Multiple trait analysis of genetic mapping for quantitative trait loci

Drought stress and tropical maize: QTL-by-environment interactions and stability of QTLs across environments for yield components and secondary traits

A recombinant inbred line (RIL) population was evaluated in seven field experiments representing four environments: water stress at flowering (WS) and well-watered (WW) conditions in Mexico and Zimbabwe. The QTLs were identified for each trait in each individual experiment (single-experiment analysis) as well as per environment, per water regime across locations and across all experiments (joint analyses). For the six target traits (male flowering, anthesis-to-silking interval, grain yield, kernel number, 100-kernel fresh weight and plant height) 81, 57, 51 and 34 QTLs were identified in the four step-wise analyses, respectively. Despite high values of heritability, the phenotypic variance explained by QTLs was reduced, indicating epistatic interactions. About 80, 60 and 6% of the QTLs did not present significant QTL-by-environment interactions (QTL x E) in the joint analyses per environment, per water regime and across all experiments. The expression of QTLs was quite stable across years at a given location and across locations under the same water regime. However, the stability of QTLs decreased drastically when data were combined across water regimes, reflecting a different genetic basis of the target traits in the drought and well-watered trials. Several clusters of QTLs for different traits were identified by the joint analyses of the WW (chromosomes 1 and 8) and WS (chromosomes 1, 3 and 5) treatments and across water regimes (chromosome 1). Those regions are clear targets for future marker-assisted breeding, and our results confirm that the best approach to breeding for drought tolerance includes selection under water stress.

Univariate/multivariate genome-wide association scans using data from families and unrelated samples

As genome-wide association studies (GWAS) are becoming more popular, two approaches, among others, could be considered in order to improve statistical power for identifying genes contributing subtle to moderate effects to human diseases. The first approach is to increase sample size, which could be achieved by combining both unrelated and familial subjects together. The second approach is to jointly analyze multiple correlated traits. In this study, by extending generalized estimating equations (GEEs), we propose a simple approach for performing univariate or multivariate association tests for the combined data of unrelated subjects and nuclear families. In particular, we correct for population stratification by integrating principal component analysis and transmission disequilibrium test strategies. The proposed method allows for multiple siblings as well as missing parental information. Simulation studies show that the proposed test has improved power compared to two popular methods, EIGENSTRAT and FBAT, by analyzing the combined data, while correcting for population stratification. In addition, joint analysis of bivariate traits has improved power over univariate analysis when pleiotropic effects are present. Application to the Genetic Analysis Workshop 16 (GAW16) data sets attests to the feasibility and applicability of the proposed method.

Quantitative trait loci controlling resistance to cadmium rhizotoxicity in two recombinant inbred populations of Arabidopsis thaliana are partially shared by those for hydrogen peroxide resistance

To understand mechanisms of cadmium (Cd) tolerance variation associated with root elongation in Arabidopsis thaliana, quantitative trait loci (QTLs) and epistasis were analyzed using relative root length (RRL: % of the root length in +Cd to -Cd) as a tolerant index. Using the composite interval mapping method, three major QTLs (P < 0.05) were detected on chromosomes 2, 4 and 5 in the recombinant inbred population derived from a cross between Landsberg erecta (Ler-0) and Columbia (Col-4). The highest logarithm of odds (LOD) of 5.6 was detected with the QTL on chromosome 5 (QTL5), which is linked to the genetic marker CDPK9 and explained about 26% of the Cd tolerance variation. There was no significant difference in Cd-translocation ratio from roots to shoots between tolerant and sensitive recombinant inbreed lines (RILs), while greater accumulations of reactive oxygen species were observed in the roots of sensitive RILs. This suggested that accumulation of ROS would explain Cd tolerance variation of the Ler/Col RILs, which is mainly controlled by the QTL on chromosome 5. The QTL5 in Ler/Col population was also detected as one of the major QTLs controlling tolerances to hydrogen peroxide and to copper, which is another ROS generating rhizotoxic metal. The same chromosomal position was detected as a common major QTL for Cd and hydrogen peroxide tolerances in a different recombinant inbreed (RI) population derived from a cross of Col-gl1 and Kashmir (Kas-1). These data, along with a multitraits QTL analysis in both sets of RILs, suggest that peroxide damage depends on the genotype at a major Cd-tolerant locus on the upper part of chromosome 5.

The long (and winding) road to gene discovery for canine hip dysplasia

Hip dysplasia is a common inherited trait of dogs that results in secondary osteoarthritis. In this article the methods used to uncover the mutations contributing to this condition are reviewed, beginning with hip phenotyping. Coarse, genome-wide, microsatellite-based screens of pedigrees of greyhounds and dysplastic Labrador retrievers were used to identify linked quantitative trait loci (QTL). Fine-mapping across two chromosomes (CFA11 and 29) was employed using single nucleotide polymorphism (SNP) genotyping. Power analyses and preferential selection of dogs for ongoing SNP-based genotyping is described with the aim of refining the QTL intervals to 1-2 megabases on these and several additional chromosomes prior to candidate gene screening. The review considers how a mutation or a genetic marker such as a SNP or haplotype of SNPs might be combined with pedigree and phenotype information to create a 'breeding value' that could improve the accuracy of predicting a dog's hip conformation.

Non-dauer larval dispersal in Caenorhabditis elegans

Species that exploit transient food patches must both effectively utilize such food sources and colonize new patches. The timing and rate of dispersal from existing patches and adaptations that aid dispersal are therefore crucial. Currently, no system exists in which dispersal has been investigated at both the ecological and genetic levels. The extensively studied model nematode Caenorhabditis elegans is potentially such a system. Dispersal between food patches in C. elegans has been found to be related to polymorphism in the npr-1 gene, which regulates the tendency of worms to aggregate on food. Here I show that this non-dauer larval dispersal is affected by various environmental variables and that variation is not fully explained by differences in aggregation behavior. Quantitative trait loci mapping identifies candidate genomic regions, separate to npr-1, which affect variation in dispersal between two isolates. These data suggest that the ecology of C. elegans is more complex than previously thought, but indicate that it is experimentally tractable.

Bayesian shrinkage mapping for multiple QTL in half-sib families

Recently, an effective Bayesian shrinkage estimation method has been proposed for mapping QTL in inbred line crosses. However, with regard to outbred populations, such as half-sib populations with maternal information unavailable, it is not straightforward to utilize such a shrinkage estimation for QTL mapping. The reasons are: (1) the linkage phase of markers in the outbred population is usually unknown; and (2) only paternal genotypes can be used for inferring QTL genotypes of offspring. In this article, a novel Bayesian shrinkage method was proposed for mapping QTL under the half-sib design using a mixed model. A simulation study clearly demonstrated that the proposed method was powerful for detecting multiple QTL. In addition, we applied the proposed method to map QTL for economic traits in the Chinese dairy cattle population. Two or more novel QTL harbored in the chromosomal region were detected for each trait of interest, whereas only one QTL was found using traditional maximum likelihood analyses in our earlier studies. This further validated that our shrinkage estimation method could perform well in empirical data analyses and had practical significance in the field of linkage studies for outbred populations.

Genetic dissection of complex endosperm traits

The endosperm of plants is a major source of food, feed and industrial raw materials. The genetic analysis of endosperm traits poses numerous challenges due to the endosperm's complex genetic composition and unique physical and developmental properties. Modern molecular techniques and statistical methods have greatly improved the mapping of quantitative trait loci underlying endosperm traits and have led to revolutionary insights regarding epistatic and epigenetic effects. This article describes the current state of the methodologies used in the genetic dissection of endosperm traits and highlights practical issues and statistical concepts and procedures.

Advanced backcross-QTL analysis in spring barley (H. vulgare ssp. spontaneum) comparing a REML versus a Bayesian model in multi-environmental field trials

A common difficulty in mapping quantitative trait loci (QTLs) is that QTL effects may show environment specificity and thus differ across environments. Furthermore, quantitative traits are likely to be influenced by multiple QTLs or genes having different effect sizes. There is currently a need for efficient mapping strategies to account for both multiple QTLs and marker-by-environment interactions. Thus, the objective of our study was to develop a Bayesian multi-locus multi-environmental method of QTL analysis. This strategy is compared to (1) Bayesian multi-locus mapping, where each environment is analysed separately, (2) Restricted Maximum Likelihood (REML) single-locus method using a mixed hierarchical model, and (3) REML forward selection applying a mixed hierarchical model. For this study, we used data on multi-environmental field trials of 301 BC(2)DH lines derived from a cross between the spring barley elite cultivar Scarlett and the wild donor ISR42-8 from Israel. The lines were genotyped by 98 SSR markers and measured for the agronomic traits "ears per m(2)," "days until heading," "plant height," "thousand grain weight," and "grain yield". Additionally, a simulation study was performed to verify the QTL results obtained in the spring barley population. In general, the results of Bayesian QTL mapping are in accordance with REML methods. In this study, Bayesian multi-locus multi-environmental analysis is a valuable method that is particularly suitable if lines are cultivated in multi-environmental field trials.

Network-based multiple locus linkage analysis of expression traits

MOTIVATION

We consider the problem of multiple locus linkage analysis for expression traits of genes in a pathway or a network. To capitalize on co-expression of functionally related genes, we propose a penalized regression method that maps multiple expression quantitative trait loci (eQTLs) for all related genes simultaneously while accounting for their shared functions as specified a priori by a gene pathway or network.

RESULTS

An analysis of a mouse dataset and simulation studies clearly demonstrate the advantage of the proposed method over a standard approach that ignores biological knowledge of gene networks.

Unraveling the complex trait of crop yield with quantitative trait loci mapping in Brassica napus

Yield is the most important and complex trait for the genetic improvement of crops. Although much research into the genetic basis of yield and yield-associated traits has been reported, in each such experiment the genetic architecture and determinants of yield have remained ambiguous. One of the most intractable problems is the interaction between genes and the environment. We identified 85 quantitative trait loci (QTL) for seed yield along with 785 QTL for eight yield-associated traits, from 10 natural environments and two related populations of rapeseed. A trait-by-trait meta-analysis revealed 401 consensus QTL, of which 82.5% were clustered and integrated into 111 pleiotropic unique QTL by meta-analysis, 47 of which were relevant for seed yield. The complexity of the genetic architecture of yield was demonstrated, illustrating the pleiotropy, synthesis, variability, and plasticity of yield QTL. The idea of estimating indicator QTL for yield QTL and identifying potential candidate genes for yield provides an advance in methodology for complex traits.

Ecological genomics of Boechera stricta: identification of a QTL controlling the allocation of methionine- vs branched-chain amino acid-derived glucosinolates and levels of insect herbivory

In the Brassicaceae, glucosinolates influence the feeding, reproduction and development of many insect herbivores. Glucosinolate production and effects on herbivore feeding have been extensively studied in the model species, Arabidopsis thaliana and Brassica crops, both of which constitutively produce leaf glucosinolates mostly derived from the amino acid, methionine. Much less is known about the regulation or role in defense of glucosinolates derived from other aliphatic amino acids, such as the branched-chain amino acids (BCAA), valine and isoleucine. We have identified a glucosinolate polymorphism in Boechera stricta controlling the allocation to BCAA- vs methionine-derived glucosinolates in both leaves and seeds. B. stricta is a perennial species that grows in mostly undisturbed habitats of western North America. We have measured glucosinolate profiles and concentrations in 192 F(2) lines that have earlier been used for genetic map construction. We also performed herbivory assays on six F(3) replicates per F(2) line using the generalist lepidopteran, Trichoplusia ni. Quantitative trait locus (QTL) analysis identified a single locus controlling both glucosinolate profile and levels of herbivory, the branched chain-methionine allocation or BCMA QTL. We have delimited this QTL to a small genomic region with a 1.0 LOD confidence interval just 1.9 cm wide, which, in A. thaliana, contains approximately 100 genes. We also found that methionine-derived glucosinolates provided significantly greater defense than the BCAA-derived glucosinolates against feeding by this generalist insect herbivore. The future positional cloning of this locus will allow for testing various adaptive explanations.

Mapping QTL for multiple traits using Bayesian statistics

The value of a new crop species is usually judged by the overall performance of multiple traits. Therefore, in most quantitative trait locus (QTL) mapping experiments, researchers tend to collect phenotypic records for multiple traits. Some traits may vary continuously and others may vary in a discrete fashion. Although mapping QTLs jointly for multiple traits is more efficient than mapping QTLs separately for individual traits, the latter is still commonly practised in QTL mapping. This is primarily due to the lack of efficient statistical methods and computer software packages to implement the methods. Mapping multiple QTLs simultaneously in a single multivariate model has not been available, especially when categorical traits are involved. In the present study, we developed a Bayesian method to map QTLs of the entire genome for multiple traits with continuous, discrete or both types of phenotypic distribution. Instead of using the reversible jump Markov chain Monte Carlo (MCMC) for model selection, we adopt a parameter shrinkage approach to estimate the genetic effects of all marker intervals. We demonstrate the method by analysing a set of simulated data with both continuous and discrete traits. We also apply the method to mapping QTLs responsible for multiple disease resistances to the blast fungus of rice. A computer program written in SAS/IML that implements the method is freely available, on request, to academic researchers.

Advances in systems biology are enhancing our understanding of disease and moving us closer to novel disease treatments

With tens of billions of dollars spent each year on the development of drugs to treat human diseases, and with fewer and fewer applications for investigational new drugs filed each year despite this massive spending, questions now abound on what changes to the drug discovery paradigm can be made to achieve greater success. The high rate of failure of drug candidates in clinical development, where the great majority of these drugs fail due to lack of efficacy, speak directly to the need for more innovative approaches to study the mechanisms of disease and drug discovery. Here we review systems biology approaches that have been devised over the last several years to understand the biology of disease at a more holistic level. By integrating a diversity of data like DNA variation, gene expression, protein-protein interaction, DNA-protein binding, and other types of molecular phenotype data, more comprehensive networks of genes both within and between tissues can be constructed to paint a more complete picture of the molecular processes underlying physiological states associated with disease. These more integrative, systems-level methods lead to networks that are demonstrably predictive, which in turn provides a deeper context within which single genes operate such as those identified from genome-wide association studies or those targeted for therapeutic intervention. The more comprehensive views of disease that result from these methods have the potential to dramatically enhance the way in which novel drug targets are identified and developed, ultimately increasing the probability of success for taking new drugs through clinical development. We highlight a number of the integrative approaches via examples that have resulted not only in the identification of novel genes for diabetes and cardiovascular disease, but in more comprehensive networks as well that describe the context in which the disease genes operate.

Replication of long-bone length QTL in the F9-F10 LG,SM advanced intercross

Quantitative trait locus (QTL) mapping techniques are frequently used to identify genomic regions associated with variation in phenotypes of interest. However, the F(2) intercross and congenic strain populations usually employed have limited genetic resolution resulting in relatively large confidence intervals that greatly inhibit functional confirmation of statistical results. Here we use the increased resolution of the combined F(9) and F(10) generations (n = 1455) of the LG,SM advanced intercross to fine-map previously identified QTL associated with the lengths of the humerus, ulna, femur, and tibia. We detected 81 QTL affecting long-bone lengths. Of these, 49 were previously identified in the combined F(2)-F(3) population of this intercross, while 32 represent novel contributors to trait variance. Pleiotropy analysis suggests that most QTL affect three to four long bones or serially homologous limb segments. We also identified 72 epistatic interactions involving 38 QTL and 88 novel regions. This analysis shows that using later generations of an advanced intercross greatly facilitates fine-mapping of confidence intervals, resolving three F(2)-F(3) QTL into multiple linked loci and narrowing confidence intervals of other loci, as well as allowing identification of additional QTL. Further characterization of the biological bases of these QTL will help provide a better understanding of the genetics of small variations in long-bone length.

Bivariate association analyses for the mixture of continuous and binary traits with the use of extended generalized estimating equations

Genome-wide association (GWA) study is becoming a powerful tool in deciphering genetic basis of complex human diseases/traits. Currently, the univariate analysis is the most commonly used method to identify genes associated with a certain disease/phenotype under study. A major limitation with the univariate analysis is that it may not make use of the information of multiple correlated phenotypes, which are usually measured and collected in practical studies. The multivariate analysis has proven to be a powerful approach in linkage studies of complex diseases/traits, but it has received little attention in GWA. In this study, we aim to develop a bivariate analytical method for GWA study, which can be used for a complex situation in which continuous trait and a binary trait are measured under study. Based on the modified extended generalized estimating equation (EGEE) method we proposed herein, we assessed the performance of our bivariate analyses through extensive simulations as well as real data analyses. In the study, to develop an EGEE approach for bivariate genetic analyses, we combined two different generalized linear models corresponding to phenotypic variables using a seemingly unrelated regression model. The simulation results demonstrated that our EGEE-based bivariate analytical method outperforms univariate analyses in increasing statistical power under a variety of simulation scenarios. Notably, EGEE-based bivariate analyses have consistent advantages over univariate analyses whether or not there exists a phenotypic correlation between the two traits. Our study has practical importance, as one can always use multivariate analyses as a screening tool when multiple phenotypes are available, without extra costs of statistical power and false-positive rate. Analyses on empirical GWA data further affirm the advantages of our bivariate analytical method.

Bayesian composite model space approach for mapping quantitative trait Loci in variance component model

In this article, we successfully apply the novel model selection method, Bayesian composite model space approach which has been used to map quantitative trait loci (QTL) for allelic substitution model, to map QTL for variance component model. The novel model selection approach has two advantages compared to the reversible jump Markov chain Monte Carlo method. Firstly, it mixes well due to the fixedness of the model dimension; secondly, it can map multiple QTL with higher power especially in genome-wide QTL mapping; finally, in the new method, it is also easy to incorporate our prior information about the variance components, which may bring precise estimate for variance components. A series of simulation experiments were conducted to demonstrate the general characters of the proposed method. The computer program is written in FORTRAN language, which is also built into a software "BayesMapQTL", and they also can be used for real data analysis and are available for request.

Expression quantitative trait loci mapping with multivariate sparse partial least squares regression

Expression quantitative trait loci (eQTL) mapping concerns finding genomic variation to elucidate variation of expression traits. This problem poses significant challenges due to high dimensionality of both the gene expression and the genomic marker data. We propose a multivariate response regression approach with simultaneous variable selection and dimension reduction for the eQTL mapping problem. Transcripts with similar expression are clustered into groups, and their expression profiles are viewed as a multivariate response. Then, we employ our recently developed sparse partial least-squares regression methodology to select markers associated with each cluster of genes. We demonstrate with extensive simulations that our eQTL mapping with multivariate response sparse partial least-squares regression (M-SPLS eQTL) method overcomes the issue of multiple transcript- or marker-specific analyses, thereby avoiding potential elevation of type I error. Additionally, joint analysis of multiple transcripts by multivariate response regression increases power for detecting weak linkages. We illustrate that M-SPLS eQTL compares competitively with other approaches and has a number of significant advantages, including the ability to handle highly correlated genotype data and computational efficiency. We provide an application of this methodology to a mouse data set concerning obesity and diabetes.

Quantitative trait loci for biomechanical performance and femoral geometry in an intercross of recombinant congenic mice: restriction of the Bmd7 candidate interval

Despite steady progress in identifying quantitative trait loci (QTLs) for bone phenotypes, relatively little progress has been made in moving from QTLs to identifying the relevant gene. We exploited the genetic structure of recombinant congenic mouse strains by performing a reciprocal intercross of the strains HcB-8 and HcB-23, phenotyped for body size, femoral biomechanical performance, and femoral diaphyseal geometry and mapped with R/qtl and QTL Cartographer. Significant QTLs are present on chromosomes 1, 2, 3, 4, 6, and 10. We found significant sex x QTL and cross-direction x QTL interactions. The chromosome 4 QTL affects multiple femoral anatomic features and biomechanical properties. The known segregating segment of chromosome 4 contains only 18 genes, among which Ece1, encoding endothelin-converting enzyme 1, stands out as a candidate. Endothelin signaling has been shown to promote the growth of osteoblastic metastases and to potentiate signaling via the Wnt pathway. The colocalizing chromosome 4 QTL Bmd7 (for bone mineral density 7) increases responsiveness to mechanical loading. By exploiting the short informative segment of chromosome 4 and the known biology, we propose that Ece1 is the gene responsible for Bmd7 and that it acts by increasing responsiveness to mechanical loading through modulation of Wnt signaling.

Effects of genetic and environmental factors on trait network predictions from quantitative trait locus data

The use of high-throughput genomic techniques to map gene expression quantitative trait loci has spurred the development of path analysis approaches for predicting functional networks linking genes and natural trait variation. The goal of this study was to test whether potentially confounding factors, including effects of common environment and genes not included in path models, affect predictions of cause-effect relationships among traits generated by QTL path analyses. Structural equation modeling (SEM) was used to test simple QTL-trait networks under different regulatory scenarios involving direct and indirect effects. SEM identified the correct models under simple scenarios, but when common-environment effects were simulated in conjunction with direct QTL effects on traits, they were poorly distinguished from indirect effects, leading to false support for indirect models. Application of SEM to loblolly pine QTL data provided support for biologically plausible a priori hypotheses of QTL mechanisms affecting height and diameter growth. However, some biologically implausible models were also well supported. The results emphasize the need to include any available functional information, including predictions for genetic and environmental correlations, to develop plausible models if biologically useful trait network predictions are to be made.

Why Do We Test Multiple Traits in Genetic Association Studies?

In studies of complex disorders such as nicotine dependence, it is common that researchers assess multiple variables related to a disorder as well as other disorders that are potentially correlated with the primary disorder of interest. In this work, we refer to those variables and disorders broadly as multiple traits. The multiple traits may or may not have a common causal genetic variant. Intuitively, it may be more powerful to accommodate multiple traits in genetic traits, but the analysis of multiple traits is generally more complicated than the analysis of a single trait. Furthermore, it is not well documented as to how much power we may potentially gain by considering multiple traits. Our aim is to enhance our understanding on this important and practical issue. We considered a variety of correlation structures between traits and the disease locus. To focus on the effect of accommodating multiple traits, we examined genetic models that are relatively simple so that we can pinpoint the factors affecting the power. We conducted simulation studies to explore the performance of testing multiple traits simultaneously and the performance of testing a single trait at a time in family-based association studies. Our simulation results demonstrated that the performance of testing multiple traits simultaneously is better than that of testing each trait individually for almost models considered. We also found that the power of association tests varies among the underlying models. The advantage of conducting a multiple traits test is minimized when some traits are influenced by the gene only through other traits; and it is maximized when there are causal relations between the traits and the gene, and among the traits themselves or when there are extraneous traits.

Multiple-trait quantitative trait locus mapping with incomplete phenotypic data

Background

Conventional multiple-trait quantitative trait locus (QTL) mapping methods must discard cases (individuals) with incomplete phenotypic data, thereby sacrificing other phenotypic and genotypic information contained in the discarded cases. Under standard assumptions about the missing-data mechanism, it is possible to exploit these cases.

Results

We present an expectation-maximization (EM) algorithm, derived for recombinant inbred and F₂ genetic models but extensible to any mating design, that supports conventional hypothesis tests for QTL main effect, pleiotropy, and QTL-by-environment interaction in multiple-trait analyses with missing phenotypic data. We evaluate its performance by simulations and illustrate with a real-data example.

Conclusion

The EM method affords improved QTL detection power and precision of QTL location and effect estimation in comparison with case deletion or imputation methods. It may be incorporated into any least-squares or likelihood-maximization QTL-mapping approach.

A bivariate whole genome linkage study identified genomic regions influencing both BMD and bone structure

Areal BMD (aBMD) and areal bone size (ABS) are biologically correlated traits and are each important determinants of bone strength and risk of fractures. Studies showed that aBMD and ABS are genetically correlated, indicating that they may share some common genetic factors, which, however, are largely unknown. To study the genetic factors influencing both aBMD and ABS, bivariate whole genome linkage analyses were conducted for aBMD-ABS at the femoral neck (FN), lumbar spine (LS), and ultradistal (UD)-forearm in a large sample of 451 white pedigrees made up of 4498 individuals. We detected significant linkage on chromosome Xq27 (LOD = 4.89) for LS aBMD-ABS. In addition, we detected suggestive linkages at 20q11 (LOD = 3.65) and Xp11 (LOD = 2.96) for FN aBMD-ABS; at 12p11 (LOD = 3.39) and 17q21 (LOD = 2.94) for LS aBMD-ABS; and at 5q23 (LOD = 3.54), 7p15 (LOD = 3.45), Xq27 (LOD = 2.93), and 12p11 (LOD = 2.92) for UD-forearm aBMD-ABS. Subsequent discrimination analyses indicated that quantitative trait loci (QTLs) at 12p11 and 17q21 may have pleiotropic effects on aBMD and ABS. This study identified several genomic regions that may contain QTLs important for both aBMD and ABS. Further endeavors are necessary to follow these regions to eventually pinpoint the genetic variants affecting bone strength and risk of fractures.

QGene 4.0, an extensible Java QTL-analysis platform

Of many statistical methods developed to date for quantitative trait locus (QTL) analysis, only a limited subset are available in public software allowing their exploration, comparison and practical application by researchers. We have developed QGene 4.0, a plug-in platform that allows execution and comparison of a variety of modern QTL-mapping methods and supports third-party addition of new ones. The software accommodates line-cross mating designs consisting of any arbitrary sequence of selfing, backcrossing, intercrossing and haploid-doubling steps that includes map, population, and trait simulators; and is scriptable.

AVAILABILITY

Software and documentation are available at http://coding.plantpath.ksu.edu/qgene. Source code is available on request.

Multi-trait association mapping in sugar beet (Beta vulgaris L.)

Association mapping promises to overcome the limitations of linkage mapping methods. The main objective of this study was to examine the applicability of multivariate association mapping with an empirical data set of sugar beet. A total of 111 diploid sugar beet inbreds was selected from the seed parent heterotic pool to represent a broad diversity with respect to sugar content (SC). The inbreds were genotyped with 26 simple sequence repeat markers chosen according to their map positions in proximity to previously identified quantitative trait loci for SC. For SC and beet yield (BY), the genotypic variances were highly significant (P < 0.01). Based on the global test of the bivariate mixed-model approach, four markers were significantly associated with SC, BY, or both at a false discovery rate of 0.025. All four markers were significantly (P < 0.05) associated with BY but only two with SC. The identification of markers associated with SC, BY, or both indicated that association mapping can be successfully applied in a sugar beet breeding context for detection of marker-phenotype associations. Furthermore, based on our results multivariate association mapping can be recommended as a promising tool to discriminate with a high mapping resolution between pleiotropy and linkage as reasons for co-localization of marker-phenotype associations for different traits.

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.

A statistical model for testing the pleiotropic control of phenotypic plasticity for a count trait

The differences of a phenotypic trait produced by a genotype in response to changes in the environment are referred to as phenotypic plasticity. Despite its importance in the maintenance of genetic diversity via genotype-by-environment interactions, little is known about the detailed genetic architecture of this phenomenon, thus limiting our ability to predict the pattern and process of microevolutionary responses to changing environments. In this article, we develop a statistical model for mapping quantitative trait loci (QTL) that control the phenotypic plasticity of a complex trait through differentiated expressions of pleiotropic QTL in different environments. In particular, our model focuses on count traits that represent an important aspect of biological systems, controlled by a network of multiple genes and environmental factors. The model was derived within a multivariate mixture model framework in which QTL genotype-specific mixture components are modeled by a multivariate Poisson distribution for a count trait expressed in multiple clonal replicates. A two-stage hierarchic EM algorithm is implemented to obtain the maximum-likelihood estimates of the Poisson parameters that specify environment-specific genetic effects of a QTL and residual errors. By approximating the number of sylleptic branches on the main stems of poplar hybrids by a Poisson distribution, the new model was applied to map QTL that contribute to the phenotypic plasticity of a count trait. The statistical behavior of the model and its utilization were investigated through simulation studies that mimic the poplar example used. This model will provide insights into how genomes and environments interact to determine the phenotypes of complex count traits.

QTL and QTL x environment effects on agronomic and nitrogen acquisition traits in rice

Agricultural environments deteriorate due to excess nitrogen application. Breeding for low nitrogen responsive genotypes can reduce soil nitrogen input. Rice genotypes respond variably to soil available nitrogen. The present study attempted quantification of genotype x nitrogen level interaction and mapping of quantitative trait loci (QTLs) associated with nitrogen use efficiency (NUE) and other associated agronomic traits. Twelve parameters were observed across a set of 82 double haploid (DH) lines derived from IR64/Azucena. Three nitrogen regimes namely, native (0 kg/ha; no nitrogen applied), optimum (100 kg/ha) and high (200 kg/ha) replicated thrice were the environments. The parents and DH lines were significantly varying for all traits under different nitrogen regimes. All traits except plant height recorded significant genotype x environment interaction. Individual plant yield was positively correlated with nitrogen use efficiency and nitrogen uptake. Sixteen QTLs were detected by composite interval mapping. Eleven QTLs showed significant QTL x environment interactions. On chromosome 3, seven QTLs were detected associated with nitrogen use, plant yield and associated traits. A QTL region between markers RZ678, RZ574 and RZ284 was associated with nitrogen use and yield. This chromosomal region was enriched with expressed gene sequences of known key nitrogen assimilation genes.

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.

Bivariate combined linkage and association mapping of quantitative trait loci

In this paper, bivariate/multivariate variance component models are proposed for high-resolution combined linkage and association mapping of quantitative trait loci (QTL), based on combinations of pedigree and population data. Suppose that a quantitative trait locus is located in a chromosome region that exerts pleiotropic effects on multiple quantitative traits. In the region, multiple markers such as single nucleotide polymorphisms are typed. Two regression models, "genotype effect model" and "additive effect model", are proposed to model the association between the markers and the trait locus. The linkage information, i.e., recombination fractions between the QTL and the markers, is modeled in the variance and covariance matrix. By analytical formulae, we show that the "genotype effect model" can be used to model the additive and dominant effects simultaneously; the "additive effect model" only takes care of additive effect. Based on the two models, F-test statistics are proposed to test association between the QTL and markers. By analytical power analysis, we show that bivariate models can be more powerful than univariate models. For moderate-sized samples, the proposed models lead to correct type I error rates; and so the models are reasonably robust. As a practical example, the method is applied to analyze the genetic inheritance of rheumatoid arthritis for the data of The North American Rheumatoid Arthritis Consortium, Problem 2, Genetic Analysis Workshop 15, which confirms the advantage of the proposed bivariate models.

Multitrait analysis of quantitative trait loci using Bayesian composite space approach

Background

Multitrait analysis of quantitative trait loci can capture the maximum information of experiment. The maximum-likelihood approach and the least-square approach have been developed to jointly analyze multiple traits, but it is difficult for them to include multiple QTL simultaneously into one model.

Results

In this article, we have successfully extended Bayesian composite space approach, which is an efficient model selection method that can easily handle multiple QTL, to multitrait mapping of QTL. There are many statistical innovations of the proposed method compared with Bayesian single trait analysis. The first is that the parameters for all traits are updated jointly by vector or matrix; secondly, for QTL in the same interval that control different traits, the correlation between QTL genotypes is taken into account; thirdly, the information about the relationship of residual error between the traits is also made good use of. The superiority of the new method over separate analysis was demonstrated by both simulated and real data. The computing program was written in FORTRAN and it can be available for request.

Conclusion

The results suggest that the developed new method is more powerful than separate analysis.

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.

A meta-analysis of QTL for diabetes-related traits in rodents

Crossbreeding studies in rodents have identified numerous quantitative trait loci (QTL) that are linked to diabetes-related component traits. To identify genetic consensus regions implicated in insulin action and glucose homeostasis, we have performed a meta-analysis of genomewide linkage scans for diabetes-related traits. From a total of 43 published genomewide scans we assembled a nonredundant collection of 153 QTL for glucose levels, insulin levels, and glucose tolerance. Collectively, these studies include data from 48 different parental strains and >11,000 individual animals. The results of the studies were analyzed by the truncated product method (TPM). The analysis revealed significant evidence for linkage of glucose levels, insulin levels, and glucose tolerance to 27 different segments of the mouse genome. The most prominent consensus regions [localized to chromosomes 2, 4, 7, 9, 11, 13, and 19; logarithm of odds (LOD) scores 10.5-17.4] cover approximately 11% of the mouse genome and collectively contain the peak markers for 47 QTL. Approximately half of these genomic segments also show significant linkage to body weight and adiposity, indicating the presence of multiple obesity-dependent and -independent consensus regions for diabetes-related traits. At least 84 human genetic markers from genomewide scans and >80 candidate genes from human and rodent studies map into the mouse consensus regions for diabetes-related traits, indicating a substantial overlap between the species. Our results provide guidance for the identification of novel candidate genes and demonstrate the presence of numerous distinct consensus QTL regions with highly significant LOD scores that control glucose homeostasis. An interactive physical map of the QTL is available online at http://www.diabesitygenes.org.

Review and evaluation of methods correcting for population stratification with a focus on underlying statistical principles

When two or more populations have been separated by geographic or cultural boundaries for many generations, drift, spontaneous mutations, differential selection pressures and other factors may lead to allele frequency differences among populations. If these 'parental' populations subsequently come together and begin inter-mating, disequilibrium among linked markers may span a greater genetic distance than it typically does among populations under panmixia [see glossary]. This extended disequilibrium can make association studies highly effective and more economical than disequilibrium mapping in panmictic populations since less marker loci are needed to detect regions of the genome that harbor phenotype-influencing loci. However, under some circumstances, this process of intermating (as well as other processes) can produce disequilibrium between pairs of unlinked loci and thus create the possibility of confounding or spurious associations due to this population stratification. Accordingly, researchers are advised to employ valid statistical tests for linkage disequilibrium mapping allowing conduct of genetic association studies that control for such confounding. Many recent papers have addressed this need. We provide a comprehensive review of advances made in recent years in correcting for population stratification and then evaluate and synthesize these methods based on statistical principles such as (1) randomization, (2) conditioning on sufficient statistics, and (3) identifying whether the method is based on testing the genotype-phenotype covariance (conditional upon familial information) and/or testing departures of the marginal distribution from the expected genotypic frequencies.

Variations in DNA elucidate molecular networks that cause disease

Identifying variations in DNA that increase susceptibility to disease is one of the primary aims of genetic studies using a forward genetics approach. However, identification of disease-susceptibility genes by means of such studies provides limited functional information on how genes lead to disease. In fact, in most cases there is an absence of functional information altogether, preventing a definitive identification of the susceptibility gene or genes. Here we develop an alternative to the classic forward genetics approach for dissecting complex disease traits where, instead of identifying susceptibility genes directly affected by variations in DNA, we identify gene networks that are perturbed by susceptibility loci and that in turn lead to disease. Application of this method to liver and adipose gene expression data generated from a segregating mouse population results in the identification of a macrophage-enriched network supported as having a causal relationship with disease traits associated with metabolic syndrome. Three genes in this network, lipoprotein lipase (Lpl), lactamase beta (Lactb) and protein phosphatase 1-like (Ppm1l), are validated as previously unknown obesity genes, strengthening the association between this network and metabolic disease traits. Our analysis provides direct experimental support that complex traits such as obesity are emergent properties of molecular networks that are modulated by complex genetic loci and environmental factors.

Gene network inference via structural equation modeling in genetical genomics experiments

Our goal is gene network inference in genetical genomics or systems genetics experiments. For species where sequence information is available, we first perform expression quantitative trait locus (eQTL) mapping by jointly utilizing cis-, cis-trans-, and trans-regulation. After using local structural models to identify regulator-target pairs for each eQTL, we construct an encompassing directed network (EDN) by assembling all retained regulator-target relationships. The EDN has nodes corresponding to expressed genes and eQTL and directed edges from eQTL to cis-regulated target genes, from cis-regulated genes to cis-trans-regulated target genes, from trans-regulator genes to target genes, and from trans-eQTL to target genes. For network inference within the strongly constrained search space defined by the EDN, we propose structural equation modeling (SEM), because it can model cyclic networks and the EDN indeed contains feedback relationships. On the basis of a factorization of the likelihood and the constrained search space, our SEM algorithm infers networks involving several hundred genes and eQTL. Structure inference is based on a penalized likelihood ratio and an adaptation of Occam's window model selection. The SEM algorithm was evaluated using data simulated with nonlinear ordinary differential equations and known cyclic network topologies and was applied to a real yeast data set.

Identifying trait clusters by linkage profiles: application in genetical genomics

MOTIVATION

Genes often regulate multiple traits. Identifying clusters of traits influenced by a common group of genes helps elucidate regulatory networks and can improve linkage mapping.

METHODS

We show that the Pearson correlation coefficient, rho L, between two LOD score profiles can, with high specificity and sensitivity, identify pairs of genes that have their transcription regulated by shared quantitative trait loci (QTL). Furthermore, using theoretical and/or empirical methods, we can approximate the distribution of rho L under the null hypothesis of no common QTL. Therefore, it is possible to calculate P-values and false discovery rates for testing whether two traits share common QTL. We then examine the properties of rho L through simulation and use rho L to cluster genes in a genetical genomics experiment examining Saccharomyces cerevisiae.

RESULTS

Simulations show that rho L can have more power than the clustering methods currently used in genetical genomics. Combining experimental results with Gene Ontology (GO) annotations show that genes within a purported cluster often share similar function.

SOFTWARE

R-code included in online Supplementary Material.

Heterosis for biomass-related traits in Arabidopsis investigated by quantitative trait loci analysis of the triple testcross design with recombinant inbred lines

Arabidopsis thaliana has emerged as a leading model species in plant genetics and functional genomics including research on the genetic causes of heterosis. We applied a triple testcross (TTC) design and a novel biometrical approach to identify and characterize quantitative trait loci (QTL) for heterosis of five biomass-related traits by (i) estimating the number, genomic positions, and genetic effects of heterotic QTL, (ii) characterizing their mode of gene action, and (iii) testing for presence of epistatic effects by a genomewide scan and marker x marker interactions. In total, 234 recombinant inbred lines (RILs) of Arabidopsis hybrid C24 x Col-0 were crossed to both parental lines and their F1 and analyzed with 110 single-nucleotide polymorphism (SNP) markers. QTL analyses were conducted using linear transformations Z1, Z2, and Z3 calculated from the adjusted entry means of TTC progenies. With Z1, we detected 12 QTL displaying augmented additive effects. With Z2, we mapped six QTL for augmented dominance effects. A one-dimensional genome scan with Z3 revealed two genomic regions with significantly negative dominance x additive epistatic effects. Two-way analyses of variance between marker pairs revealed nine digenic epistatic interactions: six reflecting dominance x dominance effects with variable sign and three reflecting additive x additive effects with positive sign. We conclude that heterosis for biomass-related traits in Arabidopsis has a polygenic basis with overdominance and/or epistasis being presumably the main types of gene action.

The role of epistasis in the manifestation of heterosis: a systems-oriented approach

Heterosis is widely used in breeding, but the genetic basis of this biological phenomenon has not been elucidated. We postulate that additive and dominance genetic effects as well as two-locus interactions estimated in classical QTL analyses are not sufficient for quantifying the contributions of QTL to heterosis. A general theoretical framework for determining the contributions of different types of genetic effects to heterosis was developed. Additive x additive epistatic interactions of individual loci with the entire genetic background were identified as a major component of midparent heterosis. On the basis of these findings we defined a new type of heterotic effect denoted as augmented dominance effect di* that comprises the dominance effect at each QTL minus half the sum of additive x additive interactions with all other QTL. We demonstrate that genotypic expectations of QTL effects obtained from analyses with the design III using testcrosses of recombinant inbred lines and composite-interval mapping precisely equal genotypic expectations of midparent heterosis, thus identifying genomic regions relevant for expression of heterosis. The theory for QTL mapping of multiple traits is extended to the simultaneous mapping of newly defined genetic effects to improve the power of QTL detection and distinguish between dominance and overdominance.