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標題: 利用混合分布模式之求配由兩自交系之雜交試驗估計數量性狀之基因效應
A Mixture-Modeling Approach to Estimating the Effect of Genes Affecting a Quantitative Trait from a Biparent Cross of Inbred Lines
作者: 張文怡
Chang, Wen-Yi
關鍵字: Mixture-Model;混合分布模式;Quantitative Trait;Effect of Genes;數量性狀;基因效應
出版社: 農藝學系
我們以一項大麥雜交試驗所獲得之株高數據(Leonard et al., 1957)為例,說明利用混合分布模式之求配估計這些參數的過程。首先,利用SAS/STAT所提供的集群分析程序(FASTCLUS),將取自F2族群的觀測值分為幾個子群,再以各子群的參數估值做為求配混合分布模式的起始值,藉由限制的EM演算法尋找模式中各項參數的最大概度估值。其次,以McLachlan and Basford (1988)提出的方法計算近似訊識矩陣(approximate information matrix)的反矩陣,藉之估計各參數估值的變方變積矩陣,或藉由參數靴環自助法(parametric bootstrap method)獲得的99個由自助重抽樣品估得的估值,直接估算這些參數估值的變方變積矩陣。由此數例的結果顯示:這種估計程序比Powers之析出法(Powers, 1963)可以由數據中獲得更多的訊息。

In this study we show that the effects of the genes contributing to the difference in a quantitative trait between the two parents (P1 and P2)in a cross experiment can be estimated by fitting a mixture model by the data sampled from P1, P2, F2, and/or F1 populations. Additionally, this approach also gives estimates for recombination rates among the loci involved.
As an example, we applied this estimation procedure to analyze the data of plant height in a biparent cross of barley (Leonard et al., 1957). The F2 data was firstly split into groups by a clustering procedure (FASTCLUS) provided in SAS/STAT. Taking the estimates given by the clustering analysis as starting values, a constrained EM algorithm was employed to find the maximum likelihood estimates for the parameters of the mixture model. The covariance matrix of the estimates was then obtained either by inverting the approximate information matrix (using the method developed by McLachlan and Basford, 1988), or by using a parametric bootstrap procedure with 99 replications. The numerical example seems to indicate that the present approach extracts more information than by using Powers' partitioning methods (Powers, 1963).
A simulation was performed to investigate the statistical behavior of the point estimates and confidence interval for the parameters obtained by this approach. The result indicates that this procedure is feasible and useful. It also shows that no great loss in precision will occur if data of F1 are not available, and the covariance matrix obtained by bootstrap resampling is far better than that obtained from inverting the approximate information matrix.
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