Mapping quantitative trait loci in outbred populations is important since development of inbred lines in livestock species is usually not feasible. Traditional genetic mapping methods, such as Least Squares and Maximum Likelihood, cannot fully accommodate complex pedigree structures, and more sophisticated methods such as Bayesian analysis are very demanding computationally. In this thesis, an alternative approach based on a Residual Maximum Likelihood method for estimation of position and variance of one or two linked QTLs and of additive polygenic and residual variances is presented. The method is based on a mixed linear model including polygenic and random QTL allelic effects. The variance-covariance matrix of QTL allelic effects and its inverse is computed conditional on incomplete information from multiple linked markers. The method is implemented using interval mapping and a derivative-free algorithm, where the required coefficient matrix of the Mixed Model Equations is derived from a Reduced Animal Model. simulation studies based on a granddaughter design with 2000 sons, 20 sires and 9 ancestors were performed to evaluate parameter estimation and power of QTL detection. Daughter Yield Deviations of sons were simulated under three QTL models, a biallelic, a multiallelic (10 alleles), and a normal-effects model. A linkage group of five or nine markers located on the same chromosome was assumed, and genotypes were available on sons, sires and ancestors. Likelihood ratio statistics were used to test for the presence of one or two linked QTLs. Parameters were estimated quite accurately for all three QTL models, showing that the method is robust to the number of alleles at the QTL. The effect of considering or ignoring relationships in the analyses did not have a major impact on parameter estimates but reduced the power of QTL detection. In general, power tended to decrease as the number of sons per sire, QTL contribution to additive genetic variance, or distance between QTLs was reduced. The method allowed for detection of a single QTL explaining 25% of the additive genetic variance, and for detection of two QTLs when jointly they accounted for 50% or 12.5% of the additive genetic variance. Although the REML analysis is an approximate method incorporating an expected covariance matrix of the QTL effects conditional on marker information, it is a computationally less expensive alternative to Bayesian analysis for accounting for the distribution of marker-QTL genotypes given marker and phenotypic information. For the designs studied, parameters were estimated accurately and QTLs mapped with satisfactory power. / Ph. D.

當線性模型中包含隨機效果項時，若將之視為固定效果或直接忽略，往往會造成嚴重的推測偏差，故應以混合線性模型為架構。若模式中只包含一個隨機效果項，則模式中有兩個變異數成份，若包含 個隨機效果項，則模式中有 個變異數成份。本論文主要在介紹至少兩個變異數成份時固定效果及隨機效果線性組合的最佳線性不偏推測量（BLUP），及其推測區間之推導與建立。然而BLUP實為變異數比率的函數，若變異數比率未知，而以最大概似法（Maximum Likelihood Method）或殘差最大概似法（Residual Maximum Likelihood Method）估計出變異數比率，再代入BLUP中，則得到的是經驗最佳線性不偏推測量（EBLUP）。至於推測區間則與EBLUP的均方誤有關，本論文先介紹如何求算其漸近不偏估計量，再介紹EBLUP之推測誤差除以 後，其自由度的估算方法，據以建構推測區間。 / When random effects are contained in the model, if they are treated as fixed effects or ignore, then it may result in serious prediction bias. Instead, mixed linear model is to be considered. If there is one source of random effects, then the model has two variance components, while it has variance components, if the model contains random effects. This study primarily presents the derivation of the best linear unbiased predictor (BLUP) of a linear combination of the fixed and random effects, and then the conduction of the prediction interval when the model contains at least two variance components. However, BLUP is a function of variance ratios. If the variance ratios are unknown, we can replace them by their maximum likelihood estimates or residual maximum likelihood estimates, then we can get empirical best linear unbiased predictor (EBLUP). Because prediction interval is relating to the mean squared error (MSE) of EBLUP, so the study first introduces how to get its approximate unbiased estimator, m_a , then introduces how to evaluate the degrees of freedom of the ratio of the prediction error for the EBLUP and m_a ^1/2 , in order to use both of them to establish the prediction interval.