The concept of individual admixture (IA) assumes that the genome of individuals is composed of alleles inherited from $K$ ancestral populations. Each copy of each allele has the same chance $q_k$ to originate from population $k$, and together with the allele frequencies $p$ in all populations at all $M$ markers, comprises the admixture model. Here, we assume a supervised scheme, i.e.\ allele frequencies $p$ are given through a reference database of size $N$, and $q$ is estimated via maximum likelihood for a single sample. We study laws of large numbers and central limit theorems describing effects of finiteness of both, $M$ and $N$, on the estimate of $q$. We recall results for the effect of finite $M$, and provide a central limit theorem for the effect of finite $N$, introduce a new way to express the uncertainty in estimates in standard barplots, give simulation results, and discuss applications in forensic genetics.
翻译:个人粘合剂概念(IA)假定个人基因组由祖传人口所继承的异名组成,每个异名的每份都有同样的机会从人口(K)美元中产生,每个异名的每份都有相同的机会从人口(K)美元中产生,并与所有人口(所有M美元标记)的异名频率(P)一起产生,由混合模型组成。我们假定一个受监督的计划,即所有异名频率($)通过一个规模为N美元的基准数据库提供,以最大可能的方式对单一样本估算美元。我们研究大量和中央限值的法律,说明有限性(M)和美元(N)对美元估计数的影响。我们回顾关于限定美元效果的结果,并为限定值(N)效应提供一个中心限值标值。我们提出一种新的方法,以表达标准区块的估计数的不确定性,提供模拟结果,并讨论法医遗传学的应用。