Sobel M J, Arnold J, Sobel M
Biometrics. 1986 Mar;42(1):45-65.
In previous work several models have been developed for genetic surveys of natural populations. Parents of unknown genotype are collected from a natural population, polymorphic at a single genetic locus. From each of these N cryptic parents a number of offspring are identified for their genotype. Our problem is to select an efficient offspring sampling plan for estimating the frequency of an allele in the cryptic adult population based on the N family profiles of juvenile genotypes. A criterion called the information per unit cost of observation is introduced to evaluate sequential sampling plans, in which the number of offspring per family examined is random. Some simple, practical schemes for stopping the sampling of offspring from a collected parent are introduced; one example is stopping when: (i) the offspring are definitive about the parental genotype(s) for the first time; (ii) a fixed number of one genotype only is seen; or (iii) a fixed maximum feasible number of offspring have been genotyped. This sampling scheme is recommended. For each sampling scheme, the best linear unbiased estimator and the sequential maximum likelihood estimator of the allele frequency are characterized. From the moments of these estimators, it is then possible to tabulate efficient sequential sampling plans, which are better (in the sense of information per unit cost), just as simple, and less costly than corresponding fixed sampling plans in use.
在之前的工作中，已经开发了几种用于自然种群基因调查的模型。从一个在单个基因座上具有多态性的自然种群中收集基因型未知的亲本。从这N个隐性亲本中的每一个中，确定一些后代的基因型。我们的问题是根据幼年基因型的N个家系图谱，选择一种有效的后代抽样方案，以估计隐性成年种群中等位基因的频率。引入了一个称为单位观察成本信息的标准来评估顺序抽样方案，其中每个家庭检查的后代数量是随机的。介绍了一些简单实用的方案来停止对已收集亲本的后代进行抽样；一个例子是在以下情况时停止：（i）后代首次明确亲本基因型；（ii）只看到固定数量的一种基因型；或（iii）已对固定的最大可行数量的后代进行了基因分型。推荐这种抽样方案。对于每种抽样方案，对等位基因频率的最佳线性无偏估计器和顺序最大似然估计器进行了表征。根据这些估计器的矩，然后可以列出有效的顺序抽样方案，这些方案（在单位成本信息方面）比使用的相应固定抽样方案更好、同样简单且成本更低。
