Ohno S
Beckman Research Institute of the City of Hope, Duarte, CA 91010-3000, USA.
Proc Natl Acad Sci U S A. 1996 Dec 24;93(26):15276-8. doi: 10.1073/pnas.93.26.15276.
The reason that the indefinite exponential increase in the number of one's ancestors does not take place is found in the law of sibling interference, which can be expressed by the following simple equation: [equation: see text] where Nn is the number of ancestors in the nth generation, ASZ is the average sibling size of these ancestors, and Nn + 1 is the number of ancestors in the next older generation (n + 1). Accordingly, the exponential increase in the number of one's ancestors is an initial anomaly that occurs while ASZ remains at 1. Once ASZ begins to exceed 1, the rate of increase in the number of ancestors is progressively curtailed, falling further and further behind the exponential increase rate. Eventually, ASZ reaches 2, and at that point, the number of ancestors stops increasing for two generations. These two generations, named AN SA and AN SA + 1, are the most critical in the ancestry, for one's ancestors at that point come to represent all the progeny-produced adults of the entire ancestral population. Thereafter, the fate of one's ancestors becomes the fate of the entire population. If the population to which one belongs is a successful, slowly expanding one, the number of ancestors would slowly decline as you move toward the remote past. This is because ABZ would exceed 2. Only when ABZ is less than 2 would the number of ancestors increase beyond the AN SA and AN SA + 1 generations. Since the above is an indication of a failing population on the way to extinction, there had to be the previous AN SA involving a far greater number of individuals for such a population. Simulations indicated that for a member of a continuously successful population, the AN SA ancestors might have numbered as many as 5.2 million, the AN SA generation being the 28th generation in the past. However, because of the law of increasingly irrelevant remote ancestors, only a very small fraction of the AN SA ancestors would have left genetic traces in the genome of each descendant of today.
一个人的祖先数量不会无限指数增长的原因在于同胞干扰定律，它可以用以下简单公式表示：[公式：见原文]，其中Nn是第n代祖先的数量，ASZ是这些祖先的平均同胞数量，Nn + 1是上一代（n + 1）祖先的数量。因此，一个人的祖先数量呈指数增长是在ASZ保持为1时出现的初始异常情况。一旦ASZ开始超过1，祖先数量的增长速度就会逐渐减缓，越来越落后于指数增长率。最终，ASZ达到2，此时祖先数量在两代中停止增长。这两代，称为AN SA和AN SA + 1，在谱系中最为关键，因为那时一个人的祖先代表了整个祖先群体中所有产生后代的成年人。此后，一个人的祖先的命运就成了整个群体的命运。如果一个人所属的群体是一个成功且缓慢扩张的群体，随着追溯到遥远的过去，祖先数量会慢慢减少。这是因为ABZ会超过2。只有当ABZ小于2时，祖先数量才会在AN SA和AN SA + 1代之后增加。由于上述情况表明一个群体在走向灭绝的过程中失败了，那么对于这样一个群体来说，之前的AN SA必然涉及数量多得多的个体。模拟表明，对于一个持续成功的群体中的一员，AN SA祖先可能多达520万，AN SA代是过去的第28代。然而，由于遥远祖先越来越不相关的定律，在今天每个后代的基因组中，只有极小一部分AN SA祖先会留下遗传痕迹。
