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目的：试建立线性代数模型，以拟合封闭近交群体内等位基因纯化的过程。方法：通过考察与性染色体Ｘ连锁的等位基因频率的变化规律，获得邻近两代（第ｎ－１代和第ｎ代）自交对基因型概率之间的关系为Ｘ~（ｎ）＝ＭＸ~（ｎ－１）。经矩阵相似变换，求得系数矩阵Ｍ的特征值、特征向量和可逆矩阵Ｐ。结果：第ｎ代自交对各种基因型的概率与起始状态基因型的概率之间的关系为Ｘ~（ｎ）＝Ｐ·Ｄ~ｎ·Ｐ~(－１)·Ｘ~（０），当ｎ→∞时，杂合自交对的基因型概率全为零，而只有纯合自交对的基因型概率非零，即自交对的等位基因都趋于纯化，只留下（Ａ，ＡＡ）和（ａ， ａ ａ）型。结论：线性代数模型定量地模拟了封闭近交群体内等位基因逐步纯化的过程，同时能客观分析不同自交代之间的生物数学特征及内在联系，根据模型还能由初始条件预报纯化基因型的频率。
OBJECTIVE: To establish a linear algebra model to fit the process of allele purification in an enclosed inbred population. Methods: The relationship between genotype frequencies of two generations (n-1 and n-th generation) of accessions was obtained by examining the variation of X-linked alleles with sex chromosome X = (n) = MX ~ (n-1). After the matrix similarity transformation, the eigenvalues, eigenvectors and invertible matrix P of the coefficient matrix M are obtained. Results: The relationship between the probability of each genotype at the nth generation and the genotype of the initial state was X ~ (n) = P · D ~ n · P ~ (-1) · X ~ (0 ). When n → ∞, the genotypes of heterozygous pairs were all zero, but only the genotypes of homozygous pairs were nonzero, that is, the alleles of selfing pairs tended to be purified, leaving only Under (A, AA) and (a, a a) types. CONCLUSION: The linear algebra model quantitatively simulates the step-by-step purification process of alleles in the closed inbred population. At the same time, it can objectively analyze the biological maths and internal relations among different selfed generations. According to the model, the initial genotypes Frequency of.