HOW SHOULD AN HONORARY learned society such as the American Philosophical Society (APS) regulate its size? This question, of obvious practical importance to the APS, is a special case of a broader scientific question: how is the size of any population, human or not human, regulated? In this broader perspective, the APS provides a valuable case study, a microcosm, of the self-regulation of a human population.
This article answers these questions: What has been the trend in the average age of a newly elected resident member? What has been the trend in the average age at death of a resident member? What has been the trend in the average duration of membership? These questions are steps en route to answering this question: How will future numbers of resident members to be elected annually affect the steady-state size of the APS resident membership? If the APS elects 35 resident members a year for the indefinite future (as it had in the 17 years preceding 2006), will there be an eventual steady-state size of the resident membership, and if so, how big will it be? What if APS elects 25 or 45 resident members a year for the indefinite future?
A reader who is interested only in the answers to these questions, and not in the data or analyses that led to these answers, is invited to skip to the section called "Conclusions." The data, analysis, and conclusions are restricted to resident members. Henceforth, "members" will be taken to refer strictly to resident members.
At the end of 2005, the APS had 753 living resident members. In the 17 years from 1989 to 2005, the number of living resident members of the APS increased by more than 200.
On 10 March 2006, Nora Monroe of the Membership Office emailed me a list of all 1,776 people who were elected to membership in the APS from 1930 through 2005. The dates of birth and ages at election of some individuals were missing. By consultation with Wikipedia http://www.wikipedia.org/ and other online information sources, my assistant, Priscilla Rogerson, and I found the year of birth of all but four individuals. One other person resigned. This study was based on the remaining 1,771 = 1,776 - 4 - 1 people. For each person in this analysis, the available data were the year of birth, the year of election, the age at election (given exactly by the individual or computed as the year of election minus the year of birth), and the year of death (taken as 0 if the individual was still alive as of 10 March 2006).
The number of living members on 10 March 2006, computed from this information, was 750. This information is exactly consistent with independent information furnished by Nora Monroe, which showed 753 living members at the end of 2005, because the data sent to me as of 10 March 2006 included three deaths during 2006: 753 - 3 = 750. Hence 1,021 = 1,771 - 750 members elected from 1930 through 2005 had died by 10 March 2006.
In the 17-year interval 1989-2005 inclusive, the APS elected 589 individuals to resident membership (an average of 34.65 members per year) and 381 of its resident members died (an average of 22.41 members per year). The excess of the number of elections over the number of deaths resulted in an increase of 208 resident members (an average increase per year of 12.24 members).
COHORT DURATION OF MEMBERSHIP AMONG MEMBERS WHO DIED
For members who had died by 10 March 2006, the "duration of membership" was defined as the year of death minus the year of election. For members still alive by 10 March 2006, no "duration of membership" was defined.
Figure 1 shows the duration of membership of all 1,021 deceased members by year of election. The downward sloping ramp of the largest duration of membership in each year of election from, approximately, 1944 to 2005 is a consequence of the fact that, for example, an individual elected in 1995 who is dead by 2006 cannot have a duration of membership longer than 11 years. …