Alcala Nicolas, Rosenberg Noah A
Department of Biology, Stanford University, California 94305-5020
Department of Biology, Stanford University, California 94305-5020.
Genetics. 2017 Jul;206(3):1581-1600. doi: 10.1534/genetics.116.199141. Epub 2017 May 5.
[Formula: see text] is one of the most widely used statistics in population genetics. Recent mathematical studies have identified constraints that challenge interpretations of [Formula: see text] as a measure with potential to range from 0 for genetically similar populations to 1 for divergent populations. We generalize results obtained for population pairs to arbitrarily many populations, characterizing the mathematical relationship between [Formula: see text] the frequency of the more frequent allele at a polymorphic biallelic marker, and the number of subpopulations We show that for fixed , [Formula: see text] has a peculiar constraint as a function of , with a maximum of 1 only if [Formula: see text] for integers with [Formula: see text] For fixed , as grows large, the range of [Formula: see text] becomes the closed or half-open unit interval. For fixed , however, some [Formula: see text] always exists at which the upper bound on [Formula: see text] lies below [Formula: see text] We use coalescent simulations to show that under weak migration, [Formula: see text] depends strongly on when is small, but not when is large. Finally, examining data on human genetic variation, we use our results to explain the generally smaller [Formula: see text] values between pairs of continents relative to global [Formula: see text] values. We discuss implications for the interpretation and use of [Formula: see text].
[公式：见正文]是群体遗传学中使用最广泛的统计量之一。最近的数学研究发现了一些限制条件，这些条件对将[公式：见正文]解释为一种衡量指标提出了挑战，该指标的取值范围理论上从基因相似群体的0到分化群体的1。我们将针对群体对得到的结果推广到任意多个群体，刻画了[公式：见正文]（多态双等位基因标记上较常见等位基因的频率）与亚群体数量之间的数学关系。我们表明，对于固定的[公式：见正文]，[公式：见正文]作为[公式：见正文]的函数有一个特殊的限制条件，只有当[公式：见正文]（其中[公式：见正文]为整数且[公式：见正文]）时，[公式：见正文]的最大值才为1。对于固定的[公式：见正文]，随着[公式：见正文]增大，[公式：见正文]的取值范围变为闭区间或半开区间[0,1]。然而，对于固定的[公式：见正文]，总是存在某个[公式：见正文]，使得[公式：见正文]的上限低于1。我们使用合并模拟表明，在弱迁移情况下，当[公式：见正文]较小时，[公式：见正文]强烈依赖于[公式：见正文]，但当[公式：见正文]较大时则不然。最后，通过研究人类遗传变异数据，我们利用我们的结果解释了相对于全球[公式：见正文]值，各大洲之间的[公式：见正文]值通常较小的原因。我们讨论了这些结果对[公式：见正文]的解释和使用的影响。
