Predictive implications of Gompertz's law

TL;DR

This paper extends Gompertz's law to ages over 100, predicts a human lifespan upper bound near 120 years, and explores its implications for mortality rates and maximum lifespan across populations.

Contribution

It demonstrates that Gompertz's law holds beyond 100 years, predicts an upper human lifespan limit near 120, and links mortality rates to population size and lifespan independence.

Findings

Gompertz's law applies beyond age 100.

Predicted maximum human lifespan is approximately 120 years.

Lifespan of the oldest individuals is independent of population size.

Abstract

Gompertz's law tells us that for humans above the age of 35 the death rate increases exponentially with a doubling time of about 10 years. Here, we show that the same law continues to hold even for ages over 100. Beyond 106 there is so far no statistical evidence available because the number of survivors is too small even in the largest nations. However assuming that Gompertz's law continues to hold beyond 106, we conclude that the mortality rate becomes equal to 1 at age 120 (meaning that there are 1,000 deaths in a population of one thousand). In other words, the upper bound of human life is near 120. The existence of this fixed-point has interesting implications. It allows us to predict the form of the relationship between death rates at age 35 and the doubling time of Gompertz's law. In order to test this prediction, we first carry out a transversal analysis for a sample of countries comprising both industrialized and developing nations. As further confirmation, we also develop a longitudinal analysis using historical data over a time period of almost two centuries. Another prediction arising from this fixed-point model, is that, above a given population threshold, the lifespan of the oldest person is independent of the size of her national community. This prediction is supported by available empirical evidence.