A study of the viability of small populations of Hymenoptera is a matter of importance to gain a better zoological, ethological, genetical and ecological knowledge of these insects, and for conservation purposes, mainly because of the consequences to the survival of colonies of many species of bees, wasps, and ants. Based on the Whiting (1943) principle, Kerr & Vencovski (1982) presented a hypothesis that states that viable populations of stingless bees (Meliponini) should have at least 40 colonies to survive. This number was later extended to 44 colonies by Kerr (1985). This would be necessary to avoid any substantial amount of homozygosis in the pair of chromosomic sexual loci, by keeping at least six different sexual gene alleles in a reproductive population. In most cases this would prevent the production of useless diploid males. However, several facts weigh against considering this as a general rule. From 1990 to 2001, 287 colony divisions were made, starting with 28 foundation colonies, in the inbreeding and population experiments with the Meliponini reported here. These experiments constitute the most extensive and longest scientific research ever made with Meliponini bees. In ten different experiments presented here, seven species (one with two subspecies) of Meliponini bees were inbred in five localities inside their wide-reaching native habitats, and in two localities far away from these habitats. This was done for several years. On the whole, the number of colonies increased and the loss of colonies over the years was small. In two of these experiments, although these populations were far (1,000 km and 1,200 km) from their native habitat, their foundation colonies were multiplied successfuly. It was possible to build up seven strong and three expanding medium populations, starting with one, two, three or even five colonies. However, in six other cases examined here, the Whiting (1943) principle and the hypothesis of Kerr & Vencovski (1982) and Kerr (1985), possibly hold up. In two other cases, the results are still unclear. Outside native habitats, most inbreeding experiments failed, possibly because of conditions that cause ecological stress. Although much more data are still needed, a new working hypothesis on the molecular level was presented to explain the results of the experiments described here. In the absence of any considerable stress, and in the eventuality of a good nutritive situation, even individual bees that are homozygous in the pair of chromosomic sexual locus would produce a sufficient amount of a sex determining substance. Therefore, the female genes of all the diploid individuals of a colony, both homozygous and heterozygous, would be activated. However, situations of considerable stress would cause a poor physiological and nutritive condition. This, together with homozygosis in the pair of chromosomic sexual locus, would lead to a smaller production of the sex determining substance. When this happens in the diploid homozygous individuals of a colony, in relation to sex, only male genes are activated. As a result, all such homozygous diploid bees of the colony become useless males. However, when there is a heterozygous situation in the chromosomic sexual locus of all bees of a colony, all diploid individuals would produce a high amount of the sex determining substance. Consequently, all diploid individuals of such a colony would become females (queens and workers). Stresses, including ecological stress, as well as the nutritive condition and the genetic situation in the chromosomic sexual loci, will have a key influence in the life and behavior of the Meliponini, including sex determination. In relation to genetic factors, hybrid vigour may often cause a greater production of biological substances. This may be due to the presence of a greater number of copies of allelic genes when there is heterozygosis. This is a hypothesis requiring further research. However, in the experiments presented here, this hypothesis seems to apply well to the production of a sex determining substance in bees (Apoidea) and other Hymenoptera.