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標題: 利用混合分布模式之求配測驗數量性狀在兩親雜交第二代之分離比
A Mixture-Modeling Approach to Testing the Segregation Ratio of a Quantitative Trait in the F2 Progeny from a Biparent Cross
作者: 陳怡茹
Chen, Yi-Ru
關鍵字: Mixture-Model;混合分布模式;Quantitative Trait;Segregation Ratio;數量性狀;分離比
出版社: 農藝學系
在數量性狀的遺傳分析中,測驗雜交第二代(F2)內的分離比是一項重要而困難的工作;而Power(1950)所提出的析出法(partitioning method)則是一個相當主觀的測驗程序。本研究之目的在探討在(1)對立擬說(H1)下之F2族群內的子族群數等於虛無擬說(H0)下之子族群數,及(2)對立擬說下之F2族群內的子族群數未知等兩種情況下,藉由混合分布之求配,以概度比統計量進行分離比測驗的可行性。
我們以一項大麥雜交試驗所獲得之F2族群的株高數據( , Leonard et al., 1957)來說明這個替代的測驗程序。首先藉由限制的EM演算法,分別在虛無擬說及對立擬說下求配F2族群的常態混合分布模式,並計算其概度比測驗統計量 ;再以參數靴環自助法(parametric bootstrap method)所進行的99次自助重抽來模擬概度比測驗之p-value。在這個數例裡,以這個方法所得到的測驗結果與由析出法測驗的結果並無明顯的差異。
(2)對立擬說下之F2族群內的子族群數等於虛無擬說下之子族群數,以及(3)各子族群之變方均質等三個條件下,探討以參數靴環自助法進行概度比測驗的效力。結果顯示在取樣數為400時,以參數靴環自助法進行模擬測驗的第一型錯誤機率與原定之顯著水準相當接近;但測驗的效力則相當低。因此進一步將取樣數提高至800、1200及1600進行模擬試驗,以探討由原始數據所估得的概度比測驗統計量 之取樣分布。結果顯示不論取樣數為400、800、1200或1600,在500次模擬試驗所獲得的 之經驗頻度分布皆與自由度為2之 分布相當接近。而將 視為 的逢機變數來進行分離比的測驗時,在500次模擬試驗中犯第一型錯誤的比率與既定的顯著水準相當接近,且測驗的效力也如預期地隨取樣數及虛無擬說與對立擬說間之差距的增大而有顯著的提升。

Testing the segregation ratio in the F2 population is an important but difficult problem in the genetic analysis of a quantitative trait. The partitioning method developed by L. Powers(1950) is a rather subjective test procedure. We propose a mixture likelihood approach to test the segregation ratio, either in case that the number of components in the F2 population under alternative hypothesis (H1) is equal to that under the null hypothesis (H0) or in case that the number of components under H1 is unknown.
We adopted the data of plant height sampled ( ) from the F2 population in a cross of barley (Leonard et al., 1957) to demonstrate this alternative test procedure. By a constrained EM algorithm, the F2 data was fitted to the normal mixture models assumed under the H0 and H1, and thus the log-likelihood-ratio test statistic was calculated. A parametric bootstrap resampling procedure with 99 replications was then employed to approximate the p-value of the test. No substantial difference occurred between the test result given by the present approach and that by Powers' partitioning method in this numerical example.
With limited computation facility, the validity of the bootstrap test was assessed only for a sample size 400 and the case that the number of components in the F2 population under H1 was equal to that under H0 and of equal component variances. It showed that the simulated type I error of the bootstrap test was very close to the prescribed significance level, but the power of this test was quite low at the sample size 400. Further simulations with sample sizes 800, 1200, and 1600 were performed to investigate the sampling distribution of the test statistic evaluated from the original sample. The results showed that the chi-squared distribution with two degrees of freedom seemed to fit very well to the empirical distribution of formed from 500 simulated values of this statistic for any of the sample sizes 400, 800, 1200, or 1600. When taking as a chi-squared distributed variable to test the segregation ratio, the simulated type I error was close to the specified significance level. And, as expected, the test power increased as the sample size and the discrepancy between H0 and H1 increase.
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