Bayesian Statistics-Based Mapping Of QTL Controlling Endosperm Traits In Cereals

The endosperm of crop seeds is an important source of human food. The genetic study of endosperm traits plays a fundamental and vital role in improving grain yield and quality. With the development of molecular marker technology and the construction of genetic linkage map, it is possible to search and map QTL controlling quantitative traits. This can be used in marker assisted selection for enhancing food production and improving food quality. Because genetic control system of endosperm is more complex than that of diploid, the mapping method for diploid traits has not been suitable to the mapping of triploid endosperm. So the researchers have proposed a series of models and methods for. QTL mapping of endosperm traits based on classical statistical algorithm to dissect the genetic architecture of quantitative traits of endosperm, such as the maximum likelihood method and iteractively reweighted least squares (IRWLS) method. In the recent ten years, with the development of modern statistics and high speed computer as well as MCMC algorithm, Bayesian statistics has been widely uesd in various research area, especically in QTL mapping of diploid traits. However, it has not been used in mapping QTL underlying triploid endosperm traits..In this paper, based on Bayesian statistics and quantitative genetic model of triploid endosperm traits, we first proposed a Bayesian method for mapping QTL underlying endosperm traits, which used the molecular marker genotypes of each plant in segregation population and the single endosperm observation of a few endosperms of each plant as data set to analyze endosperm QTL. The method was implemented via MCMC algorithm.The process of the method is summarized as follows:(1) Formulate single-QTL model and multiple-QTL model of endosperm traits. (2) Calculate the conditional probabilities of the QTL genotypes by using the molecular marker information. (3) Calculate the conditional posterior probabilities of the QTL genotypes. (4) Sample the QTL genotypes using the posterior probabilities and get the indicator variables of QTL genotypes. (5) Derive the conditional posterior distributions of population mean, additive effect, first dominance effect, second dominance effect, residual variance and the postions of QTL. (6) Sample the conditional posterior samples by using Gibbs sampling and Metropolis-Hastings algorithm. (7) Collect posterior samples and obtain the Bayesian estimates.By using the molecular marker genotypes of each plant in segregation population and the single endosperm observation of a few endosperms of each plant as data set, we proposed the interval mapping and the composite interval mapping methods for endosperm QTL. Efficiency of the methods is demonstrated via both chromosome level and genome level simulation studies.â… Bayesian Statistics-Based Interval Mapping of QTL Controlling Endosperm Traits in CerealsFor chromosome level simulation, the sample size of an F2 segeregating population was set on 200 plants and 20 endosperms of each plant. The QTL heritability was simulated at three levels:5%,10% and 20%, respectively. Each treatment of the simulation experiments was replicated 100 times. Precision and accuracy of estimates for QTL location and effects were measured by means and standard deviations of estimates respectively.For genome level simulation, a genome containing four chromosomes was simulated. Four QTL with different heritabilities were set at four different chromosomes. The QTL heritability was set at 6.07%,16.77%,23.96% and 13.21%, respectively.The results showed that (1) The power of each treatment was 100%; (2) Both the effect and position estimates of these QTL were reasonably close to the true value. (3) Higher QTL heritability tended to produce more accurate and precise estimates, whereas lower heritability produced less accurate estimates with large estimation errors, which was in accordance with our general expectations. (4) The genome level simulation showed that the proposed method not only clearly pick up the multiple QTL, but estimate the QTL parameters.â…¡Bayesian Statistics-Based Multiple Interval Mapping of QTL Controlling Endosperm Traits in Cereals Simulation study was set on 200 F2 plants each with 30 endosperms. A chromosome of length 100 cM covered by eleven evenly spaced markers was simulated. Three QTL affecting endosperm traits were set at 15cM,55cM and 95cM respectively. The population mean was set as 20. The QTL heritability was set at about 5%,10% and 15%. The simulation experiment was replicated 100 times. Precision and accuracy of estimates for QTL location and effects are measured same as above.The results showed that (1) The proposed Bayesian method had high statistical power and accurate estimates of QTL position, mean and additive effects. For example, even with the heritability of 5%, the statistical power can still reach 100%. (2) The two dominance effects were found slightly biased. This may have two possible reasons. The first reason is that the QTL genotype of F3 endosperms are just infered from the marker genotypes of F2 maternal genome other than from the marker genotypes of F3 endosperm genome. The second reason is that even if the additive and dominance effects had equal sizes, the variation caused by dominance effect just had a limited weight in the total genetic variance.