In the late seventies, a small tribal population of Paraguay, the Ache, living under natural conditions, was studied. Data from this population turn out to be useful for considerations about evolutionary hypotheses on the aging phenomenon. 1) Ache show an age-related increasing mortality, which strongly limits the mean duration of life, as observed in other studies on mammal and bird species. 2) According to current theories on aging, in the wild very few or no individual reach old age and, so, aging cannot be directly influenced by natural selection. However, data from our population show that a significant proportion of the population reaches in the wild 60 and 70 years of age. 3) Data from Ache are also in agreement with the observation about an inverse correlation between extrinsic mortality and deaths due to the age-related increasing mortality. 4) For many gerontologists, the age-related decline of vital functions is a consequence of the gradual decline of cell turnover, genetically determined and regulated by the declining duplication capacities of stem cells. The current interpretation is that these restrictions are a general defense against the proliferation of any tumoral mass. However, among wild Ache cancer is virtually unknown in non-elderly subjects, and only among older individuals are there deaths attributable to oncological diseases. Moreover, fitness decline begins long before oncological diseases have fatal effects in significant numbers. This completely disproves the current hypothesis, because a supposed defense against a deadly disease cannot exterminate a population before the disease begins to kill. These data are consistent with similar data from other species studied under natural conditions, and they bring new arguments against the non-adaptive interpretation of aging and in support of the adaptive interpretation.