Multitrait fine mapping of quantitative trait loci using combined linkage disequilibria and linkage analysis

Novel Resampling Improves Statistical Power for Multiple-Trait QTL Mapping

Multiple-trait analysis typically employs models that associate a quantitative trait locus (QTL) with all of the traits. As a result, statistical power for QTL detection may not be optimal if the QTL contributes to the phenotypic variation in only a small proportion of the traits. Excluding QTL effects that contribute little to the test statistic can improve statistical power. In this article, we show that an optimal power can be achieved when the number of QTL effects is best estimated, and that a stringent criterion for QTL effect selection may improve power when the number of QTL effects is small but can reduce power otherwise. We investigate strategies for excluding trivial QTL effects, and propose a method that improves statistical power when the number of QTL effects is relatively small, and fairly maintains the power when the number of QTL effects is large. The proposed method first uses resampling techniques to determine the number of nontrivial QTL effects, and then selects QTL effects by the backward elimination procedure for significance test. We also propose a method for testing QTL-trait associations that are desired for biological interpretation in applications. We validate our methods using simulations and Arabidopsis thaliana transcript data.

POEM: Identifying Joint Additive Effects on Regulatory Circuits

MOTIVATION

Expression Quantitative Trait Locus (eQTL) mapping tackles the problem of identifying variation in DNA sequence that have an effect on the transcriptional regulatory network. Major computational efforts are aimed at characterizing the joint effects of several eQTLs acting in concert to govern the expression of the same genes. Yet, progress toward a comprehensive prediction of such joint effects is limited. For example, existing eQTL methods commonly discover interacting loci affecting the expression levels of a module of co-regulated genes. Such "modularization" approaches, however, are focused on epistatic relations and thus have limited utility for the case of additive (non-epistatic) effects.

RESULTS

Here we present POEM (Pairwise effect On Expression Modules), a methodology for identifying pairwise eQTL effects on gene modules. POEM is specifically designed to achieve high performance in the case of additive joint effects. We applied POEM to transcription profiles measured in bone marrow-derived dendritic cells across a population of genotyped mice. Our study reveals widespread additive, trans-acting pairwise effects on gene modules, characterizes their organizational principles, and highlights high-order interconnections between modules within the immune signaling network. These analyses elucidate the central role of additive pairwise effect in regulatory circuits, and provide computational tools for future investigations into the interplay between eQTLs.

AVAILABILITY

The software described in this article is available at csgi.tau.ac.il/POEM/.

Bayesian model selection for multiple QTLs mapping combining linkage disequilibrium and linkage

Linkage disequilibrium (LD) mapping is able to localize quantitative trait loci (QTL) within a rather small region (e.g. 2 cM), which is much narrower than linkage analysis (LA, usually 20 cM). The multilocus LD method utilizes haplotype information around putative mutation and takes historical recombination events into account, and thus provides a powerful method for further fine mapping. However, sometimes there are more than one QTLs in the region being studied. In this study, the Bayesian model selection implemented via the Markov chain Monte Carlo (MCMC) method is developed for fine mapping of multiple QTLs using haplotype information in a small region. The method combines LD as well as linkage information. A series of simulation experiments were conducted to investigate the behavior of the method. The results showed that this new multiple QTLs method was more efficient in separating closely linked QTLs than single-marker association studies.

Whole-genome analysis of multienvironment or multitrait QTL in MAGIC

Multiparent Advanced Generation Inter-Cross (MAGIC) populations are now being utilized to more accurately identify the underlying genetic basis of quantitative traits through quantitative trait loci (QTL) analyses and subsequent gene discovery. The expanded genetic diversity present in such populations and the amplified number of recombination events mean that QTL can be identified at a higher resolution. Most QTL analyses are conducted separately for each trait within a single environment. Separate analysis does not take advantage of the underlying correlation structure found in multienvironment or multitrait data. By using this information in a joint analysis—be it multienvironment or multitrait — it is possible to gain a greater understanding of genotype- or QTL-by-environment interactions or of pleiotropic effects across traits. Furthermore, this can result in improvements in accuracy for a range of traits or in a specific target environment and can influence selection decisions. Data derived from MAGIC populations allow for founder probabilities of all founder alleles to be calculated for each individual within the population. This presents an additional layer of complexity and information that can be utilized to identify QTL. A whole-genome approach is proposed for multienvironment and multitrait QTL analysis in MAGIC. The whole-genome approach simultaneously incorporates all founder probabilities at each marker for all individuals in the analysis, rather than using a genome scan. A dimension reduction technique is implemented, which allows for high-dimensional genetic data. For each QTL identified, sizes of effects for each founder allele, the percentage of genetic variance explained, and a score to reflect the strength of the QTL are found. The approach was demonstrated to perform well in a small simulation study and for two experiments, using a wheat MAGIC population.

TraitCapture: genomic and environment modelling of plant phenomic data

Agriculture requires a second green revolution to provide increased food, fodder, fiber, fuel and soil fertility for a growing population while being more resilient to extreme weather on finite land, water, and nutrient resources. Advances in phenomics, genomics and environmental control/sensing can now be used to directly select yield and resilience traits from large collections of germplasm if software can integrate among the technologies. Traits could be Captured throughout development and across environments from multi-dimensional phenotypes, by applying Genome Wide Association Studies (GWAS) to identify causal genes and background variation and functional structural plant models (FSPMs) to predict plant growth and reproduction in target environments. TraitCapture should be applicable to both controlled and field environments and would allow breeders to simulate regional variety trials to pre-select for increased productivity under challenging environments.

Combined linkage disequilibrium and linkage mapping: Bayesian multilocus approach

Quantitative trait loci (QTL) affecting the phenotype of interest can be detected using linkage analysis (LA), linkage disequilibrium (LD) mapping or a combination of both (LDLA). The LA approach uses information from recombination events within the observed pedigree and LD mapping from the historical recombinations within the unobserved pedigree. We propose the Bayesian variable selection approach for combined LDLA analysis for single-nucleotide polymorphism (SNP) data. The novel approach uses both sources of information simultaneously as is commonly done in plant and animal genetics, but it makes fewer assumptions about population demography than previous LDLA methods. This differs from approaches in human genetics, where LDLA methods use LA information conditional on LD information or the other way round. We argue that the multilocus LDLA model is more powerful for the detection of phenotype-genotype associations than single-locus LDLA analysis. To illustrate the performance of the Bayesian multilocus LDLA method, we analyzed simulation replicates based on real SNP genotype data from small three-generational CEPH families and compared the results with commonly used quantitative transmission disequilibrium test (QTDT). This paper is intended to be conceptual in the sense that it is not meant to be a practical method for analyzing high-density SNP data, which is more common. Our aim was to test whether this approach can function in principle.

Combined linkage and linkage disequilibrium QTL mapping in multiple families of maize (Zea mays L.) line crosses highlights complementarities between models based on parental haplotype and single locus polymorphism

Advancements in genotyping are rapidly decreasing marker costs and increasing marker density. This opens new possibilities for mapping quantitative trait loci (QTL), in particular by combining linkage disequilibrium information and linkage analysis (LDLA). In this study, we compared different approaches to detect QTL for four traits of agronomical importance in two large multi-parental datasets of maize (Zea mays L.) of 895 and 928 testcross progenies composed of 7 and 21 biparental families, respectively, and genotyped with 491 markers. We compared to traditional linkage-based methods two LDLA models relying on the dense genotyping of parental lines with 17,728 SNP: one based on a clustering approach of parental line segments into ancestral alleles and one based on single marker information. The two LDLA models generally identified more QTL (60 and 52 QTL in total) than classical linkage models (49 and 44 QTL in total). However, they performed inconsistently over datasets and traits suggesting that a compromise must be found between the reduction of allele number for increasing statistical power and the adequacy of the model to potentially complex allelic variation. For some QTL, the model exclusively based on linkage analysis, which assumed that each parental line carried a different QTL allele, was able to capture remaining variation not explained by LDLA models. These complementarities between models clearly suggest that the different QTL mapping approaches must be considered to capture the different levels of allelic variation at QTL involved in complex traits.

Family-based association mapping in crop species

Identification of allelic variants associated with complex traits provides molecular genetic information associated with variability upon which both artificial and natural selections are based. Family-based association mapping (FBAM) takes advantage of linkage disequilibrium among segregating progeny within crosses and among parents to provide greater power than association mapping and greater resolution than linkage mapping. Herein, we discuss the potential adaption of human family-based association tests and quantitative transmission disequilibrium tests for use in crop species. The rapid technological advancement of next generation sequencing will enable sequencing of all parents in a planned crossing design, with subsequent imputation of genotypes for all segregating progeny. These technical advancements are easily adapted to mating designs routinely used by plant breeders. Thus, FBAM has the potential to be widely adopted for discovering alleles, common and rare, underlying complex traits in crop species.

Effects of Bos taurus autosome 9-located quantitative trait loci haplotypes on the disease phenotypes of dairy cows with experimentally induced Escherichia coli mastitis

Several quantitative trait loci (QTL) affecting mastitis incidence and mastitis-related traits such as somatic cell score exist in dairy cows. Previously, QTL haplotypes associated with susceptibility to Escherichia coli mastitis in Nordic Holstein-Friesian (HF) cows were identified on Bos taurus autosome 9. In the present study, we induced experimental E. coli mastitis in Danish HF cows to investigate the effect of 2 E. coli mastitis-associated QTL haplotypes on the cows' disease phenotypes and recovery in early lactation. Thirty-two cows were divided in 2 groups bearing haplotypes with either low (HL) or high (HH) susceptibility to E. coli. In addition, biopsies (liver and udder) were collected from half of the cows (n=16), resulting in a 2 × 2 factorial design, with haplotype being one factor (HL vs. HH) and biopsy being the other factor (biopsies vs. no biopsies). Each cow was inoculated with a low E. coli dose (20 to 40 cfu) in one front quarter at time 0 h. Liver biopsies were collected at -144, 12, 24, and 192 h; udder biopsies were collected at 24h and 192 h post-E. coli inoculation. The clinical parameters: feed intake, milk yield, body temperature, heart rate, respiration rate, rumen motility; and the paraclinical parameters: bacterial counts, somatic cell count (SCC), and milk amyloid A levels in milk; and white blood cell count, polymorphonuclear neutrophilic leukocyte (PMNL) count, and serum amyloid A levels in blood were recorded at different time points post-E. coli inoculation. Escherichia coli inoculation changed the clinical and paraclinical parameters in all cows except one that was not infected. Clinically, the HH group tended to have higher body temperature and heart rate than the HL group did. Paraclinically, the HL group had faster PMNL recruitment and SCC recovery than the HH group did. However, we also found interactions between the effects of haplotype and biopsy for body temperature, heart rate, and PMNL. In conclusion, when challenged with E. coli mastitis, HF cows with the specific Bos taurus autosome 9-located QTL haplotypes were associated with differences in leukocyte kinetics, with low-susceptibility cows having faster blood PMNL recruitment and SCC recovery and a tendency for a milder clinical response than the high-susceptibility cows did.

Statistical analysis of genomic data

In this chapter we describe methods for statistical analysis of GWAS data with the goal of quantifying evidence for genomic effects associated with trait variation, while avoiding spurious associations due to evidence not being well quantified or due to population structure.Single marker analysis and imputation are discussed in Sect. 1, and a Bayesian multi-locus analysis using the BayesQTLBIC R package (1, 2) is described in Sect. 2. The multi-locus analysis, applied in a genomic window, enables local inference of the QTL genetic architecture and is an alternative to imputation. Multi-locus analysis with BayesQTLBIC, including calculation of posterior probabilities for alternative models, posterior probabilities for number of QTL, marginal probabilities for markers, and Bayes factors for individual chromosomes, is demonstrated for simulated QTL data. Methods for correcting the population structure and the possible effects of population structure on power are discussed in Sect. 3. Section 4 considers analysis combining information from linkage and linkage disequilibrium when sampling from a pedigree. Section 5 considers combining information from two different studies-showing that data from an existing QTL mapping family can be profitably used in combination with an association study-prior odds are higher for candidate genes mapping into a QTL region in the QTL mapping family, and, optionally, the number of markers genotyped in an association study can be reduced. Examples using R and the R packages BayesQTLBIC, ncdf are given.

Multivariate whole genome average interval mapping: QTL analysis for multiple traits and/or environments

A major aim in some plant-based studies is the determination of quantitative trait loci (QTL) for multiple traits or across multiple environments. Understanding these QTL by trait or QTL by environment interactions can be of great value to the plant breeder. A whole genome approach for the analysis of QTL is presented for such multivariate applications. The approach is an extension of whole genome average interval mapping in which all intervals on a linkage map are included in the analysis simultaneously. A random effects working model is proposed for the multivariate (trait or environment) QTL effects for each interval, with a variance-covariance matrix linking the variates in a particular interval. The significance of the variance-covariance matrix for the QTL effects is tested and if significant, an outlier detection technique is used to select a putative QTL. This QTL by variate interaction is transferred to the fixed effects. The process is repeated until the variance-covariance matrix for QTL random effects is not significant; at this point all putative QTL have been selected. Unlinked markers can also be included in the analysis. A simulation study was conducted to examine the performance of the approach and demonstrated the multivariate approach results in increased power for detecting QTL in comparison to univariate methods. The approach is illustrated for data arising from experiments involving two doubled haploid populations. The first involves analysis of two wheat traits, α-amylase activity and height, while the second is concerned with a multi-environment trial for extensibility of flour dough. The method provides an approach for multi-trait and multi-environment QTL analysis in the presence of non-genetic sources of variation.

Polymorphisms of the ATP1A1 gene associated with mastitis in dairy cattle

Mastitis affects the concentrations of potassium and sodium in milk. Since sodium-potassium adenosine triphosphatase (Na(+), K(+)-ATPase) is critical for maintaining the homeostasis of these two ions, and is involved in cell apoptosis and pathogenesis, we presumed that polymorphism of the ATP1A1 gene, which encodes the bovine Na(+), K(+)-ATPase α1 subunit could be associated with mastitis. The ATP1A1 gene was analyzed in 320 Holstein cows using PCR low ionic strength single-strand conformation polymorphism (PCR-LIS-SSCP) and DNA sequencing methods. A C/A SNP was identified at nucleotide position -15,739 in exon 17 of the ATP1A1 gene, but it did not induce any change in amino acids. We examined a possible association of polymorphism of the ATP1A1 gene with somatic cell score and 305-day milk yields. Individuals with genotype CC in ATP1A1 had significantly lower somatic cell scores and 305-day milk yields than those with genotype CA. We also examined changes in Na(+), K(+)-ATPase activity of red cell membranes. The Na(+), K(+)-ATPase activity was significantly higher in dairy cows with genotype CC compared to the other two genotypes, and the Na(+), K(+)-ATPase activity of the resistant group was significantly higher than that of the susceptible group in dairy cows. We conclude that this polymorphism has potential as a marker for mastitis resistance in dairy cattle.

Gene prioritization for livestock diseases by data integration

Identifying causal genes that underlie complex traits such as susceptibility to disease is a primary aim of genetic and biomedical studies. Genetic mapping of quantitative trait loci (QTL) and gene expression profiling based on high-throughput technologies are common first approaches toward identifying associations between genes and traits; however, it is often difficult to assess whether the biological function of a putative candidate gene is consistent with a particular phenotype. Here, we have implemented a network-based disease gene prioritization approach for ranking genes associated with quantitative traits and diseases in livestock species. The approach uses ortholog mapping and integrates information on disease or trait phenotypes, gene-associated phenotypes, and protein-protein interactions. It was used for ranking all known genes present in the cattle genome for their potential roles in bovine mastitis. Gene-associated phenome profile and transcriptome profile in response to Escherichia coli infection in the mammary gland were integrated to make a global inference of bovine genes involved in mastitis. The top ranked genes were highly enriched for pathways and biological processes underlying inflammation and immune responses, which supports the validity of our approach for identifying genes that are relevant to animal health and disease. These gene-associated phenotypes were used for a local prioritization of candidate genes located in a QTL affecting the susceptibility to mastitis. Our study provides a general framework for prioritizing genes associated with various complex traits in different species. To our knowledge this is the first time that gene expression, ortholog mapping, protein interactions, and biomedical text data have been integrated systematically for ranking candidate genes in any livestock species.

Accuracy of multi-trait genomic selection using different methods

Background

Genomic selection has become a very important tool in animal genetics and is rapidly emerging in plant genetics. It holds the promise to be particularly beneficial to select for traits that are difficult or expensive to measure, such as traits that are measured in one environment and selected for in another environment. The objective of this paper was to develop three models that would permit multi-trait genomic selection by combining scarcely recorded traits with genetically correlated indicator traits, and to compare their performance to single-trait models, using simulated datasets.

Methods

Three (SNP) Single Nucleotide Polymorphism based models were used. Model G and BCπ0 assumed that contributed (co)variances of all SNP are equal. Model BSSVS sampled SNP effects from a distribution with large (or small) effects to model SNP that are (or not) associated with a quantitative trait locus. For reasons of comparison, model A including pedigree but not SNP information was fitted as well.

Results

In terms of accuracies for animals without phenotypes, the models generally ranked as follows: BSSVS > BCπ0 > G > > A. Using multi-trait SNP-based models, the accuracy for juvenile animals without any phenotypes increased up to 0.10. For animals with phenotypes on an indicator trait only, accuracy increased up to 0.03 and 0.14, for genetic correlations with the evaluated trait of 0.25 and 0.75, respectively.

Conclusions

When the indicator trait had a genetic correlation lower than 0.5 with the trait of interest in our simulated data, the accuracy was higher if genotypes rather than phenotypes were obtained for the indicator trait. However, when genetic correlations were higher than 0.5, using an indicator trait led to higher accuracies for selection candidates. For different combinations of traits, the level of genetic correlation below which genotyping selection candidates is more effective than obtaining phenotypes for an indicator trait, needs to be derived considering at least the heritabilities and the numbers of animals recorded for the traits involved.

A two-step method for estimating QTL effects and positions in multi-marker analysis

Quantitative trait is always controlled by multiple latent genetic loci, and genetic markers have been used to map quantitative trait loci (QTLs) auxiliarily. The method of multiple interval mapping (MIM) provides an appropriate way for mapping QTL using genetic makers. However, the computation in the MIM seems infeasible for a large number of marker intervals. Nowadays, the Dantzig selector (DS) method proves to be a more efficient method to estimate model effects in a linear model when the number of parameters is (much) larger than the sample size, which has not been applied to genetic mapping for QTL. In this paper, we developed a two-step method for mapping QTL based on the MIM, and we also illustrate the feasibility of adopting the DS to estimate marker or QTL effects. Simulation results showed that the proposed method performed satisfactorily well by comparisons with the existing MIM method, and the analysis to real data set also tested the practicability and efficiency of the DS method in genetic mapping.

Overview of techniques to account for confounding due to population stratification and cryptic relatedness in genomic data association analyses

Population-based genomic association analyses are more powerful than within-family analyses. However, population stratification (unknown or ignored origin of individuals from multiple source populations) and cryptic relatedness (unknown or ignored covariance between individuals because of their relatedness) are confounding factors in population-based genomic association analyses, which inflate the false-positive rate. As a consequence, false association signals may arise in genomic data association analyses for reasons other than true association between the tested genomic factor (marker genotype, gene or protein expression) and the study phenotype. It is therefore important to correct or account for these confounders in population-based genomic data association analyses. The common correction techniques for population stratification and cryptic relatedness problems are presented here in the phenotype-marker association analysis context, and comments on their suitability for other types of genomic association analyses (for example, phenotype-expression association) are also provided. Even though many of these techniques have originally been developed in the context of human genetics, most of them are also applicable to model organisms and breeding populations.

Quantitative trait loci analysis of swine meat quality traits

A QTL study was performed in large half-sib families to characterize the genetic background of variation in pork quality traits as well as to examine the possibilities of including QTL in a marker-assisted selection scheme. The quality traits included ultimate pH in LM and the semimembranosus, drip loss, and the Minolta color measurements L*, a*, and b* representing meat lightness, redness, and yellowness, respectively. The families consist of 3,883 progenies of 12 Duroc boars that were evaluated to identify the QTL. The linkage map consists of 462 SNP markers on 18 porcine autosomes. Quantitative trait loci were mapped using a linear mixed model with fixed factors (sire, sex, herd, month, sow age) and random factors (polygenic effect, QTL effects, and litter). Chromosome-wide and genome-wide significance thresholds were determined by Peipho's approach, and 95% Bayes credibility intervals were estimated from a posterior distribution of the QTL position. In total, 31 QTL for the 6 meat quality traits were found to be significant at the 5% chromosome-wide level, among which 11 QTL were significant at the 5% genome-wide level and 5 of these were significant at the 0.1% genome-wide level. Segregation of the identified QTL in different families was also investigated. Most of the identified QTL segregated in 1 or 2 families. For the QTL affecting ultimate pH in LM and semimembranosus and L* and b* value on SSC6, the positions of the QTL and the shapes of the likelihood curves were almost the same. In addition, a strong correlation of the estimated effects of these QTL was found between the 4 traits, indicating that the same genes control these traits. A similar pattern was seen on SSC15 for the QTL affecting ultimate pH in the 2 muscles and drip loss. The results from this study will be helpful for fine mapping and identifying genes affecting meat quality traits, and tightly linked markers may be incorporated into marker-assisted selection programs.

Detection of multiple quantitative trait loci and their pleiotropic effects in outbred pig populations

BACKGROUND

Simultaneous detection of multiple QTLs (quantitative trait loci) may allow more accurate estimation of genetic effects. We have analyzed outbred commercial pig populations with different single and multiple models to clarify their genetic properties and in addition, we have investigated pleiotropy among growth and obesity traits based on allelic correlation within a gamete.

METHODS

Three closed populations, (A) 427 individuals from a Yorkshire and Large White synthetic breed, (B) 547 Large White individuals and (C) 531 Large White individuals, were analyzed using a variance component method with one-QTL and two-QTL models. Six markers on chromosome 4 and five to seven markers on chromosome 7 were used.

RESULTS

Population A displayed a high test statistic for the fat trait when applying the two-QTL model with two positions on two chromosomes. The estimated heritabilities for polygenic effects and for the first and second QTL were 19%, 17% and 21%, respectively. The high correlation of the estimated allelic effect on the same gamete and QTL test statistics suggested that the two separate QTL which were detected on different chromosomes both have pleiotropic effects on the two fat traits. Analysis of population B using the one-QTL model for three fat traits found a similar peak position on chromosome 7. Allelic effects of three fat traits from the same gamete were highly correlated suggesting the presence of a pleiotropic QTL. In population C, three growth traits also displayed similar peak positions on chromosome 7 and allelic effects from the same gamete were correlated.

CONCLUSION

Detection of the second QTL in a model reduced the polygenic heritability and should improve accuracy of estimated heritabilities for both QTLs.

Bayesian quantitative trait loci mapping for multiple traits

Most quantitative trait loci (QTL) mapping experiments typically collect phenotypic data on multiple correlated complex traits. However, there is a lack of a comprehensive genomewide mapping strategy for correlated traits in the literature. We develop Bayesian multiple-QTL mapping methods for correlated continuous traits using two multivariate models: one that assumes the same genetic model for all traits, the traditional multivariate model, and the other known as the seemingly unrelated regression (SUR) model that allows different genetic models for different traits. We develop computationally efficient Markov chain Monte Carlo (MCMC) algorithms for performing joint analysis. We conduct extensive simulation studies to assess the performance of the proposed methods and to compare with the conventional single-trait model. Our methods have been implemented in the freely available package R/qtlbim (http://www.qtlbim.org), which greatly facilitates the general usage of the Bayesian methodology for unraveling the genetic architecture of complex traits.

Trait-trait dynamic interaction: 2D-trait eQTL mapping for genetic variation study

Background

Many studies have shown that the abundance level of gene expression is heritable. Analogous to the traditional genetic study, most researchers treat the expression of one gene as a quantitative trait and map it to expression quantitative trait loci (eQTL). This is 1D-trait mapping. 1D-trait mapping ignores the trait-trait interaction completely, which is a major shortcoming.

Results

To overcome this limitation, we study the expression of a pair of genes and treat the variation in their co-expression pattern as a two dimensional quantitative trait. We develop a method to find gene pairs, whose co-expression patterns, including both signs and strengths, are mediated by genetic variations and map these 2D-traits to the corresponding genetic loci. We report several applications by combining 1D-trait mapping with 2D-trait mapping, including the contribution of genetic variations to the perturbations in the regulatory mechanisms of yeast metabolic pathways.

Conclusion

Our approach of 2D-trait mapping provides a novel and effective way to connect the genetic variation with higher order biological modules via gene expression profiles.

Fine-mapping QTL for mastitis resistance on BTA9 in three Nordic red cattle breeds

A QTL affecting clinical mastitis and/or somatic cell score (SCS) has been reported previously on chromosome 9 from studies in 16 families from the Swedish Red and White (SRB), Finnish Ayrshire (FA) and Danish Red (DR) breeds. In order to refine the QTL location, 67 markers were genotyped over the whole chromosome in the 16 original families and 18 additional half-sib families. This enabled linkage disequilibrium information to be used in the analysis. Data were analysed by an approach that combines information from linkage and linkage disequilibrium, which allowed the QTL affecting clinical mastitis to be mapped to a small interval (<1 cM) between the markers BM4208 and INRA084. This QTL showed a pleiotropic effect on SCS in the DR and SRB breeds. Haplotypes associated with variations in mastitis resistance were identified. The haplotypes were predictive in the general population and can be used in marker-assisted selection. Pleiotropic effects of the mastitis QTL were studied for three milk production traits and eight udder conformation traits. This QTL was also associated with yield traits in DR but not in FA or SRB. No QTL were found for udder conformation traits on chromosome 9.

Mapping, fine mapping, and molecular dissection of quantitative trait Loci in domestic animals

Artificial selection has created myriad breeds of domestic animals, each characterized by unique phenotypes pertaining to behavior, morphology, physiology, and disease. Most domestic animal populations share features with isolated founder populations, making them well suited for positional cloning. Genome sequences are now available for most domestic species, and with them a panoply of tools including high-density single-nucleotide polymorphism panels. As a result, domestic animal populations are becoming invaluable resources for studying the molecular architecture of complex traits and of adaptation. Here we review recent progress and issues in the positional identification of genes underlying complex traits in domestic animals. As many phenotypes studied in animals are quantitative, we focus on mapping, fine mapping, and cloning of quantitative trait loci.

Estimating genealogies from linked marker data: a Bayesian approach

Background

Answers to several fundamental questions in statistical genetics would ideally require knowledge of the ancestral pedigree and of the gene flow therein. A few examples of such questions are haplotype estimation, relatedness and relationship estimation, gene mapping by combining pedigree and linkage disequilibrium information, and estimation of population structure.

Results

We present a probabilistic method for genealogy reconstruction. Starting with a group of genotyped individuals from some population isolate, we explore the state space of their possible ancestral histories under our Bayesian model by using Markov chain Monte Carlo (MCMC) sampling techniques. The main contribution of our work is the development of sampling algorithms in the resulting vast state space with highly dependent variables. The main drawback is the computational complexity that limits the time horizon within which explicit reconstructions can be carried out in practice.

Conclusion

The estimates for IBD (identity-by-descent) and haplotype distributions are tested in several settings using simulated data. The results appear to be promising for a further development of the method.

Fine mapping of a quantitative trait locus on chromosome 9 affecting non-return rate in Swedish dairy cattle

We previously mapped a quantitative trait locus (QTL) affecting the trait non-return rate at 56 days in heifers to bovine chromosome 9. The purpose of this study was to confirm and refine the position of the QTL by using a denser marker map and fine mapping methods. Five families that previously showed segregation for the QTL were included in the study. The mapping population consisted of 139 bulls in a granddaughter design. All bulls were genotyped for 25 microsatellite markers surrounding the QTL on chromosome 9. We also analysed the correlated trait number of inseminations per service period in heifers. Both traits describe the heifer's ability to become pregnant after insemination. Linkage analysis, linkage disequilibrium and combined linkage and linkage disequilibrium analysis were used to analyse the data. Analysis of the families jointly by linkage analysis resulted in a significant but broad QTL peak for non-return rate. Results from the combined analysis gave a sharp QTL peak with a well-defined maximum in between markers BMS1724 and BM7209, at the same position as where the highest peak from the linkage disequilibrium analysis was found. One of the sire families segregated clearly at this position and the difference in effects between the two sire haplotypes was 2.9 percentage units in non-return rate. No significant results were found for the number of inseminations in the combined analysis.

Bayesian mapping of quantitative trait loci for multiple complex traits with the use of variance components

Complex traits important for humans are often correlated phenotypically and genetically. Joint mapping of quantitative-trait loci (QTLs) for multiple correlated traits plays an important role in unraveling the genetic architecture of complex traits. Compared with single-trait analysis, joint mapping addresses more questions and has advantages for power of QTL detection and precision of parameter estimation. Some statistical methods have been developed to map QTLs underlying multiple traits, most of which are based on maximum-likelihood methods. We develop here a multivariate version of the Bayes methodology for joint mapping of QTLs, using the Markov chain-Monte Carlo (MCMC) algorithm. We adopt a variance-components method to model complex traits in outbred populations (e.g., humans). The method is robust, can deal with an arbitrary number of alleles with arbitrary patterns of gene actions (such as additive and dominant), and allows for multiple phenotype data of various types in the joint analysis (e.g., multiple continuous traits and mixtures of continuous traits and discrete traits). Under a Bayesian framework, parameters--including the number of QTLs--are estimated on the basis of their marginal posterior samples, which are generated through two samplers, the Gibbs sampler and the reversible-jump MCMC. In addition, we calculate the Bayes factor related to each identified QTL, to test coincident linkage versus pleiotropy. The performance of our method is evaluated in simulations with full-sib families. The results show that our proposed Bayesian joint-mapping method performs well for mapping multiple QTLs in situations of either bivariate continuous traits or mixed data types. Compared with the analysis for each trait separately, Bayesian joint mapping improves statistical power, provides stronger evidence of QTL detection, and increases precision in estimation of parameter and QTL position. We also applied the proposed method to a set of real data and detected a coincident linkage responsible for determining bone mineral density and areal bone size of wrist in humans.

Simultaneous fine mapping of multiple closely linked quantitative trait Loci using combined linkage disequilibrium and linkage with a general pedigree

Within a small region (e.g., <10 cM), there can be multiple quantitative trait loci (QTL) underlying phenotypes of a trait. Simultaneous fine mapping of closely linked QTL needs an efficient tool to remove confounded shade effects among QTL within such a small region. We propose a variance component method using combined linkage disequilibrium (LD) and linkage information and a reversible jump Markov chain Monte Carlo (MCMC) sampling for model selection. QTL identity-by-descent (IBD) coefficients between individuals are estimated by a hybrid MCMC combining the random walk and the meiosis Gibbs sampler. These coefficients are used in a mixed linear model and an empirical Bayesian procedure combines residual maximum likelihood (REML) to estimate QTL effects and a reversible jump MCMC that samples the number of QTL and the posterior QTL intensities across the tested region. Note that two MCMC processes are used, i.e., an (internal) MCMC for IBD estimation and an (external) MCMC for model selection. In a simulation study, the use of the multiple-QTL model clearly removes the shade effects between three closely linked QTL located at 1.125, 3.875, and 7.875 cM across the region of 10 cM, using 40 markers at 0.25-cM intervals. It is shown that the use of combined LD and linkage information gives much more useful information compared to using linkage information alone for both single- and multiple-QTL analyses. When using a lower marker density (11 markers at 1-cM intervals), the signal of the second QTL can disappear. Extreme values of past effective size (resulting in extreme levels of LD) decrease the mapping accuracy.

Bayesian reanalysis of a quantitative trait locus accounting for multiple environments by scaling in broilers1

A Bayesian method was developed to handle QTL analyses of multiple experimental data of outbred populations with heterogeneity of variance between sexes for all random effects. The method employed a scaled reduced animal model with random polygenic and QTL allelic effects. A parsimonious model specification was applied by choosing assumptions regarding the covariance structure to limit the number of parameters to estimate. Markov chain Monte Carlo algorithms were applied to obtain marginal posterior densities. Simulation demonstrated that joint analysis of multiple environments is more powerful than separate single trait analyses of each environment. Measurements on broiler BW obtained from 2 experiments concerning growth efficiency and carcass traits were used to illustrate the method. The population consisted of 10 full-sib families from a cross between 2 broiler lines. Microsatellite genotypes were determined on generations 1 and 2, and phenotypes were collected on groups of generation 3 animals. The model included a polygenic correlation, which had a posterior mean of 0.70 in the analyses. The reanalysis agreed on the presence of a QTL in marker bracket MCW0058-LEI0071 accounting for 34% of the genetic variation in males and 24% in females in the growth efficiency experiment. In the carcass experiment, this QTL accounted for 19% of the genetic variation in males and 6% in females.

Statistical methods for expression quantitative trait loci (eQTL) mapping

Traditional genetic mapping has largely focused on the identification of loci affecting one, or at most a few, complex traits. Microarrays allow for measurement of thousands of gene expression abundances, themselves complex traits, and a number of recent investigations have considered these measurements as phenotypes in mapping studies. Combining traditional quantitative trait loci (QTL) mapping methods with microarray data is a powerful approach with demonstrated utility in a number of recent biological investigations. These expression quantitative trait loci (eQTL) studies are similar to traditional QTL studies, as a main goal is to identify the genomic locations to which the expression traits are linked. However, eQTL studies probe thousands of expression transcripts; and as a result, standard multi-trait QTL mapping methods, designed to handle at most tens of traits, do not directly apply. One possible approach is to use single-trait QTL mapping methods to analyze each transcript separately. This leads to an increased number of false discoveries, as corrections for multiple tests across transcripts are not made. Similarly, the repeated application, at each marker, of methods for identifying differentially expressed transcripts suffers from multiple tests across markers. Here, we demonstrate the deficiencies of these approaches and propose a mixture over markers (MOM) model that shares information across both markers and transcripts. The utility of all methods is evaluated using simulated data as well as data from an F(2) mouse cross in a study of diabetes. Results from simulation studies indicate that the MOM model is best at controlling false discoveries, without sacrificing power. The MOM model is also the only one capable of finding two genome regions previously shown to be involved in diabetes.

Mapping density response in maize: a direct approach for testing genotype and treatment interactions

Maize yield improvement has been strongly linked to improvements in stress tolerance, particularly to increased interplant competition. As a result, modern hybrids are able to produce kernels at high plant population densities. Identification of the genetic factors responsible for density response in maize requires direct testing of interactions between genetic effects and density and evaluation of that response in multiple traits. In this article we take a broad view of the problem and use a general approach based upon mixed models to analyze data from eight segmental inbred lines in a B73 background and their crosses to the unrelated parent Mo17 (hybrids). We directly test for the interaction between treatment effects and genetic effects instead of the commonly used overlaying of results on a common map. Additionally, we demonstrate one way to handle heteroscedasticity of variances common in stress responses. We find that some SILs are consistently different from the recurrent parent regardless of the density, while others differ from the recurrent parent in one density level but not in the other. Thus, we find positive evidence for both main effects and interaction between genetic loci and density in cases where the approach of overlapping results fails to find significant results. Furthermore, our study clearly identifies segments that respond differently to density depending upon the inbreeding level (inbred/hybrid).

Application of a new IBD-based QTL mapping method to common wheat breeding population: analysis of kernel hardness and dough strength

Mapping quantitative trait loci (QTL) in plants is usually conducted using a population derived from a cross between two inbred lines. The power of such QTL detection and the estimation of the effects highly depend on the choice of the two parental lines. Thus, the QTL found represent only a small part of the genetic architecture and can be of limited economical interest in marker-assisted selection. On the other hand, applied breeding programmes evaluate large numbers of progeny derived from multiple-related crosses for a wide range of agronomic traits. It is assumed that the development of statistical techniques to deal with pedigrees in existing plant populations would increase the relevance and cost effectiveness of QTL mapping in a breeding context. In this study, we applied a two-step IBD-based-variance component method to a real wheat breeding population, composed of 374 F6 lines derived from 80 different parents. Two bread wheat quality related traits were analysed by the method. Results obtained show very close agreement with major genes and QTL already known for those two traits. With this new QTL mapping strategy, inferences about QTL can be drawn across the breeding programme rather than being limited to the sample of progeny from a single cross and thus the use of the detected QTL in assisting breeding would be facilitated.

Quantitative trait loci (QTL) detection in multicross inbred designs: recovering QTL identical-by-descent status information from marker data

Mapping quantitative trait loci in plants is usually conducted using a population derived from a cross between two inbred lines. The power of such QTL detection and the parameter estimates depend largely on the choice of the two parental lines. Thus, the QTL detected in such populations represent only a small part of the genetic architecture of the trait. In addition, the effects of only two alleles are characterized, which is of limited interest to the breeder, while common pedigree breeding material remains unexploited for QTL mapping. In this study, we extend QTL mapping methodology to a generalized framework, based on a two-step IBD variance component approach, applicable to any type of breeding population obtained from inbred parents. We then investigate with simulated data mimicking conventional breeding programs the influence of different estimates of the IBD values on the power of QTL detection. The proposed method would provide an alternative to the development of specifically designed recombinant populations, by utilizing the genetic variation actually managed by plant breeders. The use of these detected QTL in assisting breeding would thus be facilitated.

Linkage disequilibrium and association studies in higher plants: present status and future prospects

During the last two decades, DNA-based molecular markers have been extensively utilized for a variety of studies in both plant and animal systems. One of the major uses of these markers is the construction of genome-wide molecular maps and the genetic analysis of simple and complex traits. However, these studies are generally based on linkage analysis in mapping populations, thus placing serious limitations in using molecular markers for genetic analysis in a variety of plant systems. Therefore, alternative approaches have been suggested, and one of these approaches makes use of linkage disequilibrium (LD)-based association analysis. Although this approach of association analysis has already been used for studies on genetics of complex traits (including different diseases) in humans, its use in plants has just started. In the present review, we first define and distinguish between LD and association mapping, and then briefly describe various measures of LD and the two methods of its depiction. We then give a list of different factors that affect LD without discussing them, and also discuss the current issues of LD research in plants. Later, we also describe the various uses of LD in plant genomics research and summarize the present status of LD research in different plant genomes. In the end, we discuss briefly the future prospects of LD research in plants, and give a list of softwares that are useful in LD research, which is available as electronic supplementary material (ESM).

Mapping genome-genome epistasis: a high-dimensional model

MOTIVATION

The proper development of any organ or tissue requires the coordinated expression of its underlying genes that can be located on different genomes present in an organism. For instance, each step in the development of seed for a higher plant is the consequence of gene interactions from the maternal, embryo and endosperm genomes.

RESULTS

We present a multivariate statistical model for mapping quantitative trait loci (QTL) by incorporating two important aspects of seed development in plants-QTL interactions derived from different genomes, the maternal, embryo and endosperm, and genetic correlations among phenotypic traits expressed in different genome-specific tissues. This model, which has a high dimensionality, is constructed within the maximum-likelihood context based on a finite mixture model. The implementation of the expectation-maximization algorithm allows for the efficient estimation of QTL positions, their action and interaction effects and pleiotropic effects. The application of this high-dimensional model to a real rice dataset has validated its usefulness.

CONCLUSIONS

Our model was derived for self-pollinated plants, but it can be extended to cross-pollinated plants and to animals. With the burgeoning of genetic and genomic data, this high-dimensional model will have many implications for agricultural and evolutionary genetic research.

AVAILABILITY

A package of software will be provided from the corresponding author upon request.

Whole genome scan to detect chromosomal regions affecting multiple traits in dairy cattle

Chromosomal regions affecting multiple traits (multiple trait quantitative trait regions or MQR) in dairy cattle were detected using a method based on results from single trait analyses to detect quantitative trait loci (QTL). The covariance between contrasts for different traits in single trait regression analysis was computed. A chromosomal region was considered an MQR when the observed covariance between contrasts deviated from the expected covariance under the null hypothesis of no pleiotropy or close linkage. The expected covariance and the confidence interval for the expected covariance were determined by permutation of the data. Four categories of traits were analyzed: production (5 traits), udder conformation (6 traits), udder health (2 traits), and fertility (2 traits). The analysis of a granddaughter design involving 833 sons of 20 grandsires resulted in 59 MQR (alpha = 0.01, chromosomewise). Fifteen MQR were found on Bos taurus autosome (BTA) 14. Four or more MQR were found on BTA 6, 13, 19, 22, 23, and 25. Eight MQR involving udder conformation and udder health and 4 MQR involving production traits and udder health were found. Five MQR were identified for combinations of fertility and udder conformation traits, and another 5 MQR were identified for combinations of fertility and production traits. For 22 MQR, the difference between the correlation attributable to the MQR and the overall genetic correlation was >0.60. Although the false discovery rate was relatively high (0.52), it was considered important to present these results to assess potential consequences of using these MQR for marker-assisted selection.

Estimation of Quantitative Trait Loci Parameters for Milk Production Traits in German Holstein Dairy Cattle Population

The main objective of this study was to estimate the proportion of total genetic variance attributed to a quantitative trait locus (QTL) on Bos taurus autosome 6 (BTA6) for milk production traits in the German Holstein dairy cattle population. The analyzed chromosomal region on BTA6 spanned approximately 70 cM, and contained 6 microsatellite markers. Milk production data were obtained from routine genetic evaluation for 4500 genotyped German Holstein bulls. Technical aspects related to the estimation of model parameters for a large data set from routine genotype recording were outlined. A fixed QTL model and a random QTL model were introduced to incorporate marker information into parameter estimation and genetic evaluation. Estimated QTL variances, expressed as the ratio of QTL to polygenic variances, were 0.04, 0.03, and 0.07 for milk yield; 0.06, 0.08, and 0.14 for fat yield; and 0.04, 0.04, and 0.11 for protein yield, in the first 3 parities, respectively. The estimated QTL positions, expressed as distances from the leftmost marker DIK82, were 18, 31, and 17 cM for milk yield; 25, 17, and 9 cM for fat yield; and 16, 30, and 17 cM for protein yield in the 3 respective parities. Because the data for the parameter estimation well represented the current population of active German Holstein bulls, the QTL parameter estimates have been used in routine marker-assisted genetic evaluation for German Holsteins.

Bayesian association-based fine mapping in small chromosomal segments

A Bayesian method for fine mapping is presented, which deals with multiallelic markers (with two or more alleles), unknown phase, missing data, multiple causal variants, and both continuous and binary phenotypes. We consider small chromosomal segments spanned by a dense set of closely linked markers and putative genes only at marker points. In the phenotypic model, locus-specific indicator variables are used to control inclusion in or exclusion from marker contributions. To account for covariance between consecutive loci and to control fluctuations in association signals along a candidate region we introduce a joint prior for the indicators that depends on genetic or physical map distances. The potential of the method, including posterior estimation of trait-associated loci, their effects, linkage disequilibrium pattern due to close linkage of loci, and the age of a causal variant (time to most recent common ancestor), is illustrated with the well-known cystic fibrosis and Friedreich ataxia data sets by assuming that haplotypes were not available. In addition, simulation analysis with large genetic distances is shown. Estimation of model parameters is based on Markov chain Monte Carlo (MCMC) sampling and is implemented using WinBUGS. The model specification code is freely available for research purposes from http://www.rni.helsinki.fi/~mjs/.

Derivation of a Bayes factor to distinguish between linked or pleiotropic quantitative trait loci

A simple procedure to calculate the Bayes factor between linked and pleiotropic QTL models is presented. The Bayes factor is calculated from the marginal prior and posterior densities of the locations of the QTL under a linkage and a pleiotropy model. The procedure is computed with a Gibbs sampler, and it can be easily applied to any model including the location of the QTL as a variable. The procedure was compared with a multivariate least-squares method. The proposed procedure showed better results in terms of power of detection of linkage when low information is available. As information increases, the performance of both procedures becomes similar. An example using data provided by an Iberian by Landrace pig intercross is presented. The results showed that three different QTL segregate in SSC6: a pleiotropic QTL affects myristic, palmitic, and eicosadienoic fatty acids; another pleiotropic QTL affects palmitoleic, stearic, and vaccenic fatty acids; and a third QTL affects the percentage of linoleic acid. In the example, the Bayes factor approach was more powerful than the multivariate least-squares approach.

Maize selection passes the century mark: a unique resource for 21st century genomics

The Illinois Long-Term Selection Experiment for grain protein and oil concentration in maize (Zea mays) is the longest continuous genetics experiment in higher plants. A total of 103 cycles of selection have produced nine related populations that exhibit phenotypic extremes for grain composition and a host of correlated traits. The use of functional genomics tools in this unique genetic resource provides exciting opportunities not only to discover the genes that contribute to phenotypic differences but also to investigate issues such as the response of plant genomes to artificial selection, the genetic architecture of quantitative traits and the source of continued genetic variation within domesticated crop genomes.

Derivation of a Bayes Factor to Distinguish Between Linked or Pleiotropic Quantitative Trait Loci

A simple procedure to calculate the Bayes factor between linked and pleiotropic QTL models is presented. The Bayes factor is calculated from the marginal prior and posterior densities of the locations of the QTL under a linkage and a pleiotropy model. The procedure is computed with a Gibbs sampler, and it can be easily applied to any model including the location of the QTL as a variable. The procedure was compared with a multivariate least-squares method. The proposed procedure showed better results in terms of power of detection of linkage when low information is available. As information increases, the performance of both procedures becomes similar. An example using data provided by an Iberian by Landrace pig intercross is presented. The results showed that three different QTL segregate in SSC6: a pleiotropic QTL affects myristic, palmitic, and eicosadienoic fatty acids; another pleiotropic QTL affects palmitoleic, stearic, and vaccenic fatty acids; and a third QTL affects the percentage of linoleic acid. In the example, the Bayes factor approach was more powerful than the multivariate least-squares approach.