Metafounders are a useful concept to characterize relationships within and across populations, and to help genetic evaluations because they help modelling the means and variances of unknown base population animals. Current definitions of metafounder relationships are sensitive to the choice of reference alleles and have not been compared to their counterparts in population genetics—namely, heterozygosities, FST coefficients, and genetic distances. We redefine the relationships across populations with an arbitrary base of a maximum heterozygosity population in Hardy–Weinberg equilibrium. Then, the relationship between or within populations is a cross-product of the form $${\Gamma }_{\left(b,{b}^{\prime}\right)}=\left(\frac{2}{n}\right)\left(2{\mathbf{p}}_{b}-\mathbf{1}\right)\left(2{\mathbf{p}}_{{b}^{\prime}}-\mathbf{1}\right)^{\prime}$$ with $$\mathbf{p}$$ being vectors of allele frequencies at $$n$$ markers in populations $$b$$ and $$b^{\prime}$$ . This is simply the genomic relationship of two pseudo-individuals whose genotypes are equal to twice the allele frequencies. We also show that this coding is invariant to the choice of reference alleles. In addition, standard population genetics metrics (inbreeding coefficients of various forms; FST differentiation coefficients; segregation variance; and Nei’s genetic distance) can be obtained from elements of matrix $${\varvec{\Gamma}}$$ .

中文翻译：

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重新定义和解释 metafounders 的基因组关系


Metafounders 是一个有用的概念，可以描述种群内部和种群之间的关系，并有助于遗传评估，因为它们有助于对未知基础种群动物的均值和方差进行建模。目前对元创始人关系的定义对参考等位基因的选择很敏感，并且尚未与群体遗传学中的对应定义进行比较，即杂合性、FST 系数和遗传距离。我们重新定义了在 Hardy-Weinberg 均衡中具有最大杂合性种群的任意基数的种群之间的关系。然后，种群之间或种群内的关系是 $${\Gamma }_{\left（b，{b}^{\prime}\right）}=\left（\frac{2}{n}\right）\left（2{\mathbf{p}}_{b}-\mathbf{1}\right）\left（2{\mathbf{p}}_{{b}^{\prime}}-\mathbf{1}\right）^{\prime}$$ 的形式，其中 $$\mathbf{p}$$ 是种群 $$b$$ 和 $$b^{\prime}$$ 中 $$n$$ 标记处的等位基因频率向量。这只是两个基因型等于等位基因频率两倍的伪个体的基因组关系。我们还表明，这种编码与参考等位基因的选择无关。此外，标准群体遗传学指标（各种形式的近亲繁殖系数;FST 分化系数;分离方差;和 Nei 的遗传距离）可以从矩阵 $${\varvec{\Gamma}}$$ 的元素中获得。