Inbreeding – the production of offspring from parents who are genetically close together – can lead to health problems. This is because there’s an increased risk of the offspring having a ‘recessive’ genetic disease.
Recessive diseases require two copies of a harmful gene to develop – one from each parent – and if the genomes of the parents are similar, there’s a stronger chance that they’ll both carry it. However, these harmful genes are generally rare, and it takes multiple generations of inbreeding for the risks to rise significantly.
Even small Amazonian tribes have several hundred members, and tribal customs that encourage people to choose marriage partners who are not closely related are enough to keep the genes sufficiently well-mixed. Inbreeding is one of the factors that affects the success of a tribe, but land and food availability, and conflicts with Westerners and other tribes, are all bigger threats. Inbreeding only becomes a serious problem when the population drops below 50 or so.