Multiple alleles and estimation of genetic parameters: computational equations showing involvement of all alleles.
Multiple alleles and estimation of genetic parameters: computational equations showing involvement of all alleles.
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多个等位基因和遗传参数的估计：显示所有等位基因参与的计算方程。
DOI：
10.1093/genetics/130.1.231
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发表时间：
1992
期刊：
影响因子：
3.3
通讯作者：
Chakraborty,R
中科院分区：
文献类型：
--
作者：
Chakraborty,R
对于群体遗传学研究来说，表现出多个（两个以上）分离等位基因的遗传位点通常比双等位基因更有用，因为它们在观察到的等位基因数量以及群体之间的等位基因频率差异方面提供了更大的变异潜力。由于群体中某个基因座的等位基因频率在结构上受到限制（它们总是相加），因此对多等位基因座的等位基因频率数据进行矩阵处理需要从分析中删除一个等位基因。因此，所得的估计量可以解释为取决于在估计过程中消除哪个等位基因（BALAKRISHNAN 1973）。 BALAKRISHNAN 和 SANGHVI (1968) 以及 SMOUSE 和 SPIELMAN (1977) 在试图通过与多变量数据的 Mahalanobis-D2 (MA-HALANOBIS 1936) 类似的统计来估计群体之间的遗传距离时，就遇到过这种情况。 ROBERTS 和 HIORNS (1962) 还提出了一种使用等位基因频率数据估计杂交群体中遗传混合的方法，该方法需要消除多等位基因座的一个等位基因。最近，这个问题在混合群体中混合成分的最小二乘估计中再次出现（LONG 1991）。由于这些研究人员通常根据等位基因频率的“缩短”向量（通过从每个基因座删除一个等位基因）和采样等位基因频率的这种“缩短”向量的方差-协方差矩阵来提出他们的估计方程，因此一般来说，所得的估计量是否依赖于从分析中消除的等位基因并不明显。因此，此类方法因选择要消除的等位基因所涉及的主观性而受到批评（BALAKRISHNAN 1973），尽管在某些应用中进行了代数验证以表明可以删除任何等位基因而不影响估计（LONG 1991）。本次交流的目的是表明，通过利用多项分布的细胞频率的方差-协方差矩阵的众所周知的性质（KURCZYNSKI 1970），可以获得矩阵估计量的简单转换，这表明即使形式表示需要删除一个等位基因，计算方程确实需要所有等位基因的频率。因此，这样的估计量是等位基因频率的完整阵列的函数。
Genetic loci that exhibit multiple (more than two) segregating alleles are generally more useful than biallelic ones for population genetic studies simply because they offer greater potential for variation in observed number of alleles as well as allele frequency differences across populations. Since allele frequencies at a locus in a population are structurally constrained (they always add to one), a matrix treatment of allele frequency data at a multi-allelic locus requires deleting one allele from the analysis. Hence the resultant estimator may be construed as dependent on which allele is being eliminated in the process of estimation (BALAKRISHNAN 1973). Such situations have been faced by BALAKRISHNAN and SANGHVI (1968) and SMOUSE and SPIELMAN (1977) when they attempted to estimate genetic distances between populations by statistics parallel to Mahalanobis-D2 (MA-HALANOBIS 1936) for multivariate data. ROBERTS and HIORNS (1 962) also suggested a method of estimating genetic admixture in a hybrid population using allele frequency data that requires elimination of one allele of a multiallelic locus. Recently, this issue has resurfaced in the least-square estimation of admixture components in a hybrid population (LONG 1991). Since these investigators generally presented their estimating equations in terms of “shortened” vectors of allele frequencies (by deleting one allele from each locus) and the variance-covariance matrix of such “shortened” vectors of sampled allele frequencies, in general it is not obvious whether or not the resultant estimators depend upon the allele that is eliminated from the analysis. As a result, such methods are criticized on the ground of the subjectivity involved in selecting the allele to be eliminated (BALAKRISHNAN 1973) although in some applications algebraic verifications are given to show that any allele can be dropped without affecting the estimate (LONG 1991). The purpose of this communication is to show that by exploiting a well-known property of the variance-covariance matrix of the cell frequencies of a multinomial distribution (KURCZYNSKI 1970) a simple translation of the matrix estimators can be obtained, which indicates that even though the formal representation requires deleting one allele, the computational equation truly needs the frequencies of all alleles. Therefore, such estimators are functions of the full array of allele frequencies.
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DOI：
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