Robust Bayesian mapping of quantitative trait loci using Student-t distribution for residual

In most quantitative trait loci (QTL) mapping studies, phenotypes are assumed to follow normal distributions. Deviations from this assumption may affect the accuracy of QTL detection, leading to detection of false positive QTL. To improve the robustness of QTL mapping methods, we replace the normal distribution assumption for residuals in a multiple QTL model with a Student-t distribution that is able to accommodate residual outliers. A Robust Bayesian mapping strategy is proposed on the basis of the Bayesian shrinkage analysis for QTL effects. The simulations show that Robust Bayesian mapping approach can substantially increase the power of QTL detection when the normality assumption does not hold and applying it to data already normally distributed does not influence the result. The proposed QTL mapping method is applied to mapping QTL for the traits associated with physics–chemical characters and quality in rice. Similarly to the simulation study in the real data case the robust approach was able to detect additional QTLs when compared to the traditional approach. The program to implement the method is available on request from the first or the corresponding author. Xin Wang and Zhongze Piao contributed equally to this study.     

Lineage-specific mapping of quantitative trait loci

We present an approach for quantitative trait locus (QTL) mapping, termed as ‘lineage-specific QTL mapping'', for inferring allelic changes of QTL evolution along with branches in a phylogeny. We describe and analyze the simplest case: by adding a third taxon into the normal procedure of QTL mapping between pairs of taxa, such inferences can be made along lineages to a presumed common ancestor. Although comparisons of QTL maps among species can identify homology of QTLs by apparent co-location, lineage-specific mapping of QTL can classify homology into (1) orthology (shared origin of QTL) versus (2) paralogy (independent origin of QTL within resolution of map distance). In this light, we present a graphical method that identifies six modes of QTL evolution in a three taxon comparison. We then apply our model to map lineage-specific QTLs for inbreeding among three taxa of yellow monkey-flower: Mimulus guttatus and two inbreeders M. platycalyx and M. micranthus, but critically assuming outcrossing was the ancestral state. The two most common modes of homology across traits were orthologous (shared ancestry of mutation for QTL alleles). The outbreeder M. guttatus had the fewest lineage-specific QTL, in accordance with the presumed ancestry of outbreeding. Extensions of lineage-specific QTL mapping to other types of data and crosses, and to inference of ancestral QTL state, are discussed.     

Bayesian robust analysis for genetic architecture of quantitative traits

MOTIVATION: In most quantitative trait locus (QTL) mapping studies, phenotypes are assumed to follow normal distributions. Deviations from this assumption may affect the accuracy of QTL detection and lead to detection of spurious QTLs. To improve the robustness of QTL mapping methods, we replaced the normal distribution for residuals in multiple interacting QTL models with the normal/independent distributions that are a class of symmetric and long-tailed distributions and are able to accommodate residual outliers. Subsequently, we developed a Bayesian robust analysis strategy for dissecting genetic architecture of quantitative traits and for mapping genome-wide interacting QTLs in line crosses. RESULTS: Through computer simulations, we showed that our strategy had a similar power for QTL detection compared with traditional methods assuming normal-distributed traits, but had a substantially increased power for non-normal phenotypes. When this strategy was applied to a group of traits associated with physical/chemical characteristics and quality in rice, more main and epistatic QTLs were detected than traditional Bayesian model analyses under the normal assumption.     

Statistical optimization of parametric accelerated failure time model for mapping survival trait loci

Most existing statistical methods for mapping quantitative trait loci (QTL) are not suitable for analyzing survival traits with a skewed distribution and censoring mechanism. As a result, researchers incorporate parametric and semi-parametric models of survival analysis into the framework of the interval mapping for QTL controlling survival traits. In survival analysis, accelerated failure time (AFT) model is considered as a de facto standard and fundamental model for data analysis. Based on AFT model, we propose a parametric approach for mapping survival traits using the EM algorithm to obtain the maximum likelihood estimates of the parameters. Also, with Bayesian information criterion (BIC) as a model selection criterion, an optimal mapping model is constructed by choosing specific error distributions with maximum likelihood and parsimonious parameters. Two real datasets were analyzed by our proposed method for illustration. The results show that among the five commonly used survival distributions, Weibull distribution is the optimal survival function for mapping of heading time in rice, while Log-logistic distribution is the optimal one for hyperoxic acute lung injury.     

The distribution of the effects of genes affecting quantitative traits in livestock

Meta-analysis of information from quantitative trait loci (QTL) mapping experiments was used to derive distributions of the effects of genes affecting quantitative traits. The two limitations of such information, that QTL effects as reported include experimental error, and that mapping experiments can only detect QTL above a certain size, were accounted for. Data from pig and dairy mapping experiments were used. Gamma distributions of QTL effects were fitted with maximum likelihood. The derived distributions were moderately leptokurtic, consistent with many genes of small effect and few of large effect. Seventeen percent and 35% of the leading QTL explained 90% of the genetic variance for the dairy and pig distributions respectively. The number of segregating genes affecting a quantitative trait in dairy populations was predicted assuming genes affecting a quantitative trait were neutral with respect to fitness. Between 50 and 100 genes were predicted, depending on the effective population size assumed. As data for the analysis included no QTL of small effect, the ability to estimate the number of QTL of small effect must inevitably be weak. It may be that there are more QTL of small effect than predicted by our gamma distributions. Nevertheless, the distributions have important implications for QTL mapping experiments and Marker Assisted Selection (MAS). Powerful mapping experiments, able to detect QTL of 0.1σ_p, will be required to detect enough QTL to explain 90% the genetic variance for a quantitative trait.     

Test for positional candidate genes for body composition on pig chromosome 6

One QTL affecting backfat thickness (BF), intramuscular fat content (IMF) and eye muscle area (MA) was previously localized on porcine chromosome 6 in an F₂ cross between Iberian and Landrace pigs. This work was done to study the effect of two positional candidate genes on these traits: H-FABP and LEPR genes. The QTL mapping analysis was repeated with a regression method using genotypes for seven microsatellites and two PCR-RFLPs in the H-FABP and LEPR genes. H-FABP and LEPR genes were located at 85.4 and 107 cM respectively, by linkage analysis. The effects of the candidate gene polymorphisms were analyzed in two ways. When an animal model was fitted, both genes showed significant effects on fatness traits, the H-FABP polymorphism showed significant effects on IMF and MA, and the LEPR polymorphism on BF and IMF. But when the candidate gene effect was included in a QTL regression analysis these associations were not observed, suggesting that they must not be the causal mutations responsible for the effects found. Differences in the results of both analyses showed the inadequacy of the animal model approach for the evaluation of positional candidate genes in populations with linkage disequilibrium, when the probabilities of the parental origin of the QTL alleles are not included in the model.     

A note on QTL detecting for censored traits

Most existing statistical methods for mapping quantitative trait loci (QTL) assume that the phenotype follows a normal distribution and that it is fully observed. However, some phenotypes have skewed distributions and may be censored. This note proposes a simple and efficient approach to QTL detecting for censored traits with the Cox PH model without estimating the baseline hazard function which is "nuisance".     

Quantitative Genetic Analysis Indicates Natural Selection on Leaf Phenotypes Across Wild Tomato Species (Solanum sect. Lycopersicon; Solanaceae)

Adaptive evolution requires both raw genetic material and an accessible path of high fitness from one fitness peak to another. In this study, we used an introgression line (IL) population to map quantitative trait loci (QTL) for leaf traits thought to be associated with adaptation to precipitation in wild tomatoes (Solanum sect. Lycopersicon; Solanaceae). A QTL sign test showed that several traits likely evolved under directional natural selection. Leaf traits correlated across species do not share a common genetic basis, consistent with a scenario in which selection maintains trait covariation unconstrained by pleiotropy or linkage disequilibrium. Two large effect QTL for stomatal distribution colocalized with key genes in the stomatal development pathway, suggesting promising candidates for the molecular bases of adaptation in these species. Furthermore, macroevolutionary transitions between vastly different stomatal distributions may not be constrained when such large-effect mutations are available. Finally, genetic correlations between stomatal traits measured in this study and data on carbon isotope discrimination from the same ILs support a functional hypothesis that the distribution of stomata affects the resistance to CO₂ diffusion inside the leaf, a trait implicated in climatic adaptation in wild tomatoes. Along with evidence from previous comparative and experimental studies, this analysis indicates that leaf traits are an important component of climatic niche adaptation in wild tomatoes and demonstrates that some trait transitions between species could have involved few, large-effect genetic changes, allowing rapid responses to new environmental conditions.     

Genetic Architecture of Natural Variation of Telomere Length in Arabidopsis thaliana

Telomeres represent the repetitive sequences that cap chromosome ends and are essential for their protection. Telomere length is known to be highly heritable and is derived from a homeostatic balance between telomeric lengthening and shortening activities. Specific loci that form the genetic framework underlying telomere length homeostasis, however, are not well understood. To investigate the extent of natural variation of telomere length in Arabidopsis thaliana, we examined 229 worldwide accessions by terminal restriction fragment analysis. The results showed a wide range of telomere lengths that are specific to individual accessions. To identify loci that are responsible for this variation, we adopted a quantitative trait loci (QTL) mapping approach with multiple recombinant inbred line (RIL) populations. A doubled haploid RIL population was first produced using centromere-mediated genome elimination between accessions with long (Pro-0) and intermediate (Col-0) telomere lengths. Composite interval mapping analysis of this population along with two established RIL populations (Ler-2/Cvi-0 and Est-1/Col-0) revealed a number of shared and unique QTL. QTL detected in the Ler-2/Cvi-0 population were examined using near isogenic lines that confirmed causative regions on chromosomes 1 and 2. In conclusion, this work describes the extent of natural variation of telomere length in A. thaliana, identifies a network of QTL that influence telomere length homeostasis, examines telomere length dynamics in plants with hybrid backgrounds, and shows the effects of two identified regions on telomere length regulation.     

Bayesian LASSO for quantitative trait loci mapping

The mapping of quantitative trait loci (QTL) is to identify molecular markers or genomic loci that influence the variation of complex traits. The problem is complicated by the facts that QTL data usually contain a large number of markers across the entire genome and most of them have little or no effect on the phenotype. In this article, we propose several Bayesian hierarchical models for mapping multiple QTL that simultaneously fit and estimate all possible genetic effects associated with all markers. The proposed models use prior distributions for the genetic effects that are scale mixtures of normal distributions with mean zero and variances distributed to give each effect a high probability of being near zero. We consider two types of priors for the variances, exponential and scaled inverse-chi(2) distributions, which result in a Bayesian version of the popular least absolute shrinkage and selection operator (LASSO) model and the well-known Student's t model, respectively. Unlike most applications where fixed values are preset for hyperparameters in the priors, we treat all hyperparameters as unknowns and estimate them along with other parameters. Markov chain Monte Carlo (MCMC) algorithms are developed to simulate the parameters from the posteriors. The methods are illustrated using well-known barley data.     

Positional cloning of rp2 QTL associates the P450 genes CYP6Z1, CYP6Z3 and CYP6M7 with pyrethroid resistance in the malaria vector Anopheles funestus

Pyrethroid resistance in Anopheles funestus is threatening malaria control in Africa. Elucidation of underlying resistance mechanisms is crucial to improve the success of future control programs. A positional cloning approach was used to identify genes conferring resistance in the uncharacterised rp2 quantitative trait locus (QTL) previously detected in this vector using F6 advanced intercross lines (AIL). A 113 kb BAC clone spanning rp2 was identified and sequenced revealing a cluster of 15 P450 genes and one salivary protein gene (SG7-2). Contrary to A. gambiae, AfCYP6M1 is triplicated in A. funestus, while AgCYP6Z2 orthologue is absent. Five hundred and sixty-five new single nucleotide polymorphisms (SNPs) were identified for genetic mapping from rp2 P450s and other genes revealing high genetic polymorphisms with one SNP every 36 bp. A significant genotype/phenotype association was detected for rp2 P450s but not for a cluster of cuticular protein genes previously associated with resistance in A. gambiae. QTL mapping using F6 AIL confirms the rp2 QTL with an increase logarithm of odds score of 5. Multiplex gene expression profiling of 15 P450s and other genes around rp2 followed by individual validation using qRT–PCR indicated a significant overexpression in the resistant FUMOZ-R strain of the P450s AfCYP6Z1, AfCYP6Z3, AfCYP6M7 and the glutathione-s-transferase GSTe2 with respective fold change of 11.2, 6.3, 5.5 and 2.8. Polymorphisms analysis of AfCYP6Z1 and AfCYP6Z3 identified amino acid changes potentially associated with resistance further indicating that these genes are controlling the pyrethroid resistance explained by the rp2 QTL. The characterisation of this rp2 QTL significantly improves our understanding of resistance mechanisms in A. funestus.     

Effector-Triggered Immune Response in Arabidopsis thaliana Is a Quantitative Trait

We identified loci responsible for natural variation in Arabidopsis thaliana (Arabidopsis) responses to a bacterial pathogen virulence factor, HopAM1. HopAM1 is a type III effector protein secreted by the virulent Pseudomonas syringae strain Pto DC3000. Delivery of HopAM1 from disarmed Pseudomonas strains leads to local cell death, meristem chlorosis, or both, with varying intensities in different Arabidopsis accessions. These phenotypes are not associated with differences in bacterial growth restriction. We treated the two phenotypes as quantitative traits to identify host loci controlling responses to HopAM1. Genome-wide association (GWA) of 64 Arabidopsis accessions identified independent variants highly correlated with response to each phenotype. Quantitative trait locus (QTL) mapping in a recombinant inbred population between Bur-0 and Col-0 accessions revealed genetic linkage to regions distinct from the top GWA hits. Two major QTL associated with HopAM1-induced cell death were also associated with HopAM1-induced chlorosis. HopAM1-induced changes in Arabidopsis gene expression showed that rapid HopAM1-dependent cell death in Bur-0 is correlated with effector-triggered immune responses. Studies of the effect of mutations in known plant immune system genes showed, surprisingly, that both cell death and chlorosis phenotypes are enhanced by loss of EDS1, a regulatory hub in the plant immune-signaling network. Our results reveal complex genetic architecture for response to this particular type III virulence effector, in contrast to the typical monogenic control of cell death and disease resistance triggered by most type III effectors.     

Editor's Choice: Polygenic Molecular Architecture Underlying Non-Sexual Cell Aggregation in Budding Yeast

Cell aggregation in unicellular organisms, induced by either cell non-sexual adhesion to yield flocs and biofilm, or pheromone-driving sexual conjugation is of great significance in cellular stress response, medicine, and brewing industries. Most current literatures have focused on one form of cell aggregation termed flocculation and its major molecular determinants, the flocculation (FLO) family genes. Here, we implemented a map-based approach for dissecting the molecular basis of non-sexual cell aggregation in Saccharomyces cerevisiae. Genome-wide mapping has identified four major quantitative trait loci (QTL) underlying nature variation in the cell aggregation phenotype. High-resolution mapping following up with knockout and allele replacement experiments resolved the QTL into the underlying genes (AMN1, RGA1, FLO1, and FLO8) or even into the causative nucleotide. Genetic variation in the QTL genes can explain up to 46% of phenotypic variation of this trait. Of these genes, AMN1 plays the leading role, differing from the FLO family members, in regulating expression of cell clumping phenotype through inducing cell segregation defect. These findings provide novel insights into the molecular mechanism of how cell aggregation is regulated in budding yeast, and the data will be directly implicated to understand the molecular basis and evolutionary implications of cell aggregation in other fungus species.     

Objective Bayesian analysis for the Student-t regression model

We develop a Bayesian analysis based on two different Jeffreyspriors for the Student-t regression model with unknown degreesof freedom. It is typically difficult to estimate the numberof degrees of freedom: improper prior distributions may leadto improper posterior distributions, whereas proper prior distributionsmay dominate the analysis. We show that Bayesian analysis witheither of the two considered Jeffreys priors provides a properposterior distribution. Finally, we show that Bayesian estimatorsbased on Jeffreys analysis compare favourably to other Bayesianestimators based on priors previously proposed in the literature.     

Genome-wide QTL mapping of saltwater tolerance in sibling species of Anopheles (malaria vector) mosquitoes

Although freshwater (FW) is the ancestral habitat for larval mosquitoes, multiple species independently evolved the ability to survive in saltwater (SW). Here, we use quantitative trait locus (QTL) mapping to investigate the genetic architecture of osmoregulation in Anopheles mosquitoes, vectors of human malaria. We analyzed 1134 backcross progeny from a cross between the obligate FW species An. coluzzii, and its closely related euryhaline sibling species An. merus. Tests of 2387 markers with Bayesian interval mapping and machine learning (random forests) yielded six genomic regions associated with SW tolerance. Overlap in QTL regions from both approaches enhances confidence in QTL identification. Evidence exists for synergistic as well as disruptive epistasis among loci. Intriguingly, one QTL region containing ion transporters spans the 2Rop chromosomal inversion that distinguishes these species. Rather than a simple trait controlled by one or a few loci, our data are most consistent with a complex, polygenic mode of inheritance.     

Bayesian mapping of quantitative trait loci for complex binary traits

A complex binary trait is a character that has a dichotomous expression but with a polygenic genetic background. Mapping quantitative trait loci (QTL) for such traits is difficult because of the discrete nature and the reduced variation in the phenotypic distribution. Bayesian statistics are proved to be a powerful tool for solving complicated genetic problems, such as multiple QTL with nonadditive effects, and have been successfully applied to QTL mapping for continuous traits. In this study, we show that Bayesian statistics are particularly useful for mapping QTL for complex binary traits. We model the binary trait under the classical threshold model of quantitative genetics. The Bayesian mapping statistics are developed on the basis of the idea of data augmentation. This treatment allows an easy way to generate the value of a hypothetical underlying variable (called the liability) and a threshold, which in turn allow the use of existing Bayesian statistics. The reversible jump Markov chain Monte Carlo algorithm is used to simulate the posterior samples of all unknowns, including the number of QTL, the locations and effects of identified QTL, genotypes of each individual at both the QTL and markers, and eventually the liability of each individual. The Bayesian mapping ends with an estimation of the joint posterior distribution of the number of QTL and the locations and effects of the identified QTL. Utilities of the method are demonstrated using a simulated outbred full-sib family. A computer program written in FORTRAN language is freely available on request.     

Bayesian mapping of quantitative trait loci under the identity-by-descent-based variance component model

Variance component analysis of quantitative trait loci (QTL) is an important strategy of genetic mapping for complex traits in humans. The method is robust because it can handle an arbitrary number of alleles with arbitrary modes of gene actions. The variance component method is usually implemented using the proportion of alleles with identity-by-descent (IBD) shared by relatives. As a result, information about marker linkage phases in the parents is not required. The method has been studied extensively under either the maximum-likelihood framework or the sib-pair regression paradigm. However, virtually all investigations are limited to normally distributed traits under a single QTL model. In this study, we develop a Bayes method to map multiple QTL. We also extend the Bayesian mapping procedure to identify QTL responsible for the variation of complex binary diseases in humans under a threshold model. The method can also treat the number of QTL as a parameter and infer its posterior distribution. We use the reversible jump Markov chain Monte Carlo method to infer the posterior distributions of parameters of interest. The Bayesian mapping procedure ends with an estimation of the joint posterior distribution of the number of QTL and the locations and variances of the identified QTL. Utilities of the method are demonstrated using a simulated population consisting of multiple full-sib families.     

A novel sex-determining QTL in Nile tilapia (Oreochromis niloticus)

Background

Fish species often exhibit significant sexual dimorphism for commercially important traits. Accordingly, the control of phenotypic sex, and in particular the production of monosex cultures, is of particular interest to the aquaculture industry. Sex determination in the widely farmed Nile tilapia (Oreochromis niloticus) is complex, involving genomic regions on at least three chromosomes (chromosomes 1, 3 and 23) and interacting in certain cases with elevated early rearing temperature as well. Thus, sex ratios may vary substantially from 50%.

Results

This study focused on mapping sex-determining quantitative trait loci (QTL) in families with skewed sex ratios. These included four families that showed an excess of males (male ratio varied between 64% and 93%) when reared at standard temperature (28°C) and a fifth family in which an excess of males (96%) was observed when fry were reared at 36°C for ten days from first feeding. All the samples used in the current study were genotyped for two single-nucleotide polymorphisms (rs397507167 and rs397507165) located in the expected major sex-determining region in linkage group 1 (LG 1). The only misassigned individuals were phenotypic males with the expected female genotype, suggesting that those offspring had undergone sex-reversal with respect to the major sex-determining locus. We mapped SNPs identified from double digest Restriction-site Associated DNA (ddRAD) sequencing in these five families. Three genetic maps were constructed consisting of 641, 175 and 1,155 SNPs from the three largest families. QTL analyses provided evidence for a novel genome-wide significant QTL in LG 20. Evidence was also found for another sex-determining QTL in the fifth family, in the proximal region of LG 1.

Conclusions

Overall, the results from this study suggest that these previously undetected QTLs are involved in sex determination in the Nile tilapia, causing sex reversal (masculinisation) with respect to the XX genotype at the major sex-determining locus in LG 1.

Electronic supplementary material

The online version of this article (doi:10.1186/s12864-015-1383-x) contains supplementary material, which is available to authorized users.