Here are some key references to
first described in detail the phenomenon of mortality leveling-off at
Although the first notion on the
from the Gompertz law at advanced ages were made by Gompertz himself in
1825, the first article specifically devoted to the problem of
mortality at advanced ages was published in 1939 by British researchers
Greenwood and Irwin:
This 1939 article correctly describes and
forestalls the main specific
regularities of mortality at advanced ages.
The first important finding was formulated by Greenwood and Irwin in the following way: "…the increase of mortality rate with age advances at a slackening rate, that nearly all, perhaps all, methods of graduation of the type of Gompertz's formula over-state senile mortality" (Greenwood, Irwin, 1939, p.14). This observation is known now as the "late-life mortality deceleration."
The authors also suggested "the
possibility that with advancing age the rate of mortality asymptotes to
a finite value" (Greenwood, Irwin, 1939, p.14). Their
conclusion that mortality at exceptionally high ages follows a first
order kinetics (also known as the law of radioactive decay) was
confirmed later by other researchers, including A.C. Economos (see
below), who demonstrated the correctness of this law for humans and
laboratory animals. This observation is known now as the
"mortality leveling-off" at advanced ages, and as the "late-life
Moreover, Greenwood and Irwin made the first estimates for the asymptotic value of human mortality (one-year probability of death, qx) at extreme ages using data from the life insurance company. According to their estimates, "… the limiting values of qx are 0.439 for women and 0.544 for men" (Greenwood and Irwin, 1939, p.21). It is interesting that these first estimates are very close to estimates obtained later using more numerous and accurate human data including recent data on supercentenarians (those who survive to age 110).
Angelos Economos was the first
who described mortality leveling-off in animals and manufactured
products. He demonstrated mortality leveling-off at
advanced ages for invertebrates (including fruit flies and house
flies), rodents, and several manufactured products:
After study of mortality
for many biological species A. Economos came to the following
conclusion: "...Gompertz's law is only an approximation, not valid over
a certain terminal part of the lifespan, during which force of
mortality levels off." (Economos, 1980, p.317, abstract). The
phenomenon of mortality leveling-off at advanced ages he called "a
non-Gompertzian paradigm for mortality kinetics."