Ageing – a mathematical law?

Ageing – a mathematical law?

These days, it’s already old news: people are living longer and longer. In industrialized countries, life expectancy increases by two to three years every ten years. The scientists working with James Vaupel, Director at the Max Planck Institute for Demographic Research in Rostock, are hot on the trail of a physical constant. They are interested in finding out whether the current trend will continue in this way.

Is the speed of ageing a fundamental, unchanging variable of human life? This question is crucial to each individual but is also important from a social, political and economic perspective – it is not surprising that age research is gaining in influence. This discipline has developed into one of the most interesting areas of demographic research and is backed by considerable funding, especially in the USA. Max Planck Foundation is convinced of the fundamental importance of the question “Rate of human ageing – How quickly are people ageing?” and therefore supported Vaupel's team with an amount of 950,000 euros.

The research from which the forecasts for life expectancy is derived based largely on mathematics. Comprehensive data on people of all age groups is needed, to then be analyzed using various statistical methods. As this issue is linked across disciplines – not only with social sciences but also with biology, such as the issue of genetic disposition – data relating to certain human biomarkers as well as findings from the ageing processes of model organisms is also incorporated.

Life expectancy is increasing because the mortality risk is decreasing.

Calculation of life expectancy can be confusing: according to the Federal Statistical Office, life expectancy of a girl born in 2009 is 82 years and 7 months (for a boy it is 77 years and 6 months). Scientists at the Rostock-based Institute, on the other hand, have calculated that every baby born in 2009 in Germany has a 50 percent probability of living to at least 100. How can these different forecasts be explained?

The solution: the value calculated by the Federal Statistical Office only applies if living conditions remain at the level at which they were at the time of the calculation. If, in future, living conditions continue to improve as rapidly as they have in the past 150 years, the result from Rostock will be achieved. The statisticians at the institute use yet another yardstick for ageing: mortality rate, i.e. the risk of dying at a particular age. A 20-year-old Western German woman in 2009 had a very low mortality rate of 0.0002. By the time she has reached her 40th birthday, her mortality rate has more than tripled to 0.0007 but is still very low. Even at the age of 60, her risk of dying still does not change appreciably: at that stage the risk is almost 0.006. However, the risk then starts to increase rapidly: at 80 years, the probability of dying over the course of the same year is around 4 percent, rising to 15 percent at the age of 90 and almost 27 percent at 95.

Is this steep rise based on a rule? A mathematical law of nature for ageing? James Vaupel has launched a major research program to find out. His hypothesis is that a consistent percentage increase in the mortality rate exists not only in the average population but also applies to each individual.

The mortality risk increases evenly in a percentage – but starts from a low base.

A young London insurance mathematician called Benjamin Gompertz laid the foundations for this research as far back as in the late 18th century. He discovered that even if mortality rates are initially very low, they still increase from year to year by the same percentage. In adults, the rate increases every year by about 10 percent. In the early years, this is of little consequence: a tiny risk that increases by one-tenth is still tiny. It is only when the increases accumulate (like compound interest on a savings account) that the rates increase and become visible. As dynamic variables whose relative change is constant comply with an exponential function, Gompertz formulated the first statistical law of ageing: mortality risk increases exponentially with age.

An interesting divergence: from childhood to young adulthood, mortality rate does not yet increase exponentially. It increases slightly in early life, as even in developed countries infant and child mortality is still an issue. Once this critical phase has been overcome, the risk lingers at almost zero for a few years. In puberty, the mortality risk escalates for men as they endanger their lives considerably by hormonally driven bragging and showing off. At approximately 40 years, the phase known to demographers as “ageing” finally begins: the regular increase in mortality by 10 percent each year. Surprisingly, this growth in ageing remains almost constant, at least in the more recent history of humankind. The starting point of 40 years is also more or less constant.

This means: in principle, from the age of 40, all humans age equally quickly. The relative speed with which their mortality risk grows each year would then be a physical constant. According to this theory, no human being would tend towards a longer phase of ageing than another; however, this does not exclude unfortunate coincidences. Regrettably, they remain the essence of risk: for example, dying relatively early because of an illness or due to an accident.

Despite all this, there is great scope for reducing one’s own risk level through healthy behavior. Mortality risks are just average values. They are an average for the entire population and the values of each individual can be significantly higher (or lower). After all, a person’s own mortality is subject to individual behavior and physical conditions that are innate in each individual or that shaped them early in life. Everyone can postpone their own ageing.

Image: "It's all about love", Candida Performa. Creative Commons CC BY 2.0.

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