Runqing Yang

Bayesian functional mapping of dynamic quantitative traits

Without consideration of other linked QTLs responsible for dynamic trait, original functional mapping based on a single QTL model is not optimal for analyzing multiple dynamic trait loci. Despite that composite functional mapping incorporates the effects of genetic background outside the tested QTL in mapping model, the arbitrary choice of background markers also impact on the power of QTL detection. In this study, we proposed Bayesian functional mapping strategy that can simultaneously identify multiple QTL controlling developmental patterns of dynamic traits over the genome. Our proposed method fits the change of each QTL effect with the time by Legendre polynomial and takes the residual covariance structure into account using the first autoregressive equation. Also, Bayesian shrinkage estimation was employed to estimate the model parameters. Especially, we specify the gamma distribution as the prior for the first-order auto-regressive coefficient, which will guarantee the convergence of Bayesian sampling. Simulations showed that the proposed method could accurately estimate the QTL parameters and had a greater statistical power of QTL detection than the composite functional mapping. A real data analysis of leaf age growth in rice is used for the demonstration of our method. It shows that our Bayesian functional mapping can detect more QTLs as compared to composite functional mapping.

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.

Bayesian analysis of interacting quantitative trait loci (QTL) for yield traits in tomato

An F 2 population derived from the hybrid of Lycopersicon esculentum Mill.XF98-7×Lycopersicon pimpinellifolium LA2184 was used for genome-wide linkage analysis for yield traits in tomato. The genetic map, spanning the tomato genome of 808.4 cM long was constructed with 112 SSR markers distributing on 16 linkage groups. Main and epistatic effect QTLs controlling first flower node, number of flowers per truss, fruit set percentage and fruit weight were located using Bayesian model selection method. A total of 20 significant main effect QTLs and 16 pairs of epistatic QTLs were identified on 16 linkage groups. The proportions of phenotypic variation explained by the detected QTLs ranged from 1.9 to 25.9% and from 0.00 to 17.4% for main-effect and epistatic QTLs, respectively. Most QTL effects were predictable from the parental phenotypes. Additionally, one QTL was found to be pleiotropic, governing simultaneously first flower node and number of flowers per truss.

An optimal parametric proportional hazards model for mapping heading time loci in rice

Usually, statistical methods for mapping quantitative trait loci (QTL) require that the phenotypes follow the normal distribution and therefore may not be appropriate to analyze survival traits of skewed distribution. As a result, parametric and semi-parametric models in survival analysis are incorporated into the framework of the interval mapping for survival trait loci. Through formulating the effects of the QTL genotype on the survival time with a Cox proportional hazards model, we construct a general parametric model for mapping survival trait loci, in which baseline hazard function is selectable for goodness of fit to the effects of QTL genotype on survival curve. Bayesian information criterion is used to choose the optimal baseline hazard function with maximum likelihood and parsimonious parameters. Heading time, defined by days from sowing to heading is a typical survival trait. In this study, we apply the mapping method to locate QTL for heading time in rice and conclude that among the six commonly used survival distributions, Gamma distribution is the optimal baseline hazard function and by which, four QTLs are identified.

Generalized F accelerated failure time model for mapping survival trait loci.

As the two most popular models in survival analysis, the accelerated failure time (AFT) model can more easily fit survival data than the Cox proportional hazards model (PHM). In this study, we develop a general parametric AFT model for identifying survival trait loci, in which the flexible generalized F distribution, including many commonly used distributions as special cases, is specified as the baseline survival distribution. EM algorithm for maximum likelihood estimation of model parameters is given. Simulations are conducted to validate the flexibility and the utility of the proposed mapping procedure. In analyzing survival time following hyperoxic acute lung injury (HALI) of mice in an F(2) mating population, the generalized F distribution performed best among the six competing survival distributions and detected four QTLs controlling differential HALI survival.

Bayesian mapping of genome-wide epistatic imprinted loci for quantitative traits

Genomic imprinting, an epigenetic phenomenon of parent-of-origin-specific gene expression, has been widely observed in plants, animals, and humans. To detect imprinting genes influencing quantitative traits, the least squares and maximum likelihood approaches for fitting a single quantitative trait locus (QTL) and Bayesian methods for simultaneously modeling multiple QTL have been adopted, respectively, in various studies. However, most of these studies have only estimated imprinting main effects and thus ignored imprinting epistatic effects. In the presence of extremely complex genomic imprinting architectures, we introduce a Bayesian model selection method to analyze the multiple interacting imprinted QTL (iQTL) model. This approach will greatly enhance the computational efficiency through setting the upper bound of the number of QTLs and performing selective sampling for QTL parameters. The imprinting types of detected main-effect QTLs can be estimated from the Bayes factor statistic formulated by the posterior probabilities for the genetic effects being compared. The performance of the proposed method is demonstrated by several simulation experiments. Moreover, this method is applied to dissect the imprinting genetic architecture for body weight in mouse and fruit weight in tomato. Matlab code for implementing this approach will be available from the authors upon request.

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.