Method For QTL Mapping Under Complicated Mating Designs

In recent years, there has been an increasing interest in the development ofmethodology to map quantitative trait loci (QTLs) relative to known marker map inpopulation derived from inbred line crosses. However, mapping populations that can behandled by most of developed methods must be derived from the cross of two inbredlines. The drawback of these designs is that the statistical inference space is quite narrowand the mapping results of one cross can not be generalized to other crosses derived fromdifferent inbred lines. Therefore, it has become a new trend in QTL mapping communityto use segregation population derived from the cross of multiple inbred lines or tocombine multiple existent populations. But current statistical methods and computerprograms of QTL mapping are mostly designed for single line cross. In this paper,methods for QTL mapping in four-way cross design and in eight-way cross design wereproposed. Then the method of QTL mapping in multiple related populations derived fromtwo parents was proposed, which was further extended to handle multiple relatedpopulations derived from multiple parents. Computer simulations were performed tovalidate these proposed methods in this research. Furthermore, Bayesian mapping ofQTL in multiple related populations was explored in the last section of this paper.1 Maximum Likelihood Method for Mapping QTL in Four-way CrossDesignFour-way cross design is derived from the cross of four inbred lines. Althoughiteratively reweighted least squares (IRWLS) method for mapping QTL in four-waycross design has been proposed, low efficiency of this method was found due toneglecting the mixture distribution of QTL genotypes. In this paper, based on the quantitative genetic model of four-way cross design and the mixture distribution theory,a new method of QTL mapping for four-way cross design was proposed. The conditionalprobabilities of QTL genotypes at a putative QTL position on chromosome werecalculated jointly by using all of marker genotypes on this chromosome. The parameterswere estimated through a maximum likelihood method implemented via EM algorithm.The power of detection, accuracy and precision of QTL mapping under different QTLheritabilities, sample sizes and molecular marker polymorphism information contentswere studied with simulated data. The results showed: (1) In the efficiency of QTLdetection, four-way cross with incomplete genotypic information of DNA molecularmarkers was less powerful than the four-way cross without incomplete markers. (2) Theaccuracy and precision of estimates of QTL positions and effects enhanced as theincreasing of QTL heritability, sample size and polymorphism information content ofmolecular marker.2 Interval Mapping Method of QTL for Eight-Way Cross DesignBased on QTL mapping for four-way cross design, a quantitative genetic model ofeight-way cross design was proposed. Then the two-locus probabilities transition matrixof this design was inferred and a maximum likelihood method implemented via EMalgorithm was developed based on the theory of mixture distribution. Validity of themethod was demonstrated using two different simulation strategies. The first strategywas based on single chromosome and the second one was on the whole genome. Theresults showed that: (1) In the first strategy, the statistical powers of all the treatmentsreached 100%. Concerning the accuracy of parameters estimates, most of the estimateswere close to their true values in the treatments with complete molecular markerinformation. Whereas estimates of QTL effects were biased in the treatments withincomplete molecular marker information, but the biases were very small. The precisionof parameters estimates was improved with the increase of the QTL heritability, sample size and polymorphism information content. (2) In the second strategy, the statisticalpowers of all QTL reached greater than 94% as sample size was 1000. The statisticalpowers of QTL with higher heritability reached higher than 90% as sample size was 500,while the statistical powers of QTL with lower heritability was only 74%. So biggersample size will be needed to improve statistical power in the second strategy.Meanwhile, the statistical powers were not significantly influenced by two QTL locatingon the same chromosome and incomplete information. For the accuracy and precision ofQTL positions and effects estimates, except that the position estimates of five QTLswere very accurate, the estimates of other parameters performed the same trend as in thefirst strategy, i.e., the accuracy and precision of QTL estimates were increased with theincrease of sample size and QTL heritability. In addition, marker segregation distortiondoes not significantly reduce the statistical power of QTL detection, the accuracy andprecision of QTL parameter estimates.3 QTL Mapping in Multiple Related Populations Derived from TwoParentsMost of the current methods for QTL mapping are designed for the singlesegregation population derived from the cross of two inbred lines. Incorporating theexisting populations derived from two parents may improve QTL mapping andQTL-based breeding programs. However, no general maximum likelihood method hasbeen available for this strategy. In this paper, the general mapping method that cancombine multiple related populations derived from two parents was proposed. Computersimulations were performed to validate the proposed method in our research. Taking thejoint analysis of F₂ and BC populations for example, the results showed that: (1) underthe same heritability, the method jointing two populations obtained higher power than theone treating the two populations respectively. Moreover, when the sample size of jointinganalysis amounted to that of single population analysis, the statistical power of jointanalysis was also higher than that of single population analysis. For example, under 5% heritability, when 50 individuals were included in F2 and BC population respectively, thestatistical power of joint analysis was about 59%, which were, however, only 29% and39% when F2 and BC population were analyzed respectively, and there were 100individuals included in each population. The same conclusion was observed in parameterestimation. Under the same heritability, the accuracy and precision of method jointingtwo populations were higher than that of method analyzing the population respectively,especially for those treatments with lower heritabilities and smaller sample sizes.Moreover, higher QTL heritability and larger sample sizes can lead to not only higherstatistical power, but also more accurate and precise estimates. (2) A whole genome wassimulated to further verify the utility of the method. Satisfactory results were also found.4 QTL Mapping in Multiple Related Populations Derived from MultipleParentsBased on the QTL mapping in multiple related populations derived from twoparents, a ML estimation method that can incorporate several populations derived fromthree or more parents and can be used to handle different mating designs was proposed.Taking the circle design for example, simulation studies were performed to study theimpact of QTL heritability and sample size upon this proposed method. The resultsshowed that (1) Under the same heritability, higher QTL detection power and moreexact and accurate estimation of parameter can be obtained when three F₂ populationswere analyzed jointly than when only any two F₂ populations were analyzedsimultaneously. (2) Higher heritability, and especially with larger sample sizes willincrease the ability of QTL detection and improve the estimation of parameter. Potentialassets of the method are as follows: (1) The existing results of QTL mapping in singlepopulation can be compared and integrated with each other using this proposed method,so the ability of QTL detection and precision of QTL mapping can be improved. (2)Owing to multiple alleles in multiple parents, the method can exploit gene resourcemore adequately, which will establish an important genetic base for plant improvement. 5 Bayesian Mapping of QTL in Multiple Related PopulationsFirst, the Bayesian method applied to single QTL analysis in F₂ mapping populationwas introduced. The method may obtain the Bayesian estimation of QTL genotypes,position, effects and model residual variance simultaneously. Its feasibility and validitywere analyzed with simulated data. The results showed that although the accuracy ofestimates of QTL position and effects can enhance as the increasing of QTL heritability,the differences were very small among different treatments with 5%, 10%, and 20% ofQTL heritability. However, the precision of estimates enhance significantly with theincreasing of QTL heritability. This result indicates that the appropriate sample size isnecessary for the treatments with low heritability to ensure the precision of estimates ofQTL position and effects. Secondly, based on Yi and Xu's method for QTL mappingusing complicated multiple line crosses under an irregular mating system, amodel-selection-free mapping method for multiple populations was proposed in thispaper, i.e., Bayesian shrinkage estimation method and QTL jointing analysis in multiplepopulations were married. The method proceeds as follows: First, the joint posteriordistribution was inferred based on prior distribution of parameters and real experimentdata. Then, the marginal distribution of each parameter was inferred and the point andinterval estimations of each parameter were confirmed using the MCMC method.MCMC method was implemented via Metropolis-Hastings and Gibbs algorithm. Themodel parameters include QTL position in each marker interval, QTL effects and theresidual variance of model et al.