On locating multiple interacting quantitative trait loci in intercross designs

Genetic Bases of Complex Traits: From Quantitative Trait Loci to Prediction

Conceived as a general introduction to the book, this chapter is a reminder of the core concepts of genetic mapping and molecular marker-based prediction. It provides an overview of the principles and the evolution of methods for mapping the variation of complex traits, and methods for QTL-based prediction of human disease risk and animal and plant breeding value. The principles of linkage-based and linkage disequilibrium-based QTL mapping methods are described in the context of the simplest, single-marker, methods. Methodological evolutions are analysed in relation with their ability to account for the complexity of the genotype-phenotype relations. Main characteristics of the genetic architecture of complex traits, drawn from QTL mapping works using large populations of unrelated individuals, are presented. Methods combining marker-QTL association data into polygenic risk score that captures part of an individual's susceptibility to complex diseases are reviewed. Principles of best linear mixed model-based prediction of breeding value in animal- and plant-breeding programs using phenotypic and pedigree data, are summarized and methods for moving from BLUP to marker-QTL BLUP are presented. Factors influencing the additional genetic progress achieved by using molecular data and rules for their optimization are discussed.

Genetic architecture of male fertility restoration of Triticum timopheevii cytoplasm and fine-mapping of the major restorer locus Rf3 on chromosome 1B

Restoration of fertility in the cytoplasmic male sterility-inducing Triticum timopheevii cytoplasm can be achieved with the major restorer locus Rf3 located on chromosome 1B, but is also dependent on modifier loci. Hybrid breeding relies on a hybrid mechanism enabling a cost-efficient hybrid seed production. In wheat and triticale, cytoplasmic male sterility based on the T. timopheevii cytoplasm is commonly used, and the aim of this study was to dissect the genetic architecture underlying fertility restoration. Our study was based on two segregating F₂ triticale populations with 313 and 188 individuals that share a common female parent and have two different lines with high fertility restoration ability as male parents. The plants were cloned to enable replicated assessments of their phenotype and fertility restoration was evaluated based on seed set or staining for pollen fertility. The traits showed high heritabilities but their distributions differed between the two populations. In one population, a quarter of the lines were sterile, conforming to a 3:1 segregation ratio. QTL mapping identified two and three QTL in these populations, with the major QTL being detected on chromosome 1B. This QTL was collinear in both populations and likely corresponds to Rf3. We found that Rf3 explained approximately 30 and 50% of the genotypic variance, has a dominant mode of inheritance, and that the female parent lacks this locus, probably due to a 1B.1R translocation. Taken together, Rf3 is a major restorer locus that enables fertility restoration of the T. timopheevii cytoplasm, but additional modifier loci are needed for full restoration of male fertility. Consequently, Rf3 holds great potential for hybrid wheat and triticale breeding, but other loci must also be considered, either through marker-assisted or phenotypic selection.

Genetic architecture of fusarium head blight resistance in four winter triticale populations

Fusarium head blight (FHB) is a devastating disease that causes significant reductions in yield and quality in wheat, rye, and triticale. In triticale, knowledge of the genetic architecture of FHB resistance is missing but essential due to modern breeding requirements. In our study, four doubled-haploid triticale populations (N=120 to 200) were evaluated for resistance to FHB caused by artificial inoculation with Fusarium culmorum in four environments. DArT markers were used to genotype triticale populations. Seventeen quantitative trait loci (QTL) for FHB resistance were detected across all populations; six of them were derived from rye genome and located on chromosomes 4R, 5R, and 7R, which are here reported for the first time. The total cross-validated ratio of the explained phenotypic variance for all detected QTL in each population was 41 to 68%. In all, 17 QTL for plant height and 18 QTL for heading stage were also detected across all populations; 3 and 5 of them, respectively, were overlapping with QTL for FHB. In conclusion, FHB resistance in triticale is caused by a multitude of QTL, and pyramiding them contributes to higher resistance.

Effect of a rye dwarfing gene on plant height, heading stage, and Fusarium head blight in triticale (×Triticosecale Wittmack)

The rye-derived dwarfing gene Ddw1 on chromosome 5R acts in triticale in considerably reducing plant height, increasing FHB severity and delaying heading stage. Triticale, an amphiploid hybrid between durum wheat and rye, is an European cereal mainly grown in Germany, France, Poland, and Belarus for feeding purposes. Dwarfing genes might further improve the genetic potential of triticale concerning lodging resistance and yield. However, they might have pleiotropic effects on other, agronomically important traits including Fusarium head blight. Therefore, we analyzed a population of 199 doubled haploid (DH) lines of the cross HeTi117-06 × Pigmej for plant height, heading stage, and FHB severity across 2 locations and 2 years. The most prominent QTL was detected on chromosome 5R explaining 48, 77, and 71 % of genotypic variation for FHB severity, plant height, and heading stage, respectively. The frequency of recovery in cross validation was ≥90 % for all three traits. Because the markers that detect dwarfing gene Ddw1 in rye are also in our population the most closely linked markers, we assume that this major QTL resembles Ddw1. For FHB severity two, for plant height three, and for heading stage five additional QTL were detected. Caused by the considerable genetic variation for heading stage and FHB severity within the progeny with the dwarfing allele, short-strawed, early heading and FHB-resistant lines can be developed when population size is large enough.

Fence Methods for Backcross Experiments

Model search strategies play an important role in finding simultaneous susceptibility genes that are associated with a trait. More particularly, model selection via the information criteria, such as the BIC with modifications, have received considerable attention in quantitative trait loci (QTL) mapping. However, such modifications often depend upon several factors, such as sample size, prior distribution, and the type of experiment, e.g., backcross, intercross. These changes make it difficult to generalize the methods to all cases. The fence method avoids such limitations with a unified approach, and hence can be used more broadly. In this paper, this method is studied in the case of backcross experiments throughout a series of simulation studies. The results are compared with those of the modified BIC method as well as some of the most popular shrinkage methods for model selection.

Accession-specific modifiers act with ZWILLE/ARGONAUTE10 to maintain shoot meristem stem cells during embryogenesis in Arabidopsis

BACKGROUND

Stem cells located in the centre of the shoot apical meristem are required for the repetitive formation of new organs such as leaves, branches and flowers. In Arabidopsis thaliana, the ZWILLE/PINHEAD/AGO10 (ZLL) gene encodes a member of the ARGONAUTE (AGO) protein family and is required to maintain shoot meristem stem cells during embryogenesis. In the Landsberg erecta (Ler) acession, ZLL is essential for stem cell maintenance, whereas in the Columbia (Col) accession its requirement appears masked by genetic modifiers. The genetic basis for this variation has remained elusive.

RESULTS

To understand the impact of natural variation on shoot stem cell maintenance, we analysed 28 wild-type Arabidopsis accessions from around the world and show that ZLL function is essential for stem cell maintenance in accessions mainly originating from Germany, but is dispensable for accessions from other regions. Quantitative Trait Loci (QTL) mapping using Ler/Col recombinant inbred lines indicated that at least five genomic regions, referred to as FLETSCHE (FHE) 1-5, modify ZLL function in stem cell maintenance. Characterisation of Col zll near isogenic lines confirmed that the major QTL, FHE2, is preferentially maintained as a Ler allele in seedlings lacking stem cells, suggesting that this region harbours an important modifier of ZLL function. Comparison of torpedo-stage embryo expression profiles to QTL map data revealed candidate FHE genes, including the Arabidopsis Cyclophilin-40 homologue SQUINT (SQN), and functional studies revealed a previously uncharacterised role for SQN in stem cell regulation.

CONCLUSIONS

Multiple genetic modifiers from different Arabidopsis accessions influence the role of ZLL in embryonic stem cell maintenance. Of the five FHE loci modifying stem cell maintenance in Ler-0 and Col-0, FHE2 was the most prominent and was tightly linked to the SQN gene, which encodes a cofactor that supports AGO1 activity. SQN shows variable embryonic expression levels between accessions and altered ZLL-dependency in transgenic assays, confirming a key role in stem cell maintenance. Reduced SQN expression levels in Col-0 correlate with transposon insertions adjoining the transcriptional start site, which may contribute to stem cell maintenance in other ZLL-independent accessions.

High-density genotyping: an overkill for QTL mapping? Lessons learned from a case study in maize and simulations

High-density genotyping is extensively exploited in genome-wide association mapping studies and genomic selection in maize. By contrast, linkage mapping studies were until now mostly based on low-density genetic maps and theoretical results suggested this to be sufficient. This raises the question, if an increase in marker density would be an overkill for linkage mapping in biparental populations, or if important QTL mapping parameters would benefit from it. In this study, we addressed this question using experimental data and a simulation based on linkage maps with marker densities of 1, 2, and 5 cM. QTL mapping was performed for six diverse traits in a biparental population with 204 doubled haploid maize lines and in a simulation study with varying QTL effects and closely linked QTL for different population sizes. Our results showed that high-density maps neither improved the QTL detection power nor the predictive power for the proportion of explained genotypic variance. By contrast, the precision of QTL localization, the precision of effect estimates of detected QTL, especially for small and medium sized QTL, as well as the power to resolve closely linked QTL profited from an increase in marker density from 5 to 1 cM. In conclusion, the higher costs for high-density genotyping are compensated for by more precise estimates of parameters relevant for knowledge-based breeding, thus making an increase in marker density for linkage mapping attractive.

Detection of epistatic interactions in association mapping populations: an example from tetraploid potato

Epistatic interactions among loci are expected to contribute substantially to variation of quantitative traits. The objectives of our research were to (i) compare a classical mixed-model approach with a combined mixed-model and analysis of variance approach for detecting epistatic interactions; (ii) examine using computer simulations the statistical power to detect additive-additive, additive-dominance and dominance-dominance epistatic interactions and (iii) detect epistatic interactions between candidate genes for resistance to leaf blight in a set of tetraploid potato clones. Our study was based on the genotypic and phenotypic data of 184 tetraploid potato cultivars as well as computer simulations. The number of significant (α* =1 × 10(-6)) epistatic interactions ranged for the three examined traits from 3 to 32. Our findings suggested that the combined mixed-model and analysis of variance approach leads in comparison with the classical mixed-model approach not to an increased rate of false-positives. The results of the computer simulations suggested that, if molecular markers are available that are in high LD (D'>0.9) with the trait-coding loci, the statistical power to detect epistatic interactions, which explain 5-10% of the phenotypic variance, was of a size that seems promising for their detection.

New insights into the genetics of in vivo induction of maternal haploids, the backbone of doubled haploid technology in maize

Haploids and doubled haploid (DH) inbred lines have become an invaluable tool for maize genetic research and hybrid breeding, but the genetic basis of in vivo induction of maternal haploids is still unknown. This is the first study reporting comparative quantitative trait locus (QTL) analyses of this trait in maize. We determined haploid induction rates (HIR) in testcrosses of a total of 1061 progenies of four segregating populations involving two temperate haploid inducers, UH400 (HIR = 8%) and CAUHOI (HIR = 2%), one temperate and two tropical inbreds with HIR = 0%, and up to three generations per population. Mean HIR of the populations ranged from 0.6 to 5.2% and strongly deviated from the midparent values. One QTL (qhir1) explaining up to p = 66% of the genetic variance was detected in bin 1.04 in the three populations involving a noninducer parent and the HIR-enhancing allele was contributed by UH400. Segregation ratios of loci in bin 1.04 were highly distorted against the UH400 allele in these three populations, suggesting that transmission failure of the inducer gamete and haploid induction ability are related phenomena. In the CAUHOI × UH400 population, seven QTL were identified on five chromosomes, with qhir8 on chromosome 9 having p > 20% in three generations of this cross. The large-effect QTL qhir1 and qhir8 will likely become fixed quickly during inducer development due to strong selection pressure applied for high HIR. Hence, marker-based pyramiding of small-effect and/or modifier QTL influencing qhir1 and qhir8 may help to further increase HIR in maize. We propose a conceptual genetic framework for inheritance of haploid induction ability, which is also applicable to other dichotomous traits requiring progeny testing, and discuss the implications of our results for haploid inducer development.

Statistical analysis of genetic interactions

Many common human diseases and complex traits are highly heritable and influenced by multiple genetic and environmental factors. Although genome-wide association studies (GWAS) have successfully identified many disease-associated variants, these genetic variants explain only a small proportion of the heritability of most complex diseases. Genetic interactions (gene-gene and gene-environment) substantially contribute to complex traits and diseases and could be one of the main sources of the missing heritability. This paper provides an overview of the available statistical methods and related computer software for identifying genetic interactions in animal and plant experimental crosses and human genetic association studies. The main discussion falls under the three broad issues in statistical analysis of genetic interactions: the definition, detection and interpretation of genetic interactions. Recently developed methods based on modern techniques for high-dimensional data are reviewed, including penalized likelihood approaches and hierarchical models; the relationships between these methods are also discussed. I conclude this review by highlighting some areas of future research.

Genetic evaluation of dairy cattle using a simple heritable genetic ground

The evaluation of an animal is based on production records, adjusted for environmental effects, which gives a reliable estimation of its breeding value. Highly reliable daughter yield deviations are used as inputs for genetic marker evaluation. Genetic variability is explained by particular loci and background polygenes, both of which are described by the genomic breeding value selection index. Automated genotyping enables the determination of many single-nucleotide polymorphisms (SNPs) and can increase the reliability of evaluation of young animals (from 0.30 if only the pedigree value is used to 0.60 when the genomic breeding value is applied). However, the introduction of SNPs requires a mixed model with a large number of regressors, in turn requiring new algorithms for the best linear unbiased prediction and BayesB. Here, we discuss a method that uses a genomic relationship matrix to estimate the genomic breeding value of animals directly, without regressors. A one-step procedure evaluates both genotyped and ungenotyped animals at the same time, and produces one common ranking of all animals in a whole population. An augmented pedigree-genomic relationship matrix and the removal of prerequisites produce more accurate evaluations of all connected animals.

A two-phase procedure for QTL mapping with regression models

It is typical in QTL mapping experiments that the number of markers under investigation is large. This poses a challenge to commonly used regression models since the number of feature variables is usually much larger than the sample size, especially, when epistasis effects are to be considered. The greedy nature of the conventional stepwise procedures is well known and is even more conspicuous in such cases. In this article, we propose a two-phase procedure based on penalized likelihood techniques and extended Bayes information criterion (EBIC) for QTL mapping. The procedure consists of a screening phase and a selection phase. In the screening phase, the main and interaction features are alternatively screened by a penalized likelihood mechanism. In the selection phase, a low-dimensional approach using EBIC is applied to the features retained in the screening phase to identify QTL. The two-phase procedure has the asymptotic property that its positive detection rate (PDR) and false discovery rate (FDR) converge to 1 and 0, respectively, as sample size goes to infinity. The two-phase procedure is compared with both traditional and recently developed approaches by simulation studies. A real data analysis is presented to demonstrate the application of the two-phase procedure.

High congruency of QTL positions for heterosis of grain yield in three crosses of maize

The genetic basis of heterosis in maize has been investigated in a number of studies but results have not been conclusive. Here, we compare quantitative trait loci (QTL) mapping results for grain yield, grain moisture, and plant height from three populations derived from crosses of the heterotic pattern Iowa Stiff Stalk Synthetic x Lancaster Sure Crop, investigated with the Design III, and analyzed with advanced statistical methods specifically developed to examine the genetic basis of mid-parent heterosis (MPH). In two populations, QTL analyses were conducted with a joint fit of linear transformations Z (1) (trait mean across pairs of backcross progenies) and Z (2) (half the trait difference between pairs of backcross progenies) to estimate augmented additive and augmented dominance effects of each QTL, as well as their ratio. QTL results for the third population were obtained from the literature. For Z (2) of grain yield, congruency of QTL positions was high across populations, and a large proportion of the genetic variance (~70%) was accounted for by QTL. This was not the case for Z (1) or the other two traits. Further, almost all congruent grain yield QTL were located in the same or an adjacent bin encompassing the centromere. We conclude that different alleles have been fixed in each heterotic pool, which in combination with allele(s) from the opposite heterotic pool lead to high MPH for grain yield. Their positive interactions very likely form the base line for the superior performance of the heterotic pattern under study.

Look before you leap: a new approach to mapping QTL

In this paper, we present an innovative and powerful approach for mapping quantitative trait loci (QTL) in experimental populations. This deviates from the traditional approach of (composite) interval mapping which uses a QTL profile to simultaneously determine the number and location of QTL. Instead, we look before we leap by employing separate detection and localization stages. In the detection stage, we use an iterative variable selection process coupled with permutation to identify the number and synteny of QTL. In the localization stage, we position the detected QTL through a series of one-dimensional interval mapping scans. Results from a detailed simulation study and real analysis of wheat data are presented. We achieve impressive increases in the power of QTL detection compared to composite interval mapping. We also accurately estimate the size and position of QTL. An R library, DLMap, implements the methods described here and is freely available from CRAN ( http://cran.r-project.org/ ).

Deviance Information Criterion (DIC) in Bayesian Multiple QTL Mapping

Mapping multiple quantitative trait loci (QTL) is commonly viewed as a problem of model selection. Various model selection criteria have been proposed, primarily in the non-Bayesian framework. The deviance information criterion (DIC) is the most popular criterion for Bayesian model selection and model comparison but has not been applied to Bayesian multiple QTL mapping. A derivation of the DIC is presented for multiple interacting QTL models and calculation of the DIC is demonstrated using posterior samples generated by Markov chain Monte Carlo (MCMC) algorithms. The DIC measures posterior predictive error by penalizing the fit of a model (deviance) by its complexity, determined by the effective number of parameters. The effective number of parameters simultaneously accounts for the sample size, the cross design, the number and lengths of chromosomes, covariates, the number of QTL, the type of QTL effects, and QTL effect sizes. The DIC provides a computationally efficient way to perform sensitivity analysis and can be used to quantitatively evaluate if including environmental effects, gene-gene interactions, and/or gene-environment interactions in the prior specification is worth the extra parameterization. The DIC has been implemented in the freely available package R/qtlbim, which greatly facilitates the general usage of Bayesian methodology for genome-wide interacting QTL analysis.

A model selection approach for the identification of quantitative trait loci in experimental crosses, allowing epistasis

The identification of quantitative trait loci (QTL) and their interactions is a crucial step toward the discovery of genes responsible for variation in experimental crosses. The problem is best viewed as one of model selection, and the most important aspect of the problem is the comparison of models of different sizes. We present a penalized likelihood approach, with penalties on QTL and pairwise interactions chosen to control false positive rates. This extends the work of Broman and Speed to allow for pairwise interactions among QTL. A conservative version of our penalized LOD score provides strict control over the rate of extraneous QTL and interactions; a more liberal criterion is more lenient on interactions but seeks to maintain control over the rate of inclusion of false loci. The key advance is that one needs only to specify a target false positive rate rather than a prior on the number of QTL and interactions. We illustrate the use of our model selection criteria as exploratory tools; simulation studies demonstrate reasonable power to detect QTL. Our liberal criterion is comparable in power to two Bayesian approaches.

Hierarchical generalized linear models for multiple quantitative trait locus mapping

We develop hierarchical generalized linear models and computationally efficient algorithms for genomewide analysis of quantitative trait loci (QTL) for various types of phenotypes in experimental crosses. The proposed models can fit a large number of effects, including covariates, main effects of numerous loci, and gene-gene (epistasis) and gene-environment (G x E) interactions. The key to the approach is the use of continuous prior distribution on coefficients that favors sparseness in the fitted model and facilitates computation. We develop a fast expectation-maximization (EM) algorithm to fit models by estimating posterior modes of coefficients. We incorporate our algorithm into the iteratively weighted least squares for classical generalized linear models as implemented in the package R. We propose a model search strategy to build a parsimonious model. Our method takes advantage of the special correlation structure in QTL data. Simulation studies demonstrate reasonable power to detect true effects, while controlling the rate of false positives. We illustrate with three real data sets and compare our method to existing methods for multiple-QTL mapping. Our method has been implemented in our freely available package R/qtlbim (www.qtlbim.org), providing a valuable addition to our previous Markov chain Monte Carlo (MCMC) approach.

Interactions between markers can be caused by the dominance effect of quantitative trait loci

F(2) populations are commonly used in genetic studies of animals and plants. For simplicity, most quantitative trait locus or loci (QTL) mapping methods have been developed on the basis of populations having two distinct genotypes at each polymorphic marker or gene locus. In this study, we demonstrate that dominance can cause the interactions between markers and propose an inclusive linear model that includes marker variables and marker interactions so as to completely control both additive and dominance effects of QTL. The proposed linear model is the theoretical basis for inclusive composite-interval QTL mapping (ICIM) for F(2) populations, which consists of two steps: first, the best regression model is selected by stepwise regression, which approximately identifies markers and marker interactions explaining both additive and dominance variations; second, the interval mapping approach is applied to the phenotypic values adjusted by the regression model selected in the first step. Due to the limited mapping population size, the large number of variables, and multicollinearity between variables, coefficients in the inclusive linear model cannot be accurately determined in the first step. Interval mapping is necessary in the second step to fine tune the QTL to their true positions. The efficiency of including marker interactions in mapping additive and dominance QTL was demonstrated by extensive simulations using three QTL distribution models with two population sizes and an actual rice F(2) population.

Advances in Bayesian multiple quantitative trait loci mapping in experimental crosses

Many complex human diseases and traits of biological and/or economic importance are determined by interacting networks of multiple quantitative trait loci (QTL) and environmental factors. Mapping QTL is critical for understanding the genetic basis of complex traits, and for ultimate identification of genes responsible. A variety of sophisticated statistical methods for QTL mapping have been developed. Among these developments, the evolution of Bayesian approaches for multiple QTL mapping over the past decade has been remarkable. Bayesian methods can jointly infer the number of QTL, their genomic positions and their genetic effects. Here, we review recently developed and still developing Bayesian methods and associated computer software for mapping multiple QTL in experimental crosses. We compare and contrast these methods to clearly describe the relationships among different Bayesian methods. We conclude this review by highlighting some areas of future research.

Extending the modified bayesian information criterion (mBIC) to dense markers and multiple interval mapping

SUMMARY

The modified version of Bayesian Information Criterion (mBIC) is a relatively simple model selection procedure that can be used when locating multiple interacting quantitative trait loci (QTL). Our earlier work demonstrated the statistical properties of mBIC for situations where the average genetic map interval is at least 5 cM. In this work mBIC is adapted to genome searches based on a dense map and, more importantly, to the situation where consecutive QTL and interactions are located by multiple interval mapping. Easy to use formulas for the extended mBIC are given. A simulation study, as well as the analysis of real data, confirm the good properties of the extended mBIC.

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

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

Statistical modeling of candidate gene effects on milk production traits in dairy cattle

A major objective of dairy cattle genomic research is to identify genes underlying the variability of milk production traits that could be useful in breeding programs. The candidate gene approach provides tools for searching for causative polymorphisms affecting quantitative traits. Genes with a possible effect on milk traits in cattle can be involved in different physiological pathways, such as triglyceride synthesis [acyl-CoA:diacylglycerol acyltransferase 1 gene (DGAT1)], fat secretion from the mammary epithelial tissue (butyrophilin), or entire-body energy homeostasis regulation (leptin and leptin receptor). In this study, based on data from 252 Black and White bulls from the active Polish dairy population, effects and potential interactions of 9 single nucleotide polymorphisms in the butyrophilin, DGAT1, leptin, and leptin receptor genes were investigated. Additionally, the effect of the number of additive, dominance, and epistatic genetic effects fitted into the model on the estimates of model parameters and model selection was illustrated. Phenotypic records were daughter yield deviations for milk, fat, and protein yields, obtained from a routine national genetic evaluation. Out of all the analyzed polymorphisms, DGAT1 K232A had a much larger effect on milk traits than the other single nucleotide polymorphisms considered. Estimates of the additive genetic effect of K232A expressed as half of the difference between Lys- and Ala-encoding variants were -107.4 kg of milk, 5.4 kg of fat, and -1.6 kg of protein at first parity, as well as -120 kg of milk and 6.8 kg of fat at second parity. In terms of model selection, it was demonstrated that the modified version of Bayesian information criterion selects models with the parameterization reflecting the genetic background of the analyzed trait, while the Bayesian information criterion chooses models that are too highly parameterized.

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.

Locating multiple interacting quantitative trait Loci using rank-based model selection

In previous work, a modified version of the Bayesian information criterion (mBIC) was proposed to locate multiple interacting quantitative trait loci (QTL). Simulation studies and real data analysis demonstrate good properties of the mBIC in situations where the error distribution is approximately normal. However, as with other standard techniques of QTL mapping, the performance of the mBIC strongly deteriorates when the trait distribution is heavy tailed or when the data contain a significant proportion of outliers. In the present article, we propose a suitable robust version of the mBIC that is based on ranks. We investigate the properties of the resulting method on the basis of theoretical calculations, computer simulations, and a real data analysis. Our simulation results show that for the sample sizes typically used in QTL mapping, the methods based on ranks are almost as efficient as standard techniques when the data are normal and are much better when the data come from some heavy-tailed distribution or include a proportion of outliers.

Bayesian mapping of genomewide interacting quantitative trait loci for ordinal traits

Development of statistical methods and software for mapping interacting QTL has been the focus of much recent research. We previously developed a Bayesian model selection framework, based on the composite model space approach, for mapping multiple epistatic QTL affecting continuous traits. In this study we extend the composite model space approach to complex ordinal traits in experimental crosses. We jointly model main and epistatic effects of QTL and environmental factors on the basis of the ordinal probit model (also called threshold model) that assumes a latent continuous trait underlies the generation of the ordinal phenotypes through a set of unknown thresholds. A data augmentation approach is developed to jointly generate the latent data and the thresholds. The proposed ordinal probit model, combined with the composite model space framework for continuous traits, offers a convenient way for genomewide interacting QTL analysis of ordinal traits. We illustrate the proposed method by detecting new QTL and epistatic effects for an ordinal trait, dead fetuses, in a F(2) intercross of mice. Utility and flexibility of the method are also demonstrated using a simulated data set. Our method has been implemented in the freely available package R/qtlbim, which greatly facilitates the general usage of the Bayesian methodology for genomewide interacting QTL analysis for continuous, binary, and ordinal traits in experimental crosses.

Quantitative genetics of speciation: additive and non-additive genetic differentiation between Drosophila madeirensis and Drosophila subobscura

The role of dominance and epistasis in population divergence has been an issue of much debate ever since the neoDarwinian synthesis. One of the best ways to dissect the several genetic components affecting the genetic architecture of populations is line cross analysis. Here we present a study comparing generation means of several life history-traits in two closely related Drosophila species: Drosophila subobscura, D. madeirensis as well as their F1 and F2 hybrids. This study aims to determine the relative contributions of additive and non-additive genetic parameters to the differentiation of life-history traits between these two species. The results indicate that both negative dominance and epistatic effects are very important in the differentiation of most traits. We end with considerations about the relevance of these findings for the understanding of the role of non-additive effects in speciation.

Power to detect higher-order epistatic interactions in a metabolic pathway using a new mapping strategy

Epistatic interactions among quantitative trait loci (QTL) contribute substantially to the variation in complex traits. The main objectives of this study were to (i) compare three- vs. four-step genome scans to identify three-way epistatic interactions among QTL belonging to a metabolic pathway, (ii) investigate by computer simulations the power and proportion of false positives (PFP) for detecting three-way interactions among QTL in recombinant inbred line (RIL) populations derived from a nested mating design, and (iii) compare these estimates to those obtained for detecting three-way interactions among QTL in RIL populations derived from diallel and different partial diallel mating designs. The single-nucleotide polymorphism haplotype data of B73 and 25 diverse maize inbreds were used to simulate the production of various RIL populations. Compared to the three-step genome scan, the power to detect three-way interactions was higher with the four-step genome scan. Higher power to detect three-way interactions was observed for RILs derived from optimally allocated distance-based designs than from nested designs or diallel designs. The power and PFP to detect three-way interactions using a nested design with 5000 RILs were for both the 4-QTL and the 12-QTL scenario of a magnitude that seems promising for their identification.

The genetics of chronic obstructive pulmonary disease

Chronic obstructive pulmonary disease (COPD) is a heterogeneous disease caused by the interaction of genetic susceptibility and environmental influences. There is increasing evidence that genes link to disease pathogenesis and heterogeneity by causing variation in protease anti-protease systems, defence against oxidative stress and inflammation. The main methods of genomic research for complex disease traits are described, together with the genes implicated in COPD thus far, their roles in disease causation and the future for this area of investigation.