BackgroundThe Bayesian shrinkage technique has been applied to multiple quantitative trait loci (QTLs) mapping to estimate the genetic effects of QTLs on quantitative traits from a very large set of possible effects including the main and epistatic effects of QTLs. Although the recently developed empirical Bayes (EB) method significantly reduced computation comparing with the fully Bayesian approach, its speed and accuracy are limited by the fact that numerical optimization is required to estimate the variance components in the QTL model.ResultsWe developed a fast empirical Bayesian LASSO (EBLASSO) method for multiple QTL mapping. The fact that the EBLASSO can estimate the variance components in a closed form along with other algorithmic techniques render the EBLASSO method more efficient and accurate. Comparing with the EB method, our simulation study demonstrated that the EBLASSO method could substantially improve the computational speed and detect more QTL effects without increasing the false positive rate. Particularly, the EBLASSO algorithm running on a personal computer could easily handle a linear QTL model with more than 100,000 variables in our simulation study. Real data analysis also demonstrated that the EBLASSO method detected more reasonable effects than the EB method. Comparing with the LASSO, our simulation showed that the current version of the EBLASSO implemented in Matlab had similar speed as the LASSO implemented in Fortran, and that the EBLASSO detected the same number of true effects as the LASSO but a much smaller number of false positive effects.ConclusionsThe EBLASSO method can handle a large number of effects possibly including both the main and epistatic QTL effects, environmental effects and the effects of gene-environment interactions. It will be a very useful tool for multiple QTL mapping.

Arsenic hyperaccumulator fern Pteris vittata L. produces large amounts of root exudates that are hypothesized to solubilize arsenic and maintain a unique rhizosphere microbial community. Total heterotrophic counts on rich or defined media supplemented with up to 400 mmol/L of arsenate showed a diverse arsenate-resistant microbial community from the rhizosphere of P. vittata growing in arsenic-contaminated sites. Twelve bacterial isolates tolerating 400 mmol/L of arsenate in liquid culture were identified. Selected bacterial isolates belonging to different genera were tested for their resistance to osmotic and oxidative stresses. Results showed that growth was generally better under osmotic stress generated by arsenic than under that generated by NaCl or PEG 6000, demonstrating that arsenic detoxification metabolism also cross-protected bacterial isolates from arsenic-induced osmotic stress. After 32 h of growth, all arsenate at 1 mmol/L was reduced to arsenite by strains Naxibacter sp. AH4, Mesorhizobium sp. AH5, and Pseudomonas sp. AH21, but arsenite at 1 mmol/L remained unchanged. Sensitivity to hydrogen peroxide was similar to that in broad-host pathogen Salmonella enterica sv. Typhimurium wild type, except strain AH4. The results suggested that these arsenic-resistant bacteria are metabolically adapted to arsenic-induced osmotic or oxidative stresses in addition to the specific bacterial system to exclude cellular arsenic. Both these adaptations contribute to the high arsenic resistance in the bacterial isolates.

In multiple quantitative trait locus (QTL) mapping, a high-dimensional sparse regression model is usually employed to account for possible multiple linked QTLs. The QTL model may include closely linked and thus highly correlated genetic markers, especially when high-density marker maps are used in QTL mapping because of the advancement in sequencing technology. Although existing algorithms, such as Lasso, empirical Bayesian Lasso (EBlasso) and elastic net (EN) are available to infer such QTL models, more powerful methods are highly desirable to detect more QTLs in the presence of correlated QTLs. We developed a novel empirical Bayesian EN (EBEN) algorithm for multiple QTL mapping that inherits the efficiency of our previously developed EBlasso algorithm. Simulation results demonstrated that EBEN provided higher power of detection and almost the same false discovery rate compared with EN and EBlasso. Particularly, EBEN can identify correlated QTLs that the other two algorithms may fail to identify. When analyzing a real dataset, EBEN detected more effects than EN and EBlasso. EBEN provides a useful tool for inferring high-dimensional sparse model in multiple QTL mapping and other applications. An R software package 'EBEN' implementing the EBEN algorithm is available on the Comprehensive R Archive Network (CRAN).

BackgroundComplex binary traits are influenced by many factors including the main effects of many quantitative trait loci (QTLs), the epistatic effects involving more than one QTLs, environmental effects and the effects of gene-environment interactions. Although a number of QTL mapping methods for binary traits have been developed, there still lacks an efficient and powerful method that can handle both main and epistatic effects of a relatively large number of possible QTLs.ResultsIn this paper, we use a Bayesian logistic regression model as the QTL model for binary traits that includes both main and epistatic effects. Our logistic regression model employs hierarchical priors for regression coefficients similar to the ones used in the Bayesian LASSO linear model for multiple QTL mapping for continuous traits. We develop efficient empirical Bayesian algorithms to infer the logistic regression model. Our simulation study shows that our algorithms can easily handle a QTL model with a large number of main and epistatic effects on a personal computer, and outperform five other methods examined including the LASSO, HyperLasso, BhGLM, RVM and the single-QTL mapping method based on logistic regression in terms of power of detection and false positive rate. The utility of our algorithms is also demonstrated through analysis of a real data set. A software package implementing the empirical Bayesian algorithms in this paper is freely available upon request.ConclusionsThe EBLASSO logistic regression method can handle a large number of effects possibly including the main and epistatic QTL effects, environmental effects and the effects of gene-environment interactions. It will be a very useful tool for multiple QTLs mapping for complex binary traits.

Although rice yield has been doubled in most parts of the world since 1960s, thanks to the advancements in breeding technologies, the biological mechanisms controlling yield are largely unknown. To understand the genetic basis of rice yield, a number of quantitative trait locus (QTL) mapping studies have been carried out, but whole-genome QTL mapping incorporating all interaction effects is still lacking. In this paper, we exploited whole-genome markers of an immortalized F2 population derived from an elite rice hybrid to perform QTL mapping for rice yield characterized by yield per plant and three yield component traits. Our QTL model includes additive and dominance main effects of 1,619 markers and all pair-wise interactions, with a total of more than 5 million possible effects. The QTL mapping identified 54, 5, 28 and 4 significant effects involving 103, 9, 52 and 7 QTLs for the four traits, namely the number of panicles per plant, the number of grains per panicle, grain weight, and yield per plant. Most identified QTLs are involved in digenic interactions. An extensive literature survey of experimentally characterized genes related to crop yield shows that 19 of 54 effects, 4 of 5 effects, 12 of 28 effects and 2 of 4 effects for the four traits, respectively, involve at least one QTL that locates within 2 cM distance to at least one yield-related gene. This study not only reveals the major role of epistasis influencing rice yield, but also provides a set of candidate genetic loci for further experimental investigation.