A Note on the Age Structures of Learned Societies

SUMMARY Several authors have investigated the composition and age structures of learned societies. The proportion of older members, revealed by these deterministic numerical analyses, has been a cause for concern. Some techniques developed in the population mathematics context are very suitable for analysing the composition of such bodies, and the use of these techniques in dealing with these problems is demonstrated in this paper. THE age structures of learned societies have been investigated by various authors. Strachey (1892), for example, was interested in the probable effect of the limitation of the number of Ordinary Fellows elected into the Royal Society to fifteen in each year on the eventual total number of Fellows. Two other authors have been interested in the composition of the Royal Society: Schuster (1925) and Hill (1939, 1954, 1961). Similar investigations have been carried out for the National Academy of Sciences of the U.S.A. by Pearl (1925), and for the Australian Academy of Science by H. 0. Lancaster (1964) in an unpublished report. The above discussions were all of a numerical nature. Some techniques developed in the population mathematics context (Pollard, 1966, 1967) are very suitable for analysing the composition of such societies, and it is the object of this paper to demonstrate the use of these techniques in this context. We show that the proportion of members aged 70 years or more is ultimately greater than 20 per cent with a high probability (and the expected proportion close to 25 per cent) for most learned societies. 2. THE MATHEMATICS INVOLVED A learned society may be regarded as an hierarchical organization (Bartholomew, 1968, pp. 38-70) in which members are graded according to their age last birthday. We shall make use of discrete-time methods, and use a time unit of 1 year. During a calendar year, an existing member aged x may either leave the organization (by