embryonic development rates. A total of 170 doubled haploid individuals were genotyped at 222 marker loci [219 amplified fragment length polymorphism (AFLP) markers, 2 microsatellites, and p53]. A genetic linkage analysis resulted in a map consisting of 27 linkage groups with 21 of the markers remaining unlinked at a minimum LOD of 3.0 and maximum theta of 0.40. Eight of these linkage groups were matched to published rainbow trout linkage groups. Composite interval mapping (CIM) revealed evidence for two QTL influencing time to hatch, and suggestive evidence for a third. These QTL accounted for a total of 24.6% of the variation in time to hatch. One of these QTL had a large effect on development rate, especially in one family of doubled haploids, in which it explained 25.6% of the variance in time to hatch. QTL influencing embryonic length and weight at the commencement of exogenous feeding were also identified. The QTL with the strongest effect on embryonic length (lenR13) mapped to the same position as the QTL with the strongest effect on time to hatch (tthR13), suggesting a single QTL may have a pleiotropic effect on both these traits. These results suggest that the use of clonal lines with a doubled haploid crossing design is an effective way of analyzing the genetic basis of complex traits in salmonids.     

Genetic map of Triticum turgidum based on a hexaploid wheat population without genetic recombination for D genome

ABSTRACT: BACKGROUND: A synthetic doubled-haploid hexaploid wheat population, SynDH1, derived from the spontaneous chromosome doubling of triploid F1 hybrid plants obtained from the cross of hybrids Triticum turgidum ssp. durum line Langdon (LDN) and ssp. turgidum line AS313, with Aegilops tauschii ssp. tauschii accession AS60, was previously constructed. SynDH1 is a tetraploidization-hexaploid doubled haploid (DH) population because it contains recombinant A and B chromosomes from two different T. turgidum genotypes, while all the D chromosomes from Ae. tauschii are homogenous across the whole population. This paper reports the construction of a genetic map using this population. RESULTS: Of the 606 markers used to assemble the genetic map, 588 (97%) were assigned to linkage groups. These included 513 Diversity Arrays Technology (DArT) markers, 72 simple sequence repeat (SSR), one insertion site-based polymorphism (ISBP), and two high-molecular-weight glutenin subunit (HMW-GS) markers. These markers were assigned to the 14 chromosomes, covering 2048.79 cM, with a mean distance of 3.48 cM between adjacent markers. This map showed good coverage of the A and B genome chromosomes, apart from 3A, 5A, 6A, and 4B. Compared with previously reported maps, most shared markers showed highly consistent orders. This map was successfully used to identify five quantitative trait loci (QTL), including two for spikelet number on chromosomes 7A and 5B, two for spike length on 7A and 3B, and one for 1000-grain weight on 4B. However, differences in crossability QTL between the two T. turgidum parents may explain the segregation distortion regions on chromosomes 1A, 3B, and 6B. CONCLUSIONS: A genetic map of T. turgidum including 588 markers was constructed using a synthetic doubled haploid (SynDH) hexaploid wheat population. Five QTLs for three agronomic traits were identified from this population. However, more markers are needed to increase the density and resolution of this map in the future study.     

Dissecting the correlation structure of a bivariate phenotype: Common genes or shared environment?

High correlations between two quantitative traits may be either due to common genetic factors or common environmental factors or a combination of both. In this study, we develop statistical methods to extract the genetic contribution to the total correlation between the components of a bivariate phenotype. Using data on bivariate phenotypes and marker genotypes for sib-pairs, we propose a test for linkage between a common QTL and a marker locus based on the conditional cross-sib trait correlations (trait 1 of sib 1—trait 2 of sib 2 and conversely) given the identity-by-descent (i.b.d.) sharing at the marker locus. We use Monte-Carlo simulations to evaluate the performance of the proposed test under different trait parameters and quantitative trait distributions. An application of the method is illustrated using data on two alcohol-related phenotypes from a project on the collaborative study on the genetics of alcoholism.