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The Gompertz-Makeham Law and What it Means for Longevity


We all want the ability to live longer. Scientists have studied longevity for centuries, looking for the secret to delaying aging. However despite all their research, we still aren’t sure how long humans could live. Is there an upper limit to our lifespans? Or could we become immortal if we figure out the right factors that affect our longevity?

One of the models that researchers use to understand longevity is the Gompertz-Makeham Law of Mortality. This mathematical law helps predict how long a population will live. By looking at people who live beyond this law, we might be able to unlock the secrets of longevity.

What is the Gompertz-Makeham law?

gompertz mortality graph

Estimated probability of death by age, U.S., 2003. CC Attribution-ShareAlike 3.0

The Gompertz-Makeham law says that the human death rate is the sum of an age-related component that increases exponentially, and an age-independent component.

So what does that mean? It’s basically a calculation of how likely we are to die in any given year. Two factors affect this risk. The first is age. As we get older, the chance of dying of an age-related condition increases. However it isn’t just old age that kills us. The second factor covers things like accidents, illnesses, and malnutrition that can affect anybody at any time.

The age-dependent factor is calculated using the Gompertz function. This is an equation named after the mathematician Benjamin Gompertz, who invented it. It was created to show the chances of death based on a person’s age. It was first used by life insurance companies to decide who to insure!

When Gompertz wrote the function, he calculated the chances of dying of an age-related factor were very low during childhood and young adulthood. Then through middle-adulthood and toward old age, the chances of dying of an age-related factor get higher and higher. But after a certain point, our risk factors level off.

Strangely, the very oldest people have a lower chance of dying of many age-related factors than people much younger than them do.

The other part of the Gompertz-Makeham law comes from William Makeham, another mathematician. He realized that the Gompertz function overlooked causes of death that weren’t related to aging. The Makeham term can be adjusted for different risks, including socio-economic and geo-political factors. Things like nutrition, accidents, and diseases. Between Gompertz’s function and Makeham’s addition, they created a model that can accurately predict mortality.

Reducing the Makeham term

newborn baby

Researchers today know that the Gompertz-Makeham law is very effective at predicting human mortality between the ages of 30-80. The most variable factor of the law is the Makeham term — the factors unrelated to age that still affect longevity.

Before the 1950s, the human mortality rate was much higher. Advances in science, medicine, and sanitation have meant all countries now have lower mortality rates. For instance in 1800, there were 463 deaths for every 1000 live births in the U.S. By 1950, that had dropped to 40 deaths. Today, there are just 7 deaths per 1000 births.

As mortality rates improved, the Makeham term became less relevant to the Gompertz-Makeham law. Under controlled conditions, such as with lab mice, researchers found that the Gompertz function was incredibly accurate all on its own.

What does this mean? It suggests that there is a measurable link between aging and mortality. If we could remove all the other causes of death — accidents, diseases, poor nutrition, and so on — then we could predict our mortality based just on how old we are.

Exceptions to the Gompertz-Makeham law

elderly couple with children

We know the Gompertz function is accurate up to the age of 80. What happens after that time? And what can that tell us about longevity?

The key features of the function are the lower chances of death at the start and end of our lives. Dying of age-related causes before 30 is unlikely because many age-related diseases haven’t had time to appear yet. But it doesn’t make sense that the chances of dying from these diseases slow down in advanced old age.

Scientists call this the “late-life mortality deceleration theory.” This theory says that the very oldest people have a reduced risk of dying in any given year. It’s a controversial theory that not all scientists believe is true. However late-life mortality deceleration has been documented in other animals, especially insects.

Another theory is that our risk of death levels off after a certain point. Beyond approximately 100 years old, our chances of death in any given year are 50/50.

Because the Gompertz function is so accurate, it’s possible that the secret to our longevity lies in the people who live the longest. Why does the function stop working after the age of 80? What changes in people who reach that age? Why can they continue living for much longer? Researchers don’t know the answer to these questions, but there are many studies focusing on the secrets of extreme longevity. 

Final thoughts

The Gompertz-Makeham law is a reliable model for estimating human mortality throughout most of our lives. However since the 1950s, huge advances have been made in reducing age-independent causes of death. This has brought renewed attention to the age-dependent function of the law. Scientists are now researching ways to uncouple aging from mortality. If we can understand what about getting older causes our deaths, we could unlock the secret to our longevity and dramatically increase our lifespans.

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