Most of the genetic divergence that currently separates populations of Homo sapiens must have arisen during that long period when the local village (or band) was the basic unit of biological evolution. Studies of tribally intact Amerindian groups exhibiting such small-group organization have demonstrated marked genetic divergence between nearby villages. Some of this genetic radiation can be attributed to the effects of random genetic drift over time within these small demes. Some of it, however, might be better ascribed to the consequences of nonrandom genetic assortment at the time of village fission, a recurring event for such groups. Even random genetic assortment at the time of fission would lead to some genetic divergence, due to the finite size of the parent gene pool. We term the genetic consequences of random assortment the random fission effect. Routinely, village fission occurs along family lines, leading to even greater genetic divergence between the daughter villages. We use the term lineal fission effect to describe the genetic consequences of nonrandom assortment and contrast these results with those derived from random assortment.——A formal treatment of random and lineal fission effects is developed, first for the single-locus case, then for the multiple-locus extension. Using this formulation, three Yanomama fission events were examined. Fission in the Yanomama often involves a great deal of mutual hostility between the two factions, so that subsequent gene flow between the two daughter villages is minimal. The first two examples are typical of the Yanomama behavior norm, and are accompanied by a minimum of subsequent gene flow between the daughter villages. In these two cases, the observed divergence values are very large and are also very unlikely under random fission. The lineal fission effect is pronounced. The net impact of lineal fission is to reduce the effective size of the village at the time of fission by a factor of four, relative to expectation from random fission. The third example, however, involved an unusually amicable split of a village, followed by free genetic exchange between the fission products. This "friendly fission" yields an observed divergence value not much in excess of the expectation from random fission.—The long-term consequences of such fission bottlenecks in effective population size are discussed for both intra- and inter-tribal genetic diversity. It appears that the rate of genetic divergence for tribal and subtribal groups may have been somewhat greater than would be expected from classical drift arguments.