The probability to survive to the age x universally increases with the mean lifespan x̄. For species as remote as humans and flies, for a given x the rate of its evolution with x̄ is constant, except for the narrow vicinity of a certain x̄ = x* (which equals 75 years for humans and 32 days for flies and which is independent of age, population, and living conditions). At x̄ ≅ x* the evolution rate jumps to a different value. Its next jump is predicted at x̄ ≅ 87 years for humans and ≅ 59 days for flies. Such singularities are well known in physics and mathematics as phase transitions. In the considered case different population “phases” have significantly different survival evolution rates. The evolution is rapid—life expectancy may double within a lifespan of a single generation. Survival probability depends on age x and mean longevity x̄ only (for instance, survival curves of 1896 Swedes and 1947 Japanese with approximately equal x̄ are very close, although they are related to different races in different countries at different periods in their different history.) With no adjustable parameters, its presented universal law quantitatively agrees with all lifetable data. According to this law, the impact of all factors but age reduces to the mean lifespan only. In advanced and old age, this law is superuniversal—it is approximately the same for species as remote as humans and flies. It yields survival probability that linearly depends on the mean lifespan x̄. As a result, when human x̄ almost doubles (from 35.5 to 69.3 years), life expectancy at 70 years increases from 8 to 9.5 years only. Other implications of the universal law are also considered
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