Extensive demographic studies relate ageing to the increase in mortality, terminated by the species-specific lifespan limit. Meanwhile, recent experiments demonstrate that medfly mortality decreases at older ages, and challenge a limited lifespan paradigm. This paper presents a unitary mortality law, which relates the controversy to the population heterogeneity. For relatively high heterogeneity it predicts unitarily vanishing old age mortality; this is verified with medfly data. For relatively low heterogeneity it predicts precipitous drop in mortality fluctuations in old age. This is verified with demographic data. If comprehensive studies verify the life expectancy relation to a suggested genetic species-specific age, then the life expectancy may be genetically manipulated. If the studies verify a unitary law of mortality, the results may be generalized to all species. A phenomenological model of mortality is presented.