Bayesian analysis of linkage between genetic markers and quantitative trait loci. II. Combining prior knowledge with experimental evidence

Summary A Bayesian method was developed for identifying genetic markers linked to quantitative trait loci (QTL) by analyzing data from daughter or granddaughter designs and single markers or marker pairs. Traditional methods may yield unrealistic results because linkage tests depend on number of markers and QTL gene effects associated with selected markers are overestimated. The Bayesian or posterior probability of linkage combines information from a daughter or granddaughter design with the prior probability of linkage between a marker locus and a QTL. If the posterior probability exceeds a certain quantity, linkage is declared. Upon linkage acceptance, Bayesian estimates of marker-QTL recombination rate and QTL gene effects and frequencies are obtained. The Bayesian estimates of QTL gene effects account for different amounts of information by shrinking information from data toward the mean or mode of a prior exponential distribution of gene effects. Computation of the Bayesian analysis is feasible. Exact results are given for biallelic QTL, and extensions to multiallelic QTL are suggested.     

Bayesian analysis of linkage between genetic markers and quantitative trait loci. I. Prior knowledge

Summary Prior information on gene effects at individual quantitative trait loci (QTL) and on recombination rates between marker loci and QTL is derived. The prior distribution of QTL gene effects is assumed to be exponential with major effects less likely than minor ones. The prior probability of linkage between a marker and another single locus is a function of the number and length of chromosomes, and of the map function relating recombination rate to genetic distance among loci. The prior probability of linkage between a marker locus and a quantitative trait depends additionally on the number of detectable QTL, which may be determined from total additive genetic variance and minimum detectable QTL effect. The use of this prior information should improve linkage tests and estimates of QTL effects.     

Bioinformatics-Based Identification of Candidate Genes from QTLs Associated with Cell Wall Traits in Populus

Quantitative trait locus (QTL) studies are an integral part of plant research and are used to characterize the genetic basis of phenotypic variation observed in structured populations and inform marker-assisted breeding efforts. These QTL intervals can span large physical regions on a chromosome comprising hundreds of genes, thereby hampering candidate gene identification. Genome history, evolution, and expression evidence can be used to narrow the genes in the interval to a smaller list that is manageable for detailed downstream functional genomics characterization. Our primary motivation for the present study was to address the need for a research methodology that identifies candidate genes within a broad QTL interval. Here we present a bioinformatics-based approach for subdividing candidate genes within QTL intervals into alternate groups of high probability candidates. Application of this approach in the context of studying cell wall traits, specifically lignin content and S/G ratios of stem and root in Populus plants, resulted in manageable sets of genes of both known and putative cell wall biosynthetic function. These results provide a roadmap for future experimental work leading to identification of new genes controlling cell wall recalcitrance and, ultimately, in the utility of plant biomass as an energy feedstock.     

Interval mapping of quantitative trait loci in autotetraploid species.

This article presents a method for QTL interval mapping in autotetraploid species for a full-sib family derived by crossing two parents. For each offspring, the marker information on each chromosome is used to identify possible configurations of chromosomes inherited from the two parents and the locations of crossovers on these chromosomes. A branch and bound algorithm is used to identify configurations with the minimum number of crossovers. From these configurations, the conditional probability of each possible QTL genotype for a series of positions along the chromosome can be estimated. An iterative weighted regression is then used to relate the trait values to the QTL genotype probabilities. A simulation study is performed to assess this approach and to investigate the effects of the proportion of codominant to dominant markers, the heritability, and the population size. We conclude that the method successfully locates QTL and estimates their parameters accurately, and we discuss different modes of action of the QTL that may be modeled.     

Efficiency of population structures for mapping of Mendelian and imprinted quantitative trait loci in outbred pigs using variance component methods

In a simulation study different designs for a pure line pig population were compared for efficiency of mapping QTL using the variance component method. Phenotypes affected by a Mendelian QTL, a paternally expressed QTL, a maternally expressed QTL or by a QTL without an effect were simulated. In all alternative designs 960 progeny were phenotyped. Given the limited number of animals there is an optimum between the number of families and the family size. Estimation of Mendelian and parentally expressed QTL is more efficient in a design with large family sizes. Too small a number of sires should be avoided to minimize chances of sires to be non-segregating. When a large number of families is used, the number of haplotypes increases which reduces the accuracy of estimating the QTL effect and thereby reduces the power to show a significant QTL and to correctly position the QTL. Dense maps allow for smaller family size due to exploitation of LD-information. Given the different possible modes of inheritance of the QTL using 8 to16 boars, two litters per dam was optimal with respect to determining significance and correct location of the QTL for a data set consisting of 960 progeny. The variance component method combining linkage disequilibrium and linkage analysis seems to be an appropriate choice to analyze data sets which vary in marker density and which contain complex family structures.     

标记基因型中QTL基因型条件概率分布

随着分子数量遗传学的发展,人们提出了很多统计模型用于QTL定位分析。在这些模型中,首先得确定QTL在标记基因型中的条件概率分布,然后利用适当的统计方法对QTL在基因组中所处的位置进行估计。本文讨论了常见作图群体（如F2和回交群体）中在给定标记基因型下QTL的条件概率分布,提出了用Mathematics软件推导QTL基因型条件概率分布的方法。用该方法能够快速地、准确地推导出比较复杂的标记基因型中QTL基因型的条件概率分布。     

The genetic architecture of ecological specialization: correlated gene effects on host use and habitat choice in pea aphids

Genetic correlations among phenotypic characters result when two traits are influenced by the same genes or sets of genes. By reducing the degree to which traits in two environments can evolve independently (e.g., Lande 1979; Via and Lande 1985), such correlations are likely to play a central role in both the evolution of ecological specialization and in its link to speciation. For example, negative genetic correlations between fitness traits in different environments (i.e., genetic trade-offs) are thought to influence the evolution of specialization, while positive genetic correlations between performance and characters influencing assortative mating can accelerate the evolution of reproductive isolation between ecologically specialized populations. We first discuss how the genetic architecture of a suite of traits may affect the evolutionary role of genetic correlations among them and review how the mechanisms of correlations can be analyzed using quantitative trait locus (QTL) mapping. We then consider the implications of such data for understanding the evolution of specialization and its link to speciation. We illustrate this approach with a QTL analysis of key characters in two races of pea aphids that are highly specialized on different host plants and partially reproductively isolated. Our results suggest that antagonism among QTL effects on performance in the two environments leads to a genetic trade-off in this system. We also found evidence for parallel QTL effects on host-plant acceptance and fecundity on the accepted host, which could produce assortative mating. These results suggest that the genetic architecture of traits associated with host use may have played a central role in the evolution of specialization and reproductive isolation in pea aphids.     

Mapping multiple Quantitative Trait Loci by Bayesian classification

We developed a classification approach to multiple quantitative trait loci (QTL) mapping built upon a Bayesian framework that incorporates the important prior information that most genotypic markers are not cotransmitted with a QTL or their QTL effects are negligible. The genetic effect of each marker is modeled using a three-component mixture prior with a class for markers having negligible effects and separate classes for markers having positive or negative effects on the trait. The posterior probability of a marker's classification provides a natural statistic for evaluating credibility of identified QTL. This approach performs well, especially with a large number of markers but a relatively small sample size. A heat map to visualize the results is proposed so as to allow investigators to be more or less conservative when identifying QTL. We validated the method using a well-characterized data set for barley heading values from the North American Barley Genome Mapping Project. Application of the method to a new data set revealed sex-specific QTL underlying differences in glucose-6-phosphate dehydrogenase enzyme activity between two Drosophila species. A simulation study demonstrated the power of this approach across levels of trait heritability and when marker data were sparse.     

Development of a near-isogenic line population of Arabidopsis thaliana and comparison of mapping power with a recombinant inbred line population

In Arabidopsis recombinant inbred line (RIL) populations are widely used for quantitative trait locus (QTL) analyses. However, mapping analyses with this type of population can be limited because of the masking effects of major QTL and epistatic interactions of multiple QTL. An alternative type of immortal experimental population commonly used in plant species are sets of introgression lines. Here we introduce the development of a genomewide coverage near-isogenic line (NIL) population of Arabidopsis thaliana, by introgressing genomic regions from the Cape Verde Islands (Cvi) accession into the Landsberg erecta (Ler) genetic background. We have empirically compared the QTL mapping power of this new population with an already existing RIL population derived from the same parents. For that, we analyzed and mapped QTL affecting six developmental traits with different heritability. Overall, in the NIL population smaller-effect QTL than in the RIL population could be detected although the localization resolution was lower. Furthermore, we estimated the effect of population size and of the number of replicates on the detection power of QTL affecting the developmental traits. In general, population size is more important than the number of replicates to increase the mapping power of RILs, whereas for NILs several replicates are absolutely required. These analyses are expected to facilitate experimental design for QTL mapping using these two common types of segregating populations.     

Fine mapping of quantitative trait loci using linkage disequilibria with closely linked marker loci

A multimarker linkage disequilibrium mapping method was developed for the fine mapping of quantitative trait loci (QTL) using a dense marker map. The method compares the expected covariances between haplotype effects given a postulated QTL position to the covariances that are found in the data. The expected covariances between the haplotype effects are proportional to the probability that the QTL position is identical by descent (IBD) given the marker haplotype information, which is calculated using the genedropping method. Simulation results showed that a QTL was correctly positioned within a region of 3, 1.5, or 0.75 cM in 70, 62, and 68%, respectively, of the replicates using markers spaced at intervals of 1, 0.5, and 0.25 cM, respectively. These results were rather insensitive to the number of generations since the QTL occurred and to the effective population size, except that 10 generations yielded rather poor estimates of the QTL position. The position estimates of this multimarker disequilibrium mapping method were more accurate than those from a single marker transmission disequilibrium test. A general approach for identifying QTL is suggested, where several stages of disequilibrium mapping are used with increasingly dense marker spacing.     

Pyramiding QTL for multiple lateral branching in cucumber using inbred backcross lines

Multiple lateral branching (MLB) is a quantitatively inherited trait associated with yield in cucumber (Cucumis sativus L.; 2n = 2x = 14). Although quantitative trait loci (QTL) have been identified for MLB and QTL-marker associations have been verified by marker-assisted selection, the individual effects of these QTL have not been characterized. To test the effects of pyramiding QTL for MLB, molecular genotyping was utilized to create two sets (standard- and little-leaf types) of inbred backcross (IBC) lines possessing various numbers of QTL that promote branching. These IBC lines were evaluated for lateral branch number in two Wisconsin environments at three plant densities. Highly significant differences in the number of primary lateral branches were detected between spacings, leaf types, and lines, but not between locations. Lateral branch number decreased at higher plant densities in all genotypes, while genotype by environment and QTL by environment interactions were marginally non-significant. As the number of QTL increased among IBC lines, the number of branches did not generally change in the little-leaf lines, but decreased in the standard-leaf lines, demonstrating an epistatic effect related to genetic background during lateral branch development. The genomic location with the greatest effect on MLB was confirmed as the QTL that was previously mapped near the little-leaf locus (ll), while the addition of one specific QTL consistently decreased the number of lateral branches in standard-leaf lines. Although pyramiding QTL for MLB did not uniformly increase the number of lateral branches, pyramiding QTL in IBC lines allowed further characterization of individual QTL involved in MLB. Our results, coupled with those of previous studies indicate that lateral branch development in cucumber is determined by growing environment (i.e., plant spacing), genetic background, and QTL composition.     

Optimal sampling of a population to determine QTL location, variance, and allelic number

In a population intended for breeding and selection, questions of interest relative to a specific segregating QTL are the variance it generates in the population, and the number and effects of its alleles. One approach to address these questions is to extract several inbreds from the population and use them to generate multiple mapping families. Given random sampling of parents, sampling strategy may be an important factor determining the power of the analysis and its accuracy in estimating QTL variance and allelic number. We describe appropriate multiple-family QTL mapping methodology and apply it to simulated data sets to determine optimal sampling strategies in terms of family number versus family size. Genomes were simulated with seven chromosomes, on which 107 markers and six QTL were distributed. The total heritability was 0.60. Two to ten alleles were segregating at each QTL. Sampling strategies ranged from sampling two inbreds and generating a single family of 600 progeny to sampling 40 inbreds and generating 40 families of 15 progeny each. Strategies involving only one to five families were subject to variation due to the sampling of inbred parents. For QTL where more than two alleles were segregating, these strategies did not sample QTL alleles representative of the original population. Conversely, strategies involving 30 or more parents were subject to variation due to sampling of QTL genotypes within the small families obtained. Given these constraints, greatest QTL detection power was obtained for strategies involving five to ten mapping families. The most accurate estimation of the variance generated by the QTL, however, was obtained with strategies involving 20 or more families. Finally, strategies with an intermediate number of families best estimated the number of QTL alleles. We conclude that no overall optimal sampling strategy exists but that the strategy adopted must depend on the objective.Communicated by P. Langridge     

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.     

Identification and fine mapping of quantitative trait loci for the number of vascular bundle in maize stem

Studies that investigated the genetic basis of source and sink related traits have been widely conducted. However, the vascular system that links source and sink received much less attention. When maize was domesticated from its wild ancestor, teosinte, the external morphology has changed dramatically; however, less is known for the internal anatomy changes. In this study, using a large maize‐teosinte experimental population, we performed a high‐resolution quantitative trait locus (QTL) mapping for the number of vascular bundle in the uppermost internode of maize stem. The results showed that vascular bundle number is dominated by a large number of small‐effect QTLs, in which a total of 16 QTLs that jointly accounts for 52.2% of phenotypic variation were detected, with no single QTL explaining more than 6% of variation. Different from QTLs for typical domestication traits, QTLs for vascular bundle number might not be under directional selection following domestication. Using Near Isogenic Lines (NILs) developed from heterogeneous inbred family (HIF), we further validated the effect of one QTL qVb9‐2 on chromosome 9 and fine mapped the QTL to a 1.8‐Mb physical region. This study provides important insights for the genetic architecture of vascular bundle number in maize stem and sets basis for cloning of qVb9‐2.     

Fine-mapping of quantitative trait loci in half-sib families using current recombinations

Two groups of methods are being developed to fine-map quantitative trait loci (QTLs): identity-by-descent methods or methods using historical recombinations, and genetic chromosome dissection methods or methods utilizing current recombinations. Here we propose two methods that fall into the second group: contrast mapping and substitution mapping. A QTL has previously been detected via linkage mapping in a half-sib design (granddaughter or daughter design), and sires (grandsires) likely to be heterozygous at the QTL have been identified. A sire (grandsire) and its recombinant offspring are then genotyped for a series of ordered markers spanning the initial marker interval. Offspring are grouped by paternal multi-marker haplotype with haplotypes differing in the location of the recombination event. In the contrast method, contrasts between the phenotypic averages of haplotypes or offspring groups are calculated which correspond to marker intervals within the original interval. The expected value of the contrast for the true QTL interval is always maximum, hence the interval with maximum observed contrast is assumed to contain the QTL. Alternative statistics for determining the interval most likely to contain a QTL are presented for contrast mapping, as well as a bootstrap estimation of the probability of having identified the correct interval. For an initial marker bracket of 20 cM and 10 additional equidistant markers, the probability of assigning the QTL to the correct 2 cM marker interval or to a combined 4 cM interval was calculated. For substitution effects of 0.093, 0.232, 0.464, 0.696 and 0.928 (in additive genetic SD), power values near 0.14, 0.26, 0.48, 0.67 and 0.80 (0.25, 0.53, 0.86, 0.97 and 0.99) are achieved for a family of 200 (1000) sons, respectively. In substitution mapping, QTL segregation status of recombinant sons must be determined using daughter genotyping. Combinations of two haplotypes with their segregation status are required to assign the QTL to an interval. Probabilities of correct QTL assignment were calculated assuming absence of the mutant QTL allele in dams of sons. For a 2 cM interval and a QTL at the midpoint of an interval, power near 0.95 (0.90) is reached when the number of recombinant sons is 70 (60), or total number of sons is 424 (363). For QTL positions away from the midpoint, power decreases but can be improved by combining marker intervals. For a QTL located halfway to the midpoint, and 182 sons in a family resulting in 30 recombinant sons, probability is 0.94 for assignment to either a 2 cM or a combined 4 cM interval. Effect of type I and type II errors in segregation status determination on power of QTL assignment was found to be small. Errors in segregation status due to QTL segregation in dams have an impact if the frequency of the mutant QTL allele is intermediate to high.     

Use of maternal information for QTL detection in a (grand)daughter design

In a (grand)daughter design, maternal information is often neglected because the number of progeny per dam is limited. The number of dams per maternal grandsire (MGS), however, could be large enough to contribute to QTL detection. But dams and MGS usually are not genotyped, there are two recombination opportunities between the MGS and the progeny, and at a given location, only half the progeny receive a MGS chromosomal segment. A 3-step procedure was developed to estimate: (1) the marker phenotypes probabilities of the MGS; (2) the probability of each possible MGS haplotype; (3) the probabilities that the progeny receives either the first, or second MGS segment, or a maternal grandam segment. These probabilities were used for QTL detection in a linear model including the effects of sire, MGS, paternal QTL, MGS QTL and maternal grandam QTL. Including the grandam QTL effect makes it possible to detect QTL in the grandam population, even when MGS are not informative. The detection power, studied by simulation, was rather high, provided that MGS family size was greater than 50. Using maternal information in the French dairy cattle granddaughter design made it possible to detect 23 additional QTL genomewise significant.     

Clusthaplo: a plug-in for MCQTL to enhance QTL detection using ancestral alleles in multi-cross design

Key message

We enhance power and accuracy of QTL mapping in multiple related families, by clustering the founders of the families on their local genomic similarity.

Abstract

MCQTL is a linkage mapping software application that allows the joint QTL mapping of multiple related families. In its current implementation, QTLs are modeled with one or two parameters for each parent that is a founder of the multi-cross design. The higher the number of parents, the higher the number of model parameters which can impact the power and the accuracy of the mapping. We propose to make use of the availability of denser and denser genotyping information on the founders to lessen the number of MCQTL parameters and thus boost the QTL discovery. We developed clusthaplo, an R package (http://cran.r-project.org/web/packages/clusthaplo/index.html), which aims to cluster haplotypes using a genomic similarity that reflects the probability of sharing the same ancestral allele. Computed in a sliding window along the genome and followed by a clustering method, the genomic similarity allows the local clustering of the parent haplotypes. Our assumption is that the haplotypes belonging to the same class transmit the same ancestral allele. So their putative QTL allelic effects can be modeled with the same parameter, leading to a parsimonious model, that is plugged in MCQTL. Intensive simulations using three maize data sets showed the significant gain in power and in accuracy of the QTL mapping with the ancestral allele model compared to the classical MCQTL model. MCQTL_LD (clusthaplo outputs plug in MCQTL) is a versatile and powerful tool for QTL mapping in multiple related families that makes use of linkage and linkage disequilibrium (web site http://carlit.toulouse.inra.fr/MCQTL/).     

Fine mapping of multiple QTL using combined linkage and linkage disequilibrium mapping – A comparison of single QTL and multi QTL methods

Two previously described QTL mapping methods, which combine linkage analysis (LA) and linkage disequilibrium analysis (LD), were compared for their ability to detect and map multiple QTL. The methods were tested on five different simulated data sets in which the exact QTL positions were known. Every simulated data set contained two QTL, but the distances between these QTL were varied from 15 to 150 cM. The results show that the single QTL mapping method (LDLA) gave good results as long as the distance between the QTL was large (> 90 cM). When the distance between the QTL was reduced, the single QTL method had problems positioning the two QTL and tended to position only one QTL, i.e. a "ghost" QTL, in between the two real QTL positions. The multi QTL mapping method (MP-LDLA) gave good results for all evaluated distances between the QTL. For the large distances between the QTL (> 90 cM) the single QTL method more often positioned the QTL in the correct marker bracket, but considering the broader likelihood peaks of the single point method it could be argued that the multi QTL method was more precise. Since the distances were reduced the multi QTL method was clearly more accurate than the single QTL method. The two methods combine well, and together provide a good tool to position single or multiple QTL in practical situations, where the number of QTL and their positions are unknown.     

An efficient Bayesian model selection approach for interacting quantitative trait loci models with many effects

We extend our Bayesian model selection framework for mapping epistatic QTL in experimental crosses to include environmental effects and gene-environment interactions. We propose a new, fast Markov chain Monte Carlo algorithm to explore the posterior distribution of unknowns. In addition, we take advantage of any prior knowledge about genetic architecture to increase posterior probability on more probable models. These enhancements have significant computational advantages in models with many effects. We illustrate the proposed method by detecting new epistatic and gene-sex interactions for obesity-related traits in two real data sets of mice. Our method has been implemented in the freely available package R/qtlbim (http://www.qtlbim.org) to facilitate the general usage of the Bayesian methodology for genomewide interacting QTL analysis.     

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.