Azbel' M Y
School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel.
Proc Natl Acad Sci U S A. 1999 Mar 16;96(6):3303-7. doi: 10.1073/pnas.96.6.3303.
The probability to survive to the age x universally increases with the mean lifespan x(bar). For species as remote as humans and flies, for a given x the rate of its evolution with x is constant, except for the narrow vicinity of a certain x(bar) = x* (which equals 75 years for humans and 32 days for flies and which is independent of age, population, and living conditions). At x(bar) approximately x* the evolution rate jumps to a different value. Its next jump is predicted at x(bar) approximately 87 years for humans and approximately 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 x(bar) only (for instance, survival curves of 1896 Swedes and 1947 Japanese with approximately equal x(bar) 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 x(bar). As a result, when human x(bar) 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.
活到年龄x的概率普遍随平均寿命x(bar)的增加而提高。对于像人类和苍蝇这样差异极大的物种，对于给定的x，其随x的进化速率是恒定的，除了在某个特定的x(bar)=x*（人类为75岁，苍蝇为32天）的狭窄邻域内，该值与年龄、种群和生活条件无关。在x(bar)约等于x*时，进化速率跃升至不同的值。预测人类在x(bar)约为87岁、苍蝇在x(bar)约为59天时会出现下一次跃升。这种奇异性在物理学和数学中作为相变是众所周知的。在所考虑的情况下，不同的种群“相”具有显著不同的生存进化速率。进化是快速的——预期寿命可能在一代的寿命内翻倍。生存概率仅取决于年龄x和平均寿命x(bar)（例如，1896年瑞典人和1947年日本人的生存曲线，其x(bar)大致相等，尽管它们与不同国家、不同时期、不同种族相关，但非常接近）。在没有可调参数的情况下，所提出的通用定律在数量上与所有生命表数据一致。根据该定律，除年龄外的所有因素的影响都仅归结为平均寿命。在老年阶段，该定律具有超通用性——对于像人类和苍蝇这样差异极大的物种大致相同。它得出的生存概率与平均寿命x(bar)呈线性关系。结果，当人类的x(bar)几乎翻倍（从35.5岁增至69.3岁）时，70岁时的预期寿命仅从8岁增至9.5岁。还考虑了该通用定律的其他含义。
