Here are some key references to pioneer scientific publications, which first introduced the idea of population heterogeneity (gamma-distributed individual risk) to explain a logistic function for mortality rate, late-life mortality deceleration, mortality levelling-off, and mortality plateaus:

- Beard, R.E. 1959. Note on some mathematical mortality models. In: G.E.W.Wolstenholme and M.O'Connor (eds.). The Lifespan of Animals. Little, Brown, Boston, 302-311

- Beard, R.E. 1964 Some observations on stochastic process with particular reference to mortality studies. International Congress of Actuaries, vol.3, p.463-477

This logistic model with gamma distributed individual risk and late-life mortality deceleration became widely known to biologists and demographers in 1971, when Dr. Beard published a detailed review of his studies in the book "Biological Aspects of Demography":

- Beard RE. 1971. Some aspects of
theories of
mortality, cause of death
analysis, forecasting and stochastic processes. In. Biological aspects
of demography (Brass W.,
Ed.), Taylor & Francis, London, 57-68

The heterogeneity mortality model
with gamma distributed individual
risk (producing logistic function for mortality rate) was developed by
famous British statistician and actuary Robert Eric Beard in
1959. Dr. Beard also
became famous for his book "Risk Theory", which had three editions:

- Risk Theory by Beard, Pentilkainen and Pesonen,
Chapman and Hall.

Beard, Robert Eric (1911—1983)