Senescence presents not only a medical problem, but also an evolutionary paradox because it should be opposed by natural selection. Evolutionary hypotheses propose that ageing evolves as the necessary cost of processes increasing early reproductive success(1,2), or because of weaker selection against late-acting mutations(3). A prediction of these hypotheses is that the rate of ageing should increase and the average lifespan decrease as the rate of extrinsic mortality increases(1-7). Alternatively, non-adaptive, purely mechanistic hypotheses invoke damage to DNA, cells, tissues and organs as being the unique cause of senescence and ineluctable death of organisms(8). Here we show that the evolution of eusociality is associated with a 100-fold increase in insect lifespan. Such an increase is predicted by evolutionary theories because termite, bee and ant queens live in colonies that are sheltered and heavily defended against predators. Moreover, a comparison of ants with contrasting life histories also reveals an association between lifespan and extrinsic rate of mortality. These results provide strong support for evolutionary theories of ageing, as purely mechanistic hypotheses of senescence do not propose any association between the rate of extrinsic mortality and lifespans.