CAIRN-INT.INFO : International Edition

1The dynamics of small populations sometimes receive special attention from demographers. A distinctive case is that of professional organizations and bodies, of which Henri Leridongives a remarkable example here. Through a detailed reconstruction of the changes in the population of a learned society since its foundation, he shows us the links between the factors that contribute to those changes — notably intake, population size, mean age of members, and length of tenure — while emphasizing the impact of demographic variables such as mortality. This type of exercise assumes greater relevance when, as is the case with the French Académie des Sciences, an organization is preparing to reform itself. The skills of the demographer prove valuable here. By using projections to assess the consequences of alternative hypotheses, the demographer can cast substantial light on the choice of new operating rules.

2The demography of professional organizations and bodies is a relatively underdeveloped branch of demographic science, despite the apparent simplicity of the basic undertaking — namely, to measure, within a hierarchical group, the pace of transition from one “rank” to another, and the distribution of ages and lengths of stay in each rank. But many factors need to be taken into account: statutory requirements (seniority rules to qualify for promotion to a higher rank, for example) ; the age distribution at induction or at entry into a given rank ; the (statutory) retirement age ; the number of exits due to resignation, dismissal, or death ; the rate of intake ; and the change in total population size (usually defined in the statutes). In practice, the diversity of transition rules and their varying strictness make it hard to establish general “laws” except in special cases, such as a perfect stationary regime. These rules make it preferable to conduct simple projection or simulation exercises, such as those presented at the end of this article.

3For France, special mention must be made of the pioneering work of Louis Henry (1971, 1972, 1975). In his studies of hierarchical bodies with well-defined operating rules, such as the French civil service, Henry showed that sharp fluctuations in the rate of intake had inevitable effects on the likelihood of promotion through the ranks and on the mean ages of entry into each rank. In particular, the establishment of a new body usually creates exceptional conditions because the age structure of the first entrants is very unlikely to match the expected structure of the population in a stationary regime. A number of older persons (though not too close to retirement) are co-opted to oversee a larger group of younger entrants, thereby creating from the outset a bimodal age distribution that can never spontaneously acquire a more regular profile later on. Moreover, as a rule, the number of entrants is strictly determined by the number of leavers, and hence by the number of retirements. It is very difficult for an administrative body to attempt to smooth out these fluctuations, since this would require anticipating on the likely situation in the years ahead. In the specific case of the French judiciary, F. Munoz-Pérez and M. Tribalat observed that, if “the annual intake matches the number of departures due to retirement, that number is already built into the population pyramid of the judiciary for the next 30-35 years” (Munoz-Pérez and Tribalat, 1993).

4Nathan Keyfitz is one of the few specialists to have attempted to formalize some of the relationships that are useful for administering a professional body (1973, 1985). The findings from his study of the relationship between the growth rate of the organization and the length of stay in a given rank, confirm what experience has often shown, i.e. that one remedy for career bottlenecks is to increase the intake, and hence the group’s total population. The question then is to know how long this “escalation” can be sustained.

5Learned societies of the kind created in western Europe in the seventeenth and eighteenth centuries represent a fairly straightforward example: members enter by election and remain until death (there is usually no mandatory “retirement age”) ; the total membership size remains constant, at least over a long period (the Académie Française has had 40 members since… 1635!). The demography of a closed population of this kind is simple: the annual intake is strictly determined by the number of “exits”, i.e. deaths, an exogenous variable. However, there is one degree of freedom: age at entry, that is, at election. In principle, voters are entirely free to choose among potential candidates, and although age restrictions sometimes apply they are generally not onerous (for example, a minimum age of 25, or a maximum age of 75). But this freedom has a direct counterpart: it determines the number of persons elected each year, and hence the pace of membership renewal. In a stationary regime, the younger the age at election, the longer the tenure in the body, and the lower the rate of intake. We shall formalize these relationships later on.

6The total number of members is set either by the group itself, acting on its own, or by a statute that can only be changed with the consent of a “supervisory” authority. In particular, if members are remunerated, any change in their number will obviously depend on the position of the authority that pays the stipends. This is the case for the five academies that form the Institut de France: the members of the Académie Française, Académie des Inscriptions et Belles-Lettres, Académie des Sciences, Académie des Beaux-Arts, and Académie des Sciences Morales et Politiques are all “members of the Institut”, whose statutes cannot be altered without the approval of the Conseil d’État. The President of the Republic is “Protector” of the Academies and formally appoints the members after their election by one of the five bodies.

7The rapid increase in life expectancy after age 60 — first observed in the French population in the mid-twentieth century — has brought about an almost mechanical increase in the average age of the members of such institutions. This is a disadvantage in a field where it is important for an academy to stay in touch with the community of working researchers if it is to continue to play a useful role as an advisory body in society. That is one of the reasons that prompted the Académie des Sciences to undertake a major reform in 2002 and which involves (1) raising the number of members forming the “reference population” from 120 to 250, and (2) limiting this “reference population” solely to members under age 75. As a result, the membership is expected to number around 300 in twenty years time, and 350 some years later, of whom 250 will be aged under 75. The reform thus introduces a sharp discontinuity, albeit attenuated, as will be seen, by the gradual phasing out of the “Corresponding Members” category.

8This was the context in which we (1) prepared a set of projections to assist in the choice of new operating rules, and (2) reconstructed the population of the Academy from its foundation up to the latest reform. Our article presents the following:

  • a reconstruction of the changes in the population of the members of the Académie des Sciences since 1666 ;
  • comparisons with data available for other learned societies, belonging to the Institut de France or not (Académie Nationale de Méde-cine, foreign academies) ;
  • a brief review of the mechanisms at work in a population whose size is kept stationary ;
  • an outline of the May 2002 reform and the expected change in the membership of the Académie des Sciences over the next 30 years.

I – The Académie des Sciences between 1666 and 2001

1 – A brief history of the Academy

9We will not give a detailed history of the Académie des Sciences, of which there are already many accounts (Maindron, 1888 ; Aucoc, 1889 ; de Franqueville, 1895 ; Daumas, 1957 ; Hahn, 1971 ; McClellan, 1985 ; Leclant, 1999 and 2001 ; etc.) [1]. However, some of the major events need to be recalled (see Table 1). Like the Académie Française, founded by Cardinal Richelieu in 1634 on the basis of an existing group, the Académie des Sciences was established in 1666 at the behest of Jean-Baptiste Colbert, Louis XIV’s chief minister, in order to give a more visible and more official role to the circle that Abbé Mersenne had started to convene some thirty years earlier. This “Académie Royale des Sciences” had about fifteen members at its founding in 1666, plus a few “External (i.e. unremunerated) Members” (membres externes) and some “Pupils” (élèves). In practice, none of these categories was clearly defined. In 1699, Louis XIV conferred official status on the group, which until then had no written rules. The King set the number of “Stipended Members” (pensionnaires) at 20, that of the “Pupils” at 20 as well (each “Pupil” being assigned to a Stipended Member), and that of “Honorary Members” (honoraires) at ten. But he also created new categories: “Associate Members” (associés), of whom twelve were “kingdom-dwellers” (régnicoles, i.e. subject to the King’s sovereignty — in other words, “National Members”) and eight “Unaffiliated Members” (membres libres), who could be foreigners ; and “Senior Members” (vétérans). To fulfill one of the missions entrusted to the Academy, a fairly large number (85) of “Corresponding Members” (correspondants) were also co-opted, but this category is not explicitly mentioned in the 1699 statutes ; in fact, it was eliminated in 1785 under Lavoisier’s reform, then restored in 1803.

10To understand the diversity of these titles, we must bear in mind a powerful constraint: the functioning of an academy required its members to be able to meet regularly (once a week) to discuss scientific progress, recent discoveries, research projects to encourage, and so on. The Stipended Members (and Pupils) were therefore obliged to reside in or near Paris — a requirement that did not apply to Associate Members, Senior Members and, especially, Corresponding Members. The latter category was intended to foster dialogue between scientists in the French provinces and those in Paris, a dialogue that necessarily involved the Stipended Members, with whom the provincial members “corresponded” in writing. Likewise, a Stipended Member who ceased to reside in Paris was usually named Senior Member and his seat was declared vacant. Surprisingly, the residence obligation was not formally abolished until… 1964, at which date the Academy also allowed the election of Corresponding Members residing in Paris. In practice, there is a definite hierarchy between these categories, which is respected by Table 1. The “full” members, endowed with all rights (in particular, that of co-opting colleagues in any category), have been called successively académiciens, pensionnaires, and, lastly, just membres (column M in Table 1). The other categories have an inferior status and can serve as a source of future members, except Honorary Members and Senior Members, whose titles make clear the honorific nature of their positions: we shall return to this issue.

Table 1

Changes In membership of académie des sciences

Table 1
Date Associate Members, Corresponding Members, Pupils, etc. Full Members (M) Honorary Members, Veteran Members, etc. Number of “members” (M) Total membership, excluding Honorary and Foreign Members Académie royale des sciences 1666 (Colbert) 3-6 Pupils 14-20 Academicians 1 Secretary (40 appointments, 1666-1698) 8 “non-stipended” (or “external”) appointments, 1691-1698 15-21 20-25 20 Jan. 1699 (Louis xiv) 20 Pupils (resident) 12 kingdom-dwelling Associate Members 8 Unaffiliated Associate Members 85 Corresponding Members* in 1699 20 Stipended Members (resident) {inch 1 Secretary and 1 Treasurer) 10 Honorary Members (kingdom-dwelling)+ Veteran Members (non-resident) 20 52-137 3 Jan. 1716 12 Adjunct Members (resident) 12 kingdom-dwelling Associate Members 12 Unaffiliated Associate Members {inch 4 kingdom-dwelling and 8 foreign) 85 (?) Corresponding Members* 20 Stipended Members (resident) {inch 1 Director and 1 Deputy Director) Supernumerary Stipended Members (43 appointed 1716-1785) + 6 Supernumerary Adjunct Members in 1716 12 Honorary + Veteran Members (Stipended or Associate) 20 48-133 22 May 1730 Same + 1 Adjunct Geographer Same Same 20 Same 23 March 1753 {Corresponding Members now elected and non-resident) 20 Same 1731,1762,1765 Same, except 6, 8 then 12 kingdom-dwelling Unaffiliated Associate Members (instead of 4) Same Same 20 50-141 23 April 1785 (Lavoisier) 24+1 Associate Members 12 Unaffiliated Associate Members (kingdom-dwelling) 8 Foreign Associate Members 24 Stipended Members (resident) 1 Secretary 1 Treasurer 12 Honorary Members + Veteran Members (7 in 1785) (Supernumeraries abolished) 26 63 Academies abolished 8 Aug. 1793 ------ ------- ----- 0 0 Institut national 22 Aug. 1795 (Class I) 60 Non-Resident Associate Members 8 Foreign Associate Members 60 Members (resident) 2 Secretaries 62 122 23 Jan. 1803 100 Corresponding Members (non-resident) 8 Foreign Associate Members 63 Members (resident) 2 Perpetual Secretaries 65 165 Institut de France 21 March 1816 (Académie des sciences) Same 63 Members (resident) 2 Perpetual Secretaries 10 Unaffiliated Members 75 175
Table 1
8 Jan. 1866 Same 66 Members (resident) 2 Perpetual Secretaries 10 Unaffiliated Members 78 178 24 June 1899 116 Corresponding Members 8 Foreign Associate Members Same 78 194 1 Dec. 1909 116 Corresponding Members 12 Foreign Associate Members Same 78 194 17 March 1913 Same Same + 6 Non-Resident Members (French) 84 200 23 Jan. 1918 Same Same + 6 Members in “Applications” Section 90 206 5 Nov. 1945 Same Same except Non-Resident Members now 12 96 212 25 Aug. 1954 120 Corresponding Members 20 Foreign Associate Members Same 96 216 29 June 1964 (End of non-residence requirement) (End of residence requirement) 96 216 14 June 1965 Same Same except Unaffiliated Members now 14 100 220 15 Nov. 1976 60 Corresponding Members 80 Foreign Associate Members 130 Members {inch 2 Perpetual Secretaries) 130 190 1982 Same Same CADAS established(a) 130 190 27 July 1987 180 Corresponding Members < 70 yrs 120 Foreign Associate Members 110 Members < 80 yrs (inch 2 Perpetual Secretaries) inch at least 30 < 60 yrs > 110 (134 m 1988) > 290 26 May 1997 240 Corresponding Members < 70 yrs(b) 150 Foreign Associate Members 120 Members < 80 yrs (inch 2 Perpetual Secretaries) inch at least 30 < 60 yrs > 120 > 360 12 Dec. 2000 Same Same CADAS becomes Académie des Technologies (separate from Institut de France) > 120(140 m 2001) > 360 2 May 2002 and 31 Jan. 2003 (End of election of Corresponding Members) 150 Foreign Associate Members 250 Members < 75 yrs(c) (in stages) (incl. 2 Perpetual Secretaries) >250 (in the long run) >250 * The “Corresponding Members” category was not defined in 1699, and their number was not set until 1803. (a) In 2001, the Conseil pour les Applications de l’Académie des Sciences had 95 Active or Emeritus Members, of whom half belonged to the Académie des Sciences. C<’ In practice, the number of Members aged under 70 has never exceeded 180. (c) Age at which current Members become ineligible to take part in election of new Members. Source: Author’s reconstruction based on successive Académie des Sciences regulations.

Changes In membership of académie des sciences

11The category of Associate Members met a variety of needs. These included spotting future full members, involving non-residents in the Academy’s work, and honouring foreign scientists, under arrangements that varied from one reform to another. Honorary Members were prominent individuals who it was assumed would understand (and defend) scientific interests, but who usually had no real scientific expertise. From their ranks, the King appointed a President and Vice President, who were to some extent his instruments for controlling the Academy. Among those who served as Honorary Members were Cardinals André de Fleury and Paul de Luynes, Marshals Charles de Castries and Sébastien de Vauban, Duke Louis de Richelieu, the financier John Law, and the ministers Chrétien-Guillaume de Malesherbes and Jean-Frédéric de Maurepas.

12In 1716, a reform complicated the picture somewhat more. The “Pupils” — who were often much older than was usual for students — became “Adjuncts” (adjoints) and their number was reduced to twelve. Also, a new category of “Supernumerary Stipended Members” (pensionnaires surnuméraires) was created. In most cases, these were scientists that the King wanted to see elected to the Academy and that he placed in a supernumerary position without waiting for a vacancy. As soon as a vacancy appeared, the Supernumerary was co-opted as a regular Stipended Member. Lavoisier’s 1785 reform suppressed Adjuncts, Corresponding Members, and Supernumeraries, and increased the number of Stipended Members to 24.

13In August 1793, the Convention (revolutionary legislative body) abolished all the Academies. They re-emerged two years later under the name of Institut National. “Class I” of the Institut (Physical and Mathematical Sciences) had 62 members (including the two Secretaries) [2] grouped into ten Sections, plus 60 Non-Resident Associate Members and 8 Foreign Associate Members. The Non-Resident Associate Members were replaced by 100 Corresponding Members in 1803, and the number of regular Members was raised to 65. The 1816 reform established the Institut de France with four Academies (Académie Française, Académie des Inscriptions et Belles-Lettres, Académie des Sciences, and Académie des Beaux-Arts) ; the Académie des Sciences Morales et Politiques was added in 1832. The initial membership of 65 was supplemented by 10 “Unaffiliated Academicians” (académiciens libres), i.e. not attached to a specific Section of the Academy. The addition of a few non-resident members, then of members of a new “Applications of Science” Section, raised the membership by stages to 100 by 1965.

14In 1976, the membership was expanded to 130, the number of Corresponding Members was reduced to 60, and the number of Foreign Associate Members was increased to 80: the Academy was becoming more international. This reform — like that eleven years later, in 1987 — had the threefold aim of expanding the Academy’s membership, diversifying the disciplines represented, and counteracting internal aging. Co-opting procedures were made more flexible by abandoning the old practice of linking seats to specific Sections (under the old system, replacements occurred only within each Section), and by reorganizing the Academy’s internal structure to accommodate new disciplines. The Academy also committed itself to the rule that one-half of the new members chosen in each annual election cycle should be aged under 55.

15In 1987, to meet the first two goals, the number of Corresponding Members was raised to 180 (aged under 70). The third objective was pursued, in a somewhat contradictory manner, by reducing the number of members but by introducing a dual constraint. First, the reference population became the membership under 80 — the age at which a member could be replaced while continuing to participate fully in the activities of the Academy. That number was set at 110 (then 120 in 1997, the arrival of the “depleted birth cohorts” of 1915-1919 having abruptly blocked the intake). Second, at least 30 members of the reference population had to be under 60. As we shall see later, the introduction of this “stock” restriction (rather than a “flow” restriction) would eventually create a new blockage. On the other hand, the rule that one-half of new entrants had to be under 55 was abolished.

16It can be added that Alfred Kastler had caused something of a stir in 1973 by publishing a Note in the Academy’s proceedings (Comptes Rendus) showing that if the curves for mean age at election and exit were extrapolated, the second would meet the first in the twenty-first century (Kastler, 1973). This trend-based interpretation was, in fact, slightly tendentious. First, the slope of the line showing the change in age at election was exaggerated (relative to our reconstruction) ; second, the age at election had already begun to stabilize several years before, at 62.7 years in 1965-1969 and 61.2 in 1970-1974, versus 64.9 in 1960-1964. But the alarm call was justified!

2 – Reconstruction of the population of members, 1666-2001

17The reconstruction seemed on the face of it a fairly simple task, as there are good biographical directories of members. We have relied mainly on the Index biographiques published by Gauthier-Villars (Index 1666-1978, Supplément 1978-1994, and Annuaires for 1995-2001). The volume of material, however, was substantial: information had to be extracted from over a thousand entries, when attention was limited to the field described below. The population to be studied had to be strictly defined. For the period from 1795 to the present, the situation is clear. Neither Corresponding Members nor Associate Members were full-fledged members of the Academy or, therefore, of the Institut. Regular Members were often — but not always — co-opted from the ranks of Corresponding Members. We counted all the full members, including the “Unaffiliated Academicians”, “Non-Resident Members”, and members of the Applications Section, but not those elected directly to the Applications Council of the Academy of Science [CADAS], formed in 1982, which became the Académie des Technologies in 2001.

18The situation was far more complex before 1793, as we have seen. We decided to include only the “Academicians” elected between 1666 and 1699, the (resident) “Stipended Members” elected between 1699 and 1793, the Secretaries, and the Treasurers. The hierarchical position of Pupils (who became Adjunct Members in 1716) and Associate Members was clearly defined in the 1699 statute, which stipulated that some Associate Members could be co-opted from the ranks of Pupils, and that Stipended Members could be elected from the ranks of Associate Members and Pupils. These two groups therefore had to be left out. Supernumerary Members were appointed pending the vacancy of a seat ; they are not counted in the membership and we therefore excluded them. The impact of this decision is negligible, as the election to Stipended Member typically occurred a few months, or at most one to two years, after the appointment as Supernumerary Member. As noted earlier, few Honorary Members were scientists, and there was little reason to include them, although the Presidents and Vice-Presidents were chosen from their ranks. As for the Senior Members, they were rather like retirees, who vacated their seats.

19The age at entry into the Academy is therefore that of election to the category of Stipended Member or regular Member. Many of these entrants were already, in fact, “affiliated” with the Academy as Pupils, Associate Members or Corresponding Members. The age “at first entry” might also be interesting to analyse in its own right, but we shall not do so here.

20Most exits from the Academy were through death. In the past, however, there were instances of resignations and removals, which we have taken into account since the resulting vacancies occasioned new elections. Members could be struck from the rolls (under the Ancien Régime) if they failed to take part in the Academy’s work, or if they left Paris for the provinces or another country. A handful of expulsions also occurred for political reasons: Carnot even managed to be elected twice (in 1796 and 1800) and expelled twice (in 1797 and in 1816). In all, we have identified 9 removals, 7 resignations, and 26 transfers to other categories, most often to that of Senior Member. Four members were elected twice, the second time after a removal or resignation. The last removal occurred in 1944 ; the last resignation was in 1872, and involved a member whose proposal for reforming the Academy had just been rejected.

21We compiled a data file comprising 1,039 members (4 having been elected twice) and containing the following information:

  • last name and first name ;
  • dates (day, month, year) of birth, first entry into the Academy, election as Member, death, and, where appropriate, exit before death ;
  • status at first entry (Pupil, Associated Member, Corresponding Member, etc.), status when elected regular Member (Stipended Member, Unaffiliated Member, etc.), and the affiliation Section(s) ;
  • additional information, if available, on the reason for exit before death, or on category changes.
In 4 cases, we had to impute a year of death (to prevent those academicians from indeed becoming “immortal” in our study! [3] and, in 13 cases, a year of birth. We chose these dates to be consistent with the mean ages at entry and death of the corresponding election cohorts ; consequently, there is no bias in the calculation of those mean ages, but some imprecision for the periods most affected by the phenomenon: the 4 unknown dates of death and 13 unknown dates of birth all concern members elected before 1725, of whom there were 72 in all.

22A similar data file was compiled for the 55 Honorary Members and the 6 individuals appointed “Senior Members” without having served as regular Members beforehand ; this group will be considered separately.

23The membership was reconstructed at 1 July of each year. The mean ages at election or exit were computed initially for ten-year periods because of the small numbers involved (one election per year, on average, until the Revolution), then for five-year periods (there were three or four elections per year, on average, until 1976).

24It should also be noted that the Academy has long been an all-male institution. Only five women have ever become members: the first was the mathematician Yvonne Choquet-Bruhat, elected in 1979 (who had been preceded by Marguerite Perey, as Corresponding Member, in 1962) ; more recently, Marianne Grunberg-Manago was the first female President (for years 1995-96) and Nicole Le Douarin the first female Perpetual Secretary (from 2001 on). Marie Curie, Nobel Prize in Chemistry in 1903 (and again in 1911), applied to join in 1910, but the General Assembly of the Institut decided that a female candidacy could not be considered.

3 – Changes in numbers

25The reconstructed membership populations must naturally be consistent with those defined in the statutes and reported in Table 1. But the situation was fairly blurred under the Ancien Regime, as the royal authority could transgress its own rules. Moreover, between a vacancy and the election to fill it there can be a delay. However, the changes in numbers since 1666 obtained with our reconstruction (Figure 1) were ultimately quite consistent with those of Table 1.

Figure 1

Académie des Sciences membership (at 1 July of each year), 1666-2001

Figure 1

Académie des Sciences membership (at 1 July of each year), 1666-2001

Source: Author’s reconstruction based on biographical indexes and yearbooks published by Institut de France.

26The total membership remained very small until 1800 (below 25): in the same period, the Académie Française already had 40 members. But it is true that the Académie des Sciences had larger “human reserves”, since the total number of Associate Members, Corresponding Members, and Pupils exceeded 120 by the early eighteenth century. The first major change dates from 1795-1816, when the membership exceeded 70 ; of the 62 members of Class I (scientists) appointed at the re-establishment in 1795, 40 were newcomers and 22 had belonged to the Académie Royale des Sciences dissolved in 1793. The increase was slow and uneven between 1913 and 1976. After 1987, the total population was no longer “regulated”, since it was the number of Academicians aged under 80 that had to be kept constant (at 110, then 120). The same is true of the 2002 reform: the reference population is now that of the under-75s (250). With 180 Corresponding Members under 70, plus the 120 regular Members in the reference population, the Academy at the close of the twentieth century had a theoretical number of 300 scientists eligible to participate in its proceedings (which is not the case of foreign Associate Members). This figure will not be equalled under the new statutes (250 Members) when the present Corresponding Members will all have reached age 70, since no more Corresponding Members will be elected.

4 – Changes in mean ages

27Figure 2 shows the change over time in the mean age of the members: the age is computed by calendar year difference. The Appendix contains the population pyramids at selected dates. To interpret the curve, we must rely on (1) the changes in the mean ages at entry and exit, which are plotted in Figure 3a (we have used identical scales for both figures), and (2) the number of elected and deceased members in later periods (Figure 4). The number of deaths will be taken here as equal to the number of “leavers” regardless of cause: the two figures are by and large very close except after 1987, when members were automatically removed from the reference population at age 80.

Figure 2

Mean age of Académie des Sciences members, 1666-2001

Figure 2

Mean age of Académie des Sciences members, 1666-2001

Source: Author’s reconstruction based on biographical indexes and yearbooks published by Institut de France.
Figure 3a

Mean age at election (by year of election) and at death (by year of death) of Académie des Sciences members 1666-2001 (ten-year periods to 1800, five-year periods thereafter)

Figure 3a

Mean age at election (by year of election) and at death (by year of death) of Académie des Sciences members 1666-2001 (ten-year periods to 1800, five-year periods thereafter)

Source: Author’s reconstruction based on biographical indexes and yearbooks published by Institut de France.
Figure 4

Number of members elected to Académie des Sciences and number of deaths (ten-year periods to 1800, five-year periods thereafter ; from 1987 on, seats are vacated at age 80)

Figure 4

Number of members elected to Académie des Sciences and number of deaths (ten-year periods to 1800, five-year periods thereafter ; from 1987 on, seats are vacated at age 80)

Source: Author’s reconstruction based on biographical indexes and yearbooks published by Institut de France.

28The mean age of the 15 members appointed by the King in 1666 was 53. The ten members elected in 1675-1684 were particularly young (36 years, on average). The group’s mean age declined during that decade, but then rose again. The periods 1700-1740 and 1820-1840 also saw the mean age of newly elected members fall more than 10 years, which had an impact on the mean age of the total membership: a historical low was reached in 1740-45, with a mean of 51 for the 20 members. In the intermediate periods, when the entrants were older (and the intake sometimes smaller), the mean age rose, also because of an upward trend in the age at death: the latter rose from 67 years around 1700 to 71 in 1810-1814, peaking at over 80 for the 8 deceased in 1815-1819.

29The expansion in membership in 1795 was responsible for an abrupt fall in the mean age, as the 40 new members had a mean age of 50: the mean age of the total membership fell to 55, a level never matched since. While the age at death remained virtually constant between 1820 and 1910, the age at election rose steadily as of 1840 — from 50 in 1845-1849 to 60 in 1910-1914. The aging process had thus begun to affect the group well before the fall in mortality (after age 60) began to have an impact. Both effects were combined in the 1920-1965 period: the mean age at election continued to rise, reaching 65 in 1960-1964, while the age at death rose from 77 to 83 ; this drove up the mean age of members from 63 in 1920 to 73 in 1965.

30Recent decades have seen a reversal of the trend. While age at death continues to rise (more slowly), the age at election fell to 55 in 2000-2001. This is the result of a deliberate policy, initially purely of principle, then under the dual requirement adopted in 1987: 120 members aged under 80, including 30 members aged under 60. The consequence has been a fall in the membership’s mean age and its subsequent stabilization at around 70, for all members taken together (i.e. including those over 80, who retain their full rights).

31The length of tenure in the Academy (Figure 3b) has varied little in 335 years. It settled at 20 years at the outset and was still at that value in the 1980s. The very recent rise (since 1990) is due to the fact that the age at entry has fallen since the mid-1960s.
Figure 3b

Mean length of tenure at Académie des Sciences (by year of death), 1666-2001 (ten-year periods to 1800, five-year periods thereafter)

Figure 3b

Mean length of tenure at Académie des Sciences (by year of death), 1666-2001 (ten-year periods to 1800, five-year periods thereafter)

Source: Author’s reconstruction based on biographical indexes and yearbooks published by Institut de France.
Figure 4 shows the number of members elected and deceased by period. In principle, these two series should coincide, except when the Academy expanded its membership (peaks in 1795, 1816, 1945, and 1976, in particular) and after 1987, because of the rule excluding members from the reference population at age 80. As we can see, the intake rose from an annual average of about 1 before 1800 to 5-6 after 1945 ; since the new members are distributed between 10 or 12 Sections, the rate of replacement is therefore hardly high.

32Some individual records deserve mention. The mathematician Alexis-Claude Clairaut was elected Stipended Member in 1733 when he had just turned 25. He had already been appointed “Adjunct Member” in Mechanics [adjoint-mécanicien] two years earlier by special dispensation. Arago was elected member of the First Class of the Institut National in 1809 at 23. A total of 13 members were elected before age 30, all before 1833. At the other extreme, Henri Hartmann was elected member of the Medicine Section aged nearly 85 in 1945, Alexandre Pingré was elected to the Astronomy Section in 1795 at 84 (he died five months later) and Henri Devaux at the same age in 1946 in the Botany Section. A total of 13 members were elected after turning 80. The longevity record is held by René Wurmser, who died in 1993 aged 103 years and 15 days. The previous record had long been held by Michel-Eugène Chevreul, who died at 102 years and 7 months in 1889. Some members had particularly long tenures: Chevreul was in place for nearly 63 years, Jean-Baptiste Biot (died 1862) for 58 years, Claude-Louis Mathieu (died 1875) for almost as long, and 11 others held office for over 50 years.

5 – Honorary Members

33The “Honorary Members” category existed only between 1699 and 1793. A total of 55 individuals were named by the King, often at an early age. Their mean age at appointment does not differ significantly from that of regular Members, fluctuating between 45 and 55. Seven Honorary Members were even appointed before age 30. Their mean age at death (around 70 years) is also very comparable to that of the other members, as is their length of service (around 20 years).

II – Comparisons with other academies

34France has a fairly large number of academies. In addition to the five that together form the Institut de France, we should mention the Académie Nationale de Médecine (130 regular members) and the Académie d’Agriculture de France (120 members), which enjoy official recognition and maintain regular contact with the Académie des Sciences. But there are also an architecture academy, a naval academy, a pharmacy academy, a veterinary-medicine academy, and many regional academies. Discussion here is limited to some comparisons between comparable (and available!) data on the Académie Française (since 1639) and the Académie des Sciences Morales et Politiques (since 1832), recently studied by Jacques Dupâquier (Dupâquier, 2000) [4], and the Académie Nationale de Médecine (since 1850), studied by Georges David and the author of this article (David and Leridon, 1999) [5].

35There are strong similarities (Table 2). In the two oldest bodies — Académie Française and Académie des Sciences — the mean ages of members were nearly identical around 1650 (52 and 53 years respectively), but the age at election was slightly younger in the former. We have figures for all four academies in or around 1850: the mean age was youngest for the newly founded Académie de Médecine (46), followed by the Académie des Sciences (57), Académie Française (61.5), and Académie des Sciences Morales et Politiques (67). The figures converged in subsequent decades, and became very consistent by 1950: the mean ages ranged between 70 (Académie des Sciences) and 74 (Académie Française) ; ages at entry, between 60 and 66 ; ages at death, between 77 and 79.

Table 2

Change in memberships and mean ages of selected french academies

Table 2
Year or period 1670 1750 1850 1950 2000 Number of members (statutory) Académie Française 40 40 40 40 40 Académie des Sciences 20 20 75 96 > 120 Académie des Sciences Morales et Politiques – – 35 48 48 Académie Nationale de Médecine – – 100 140 130 Mean age of members Académie Française 52 yrs 58 yrs 61 yrs 74 yrs 78 yrs Académie des Sciences 53 yrs 52 yrs 57 yrs 70 yrs 70 yrs Académie des Sciences Morales et Politiques – – 67 yrs 71 yrs 78 yrs Académie Nationale de Médecine – – 46 yrs 71 yrs 78 yrs Académie Française 1639- 1700- 1800- 1900- 1996-2000 1699 1799 1899 1999 Mean age at election 42.3 45.9 53.3 64.1 70.9 Mean age at death 68.6 70.4 73.0 78.9 85.3 Length of tenure* 22.3 22.7 20.0 16.7 19.9 Académie des Sciences 1666- 1700- 1800- 1900- 2000-2001 1699 1799 1899 1999 Mean age at election 47.3 47.6 51.0 60.1 59.8 Mean age at death 67.1 69.8 72.2 79.2 80.6 Length of tenure* – 21.0 21.3 19.2 22.4** Académie des Sciences Morales et Politiques 1832-1899 1900-1949 1950-1999 Mean age at election – – 58.0 62.2 68.2 Mean age at death – – 75.7 78.7 82.7 Length of tenure* – – 17.0 16.7 14.7 Académie Nationale de Médecine c. 1850 c. 1950 c. 2000 Mean age at election – – 46 66 67 Mean age at death – – – 77 85 Length of tenure* – – – 17 18 * Tenure computed for members who died during the period. ** Length of stay in reference population (< age 80). Sources: David and Leridon (1999), Dupâquier (2000), and author’s computations.

Change in memberships and mean ages of selected french academies

36Thereafter, aging continued in three of the academies. The mean age reached 78 in around 2000 except in the Académie des Sciences, where — as seen earlier — it fell, standing at 70 in 2000. The Académie des Sciences is in fact the only body to have implemented a recruitment policy capable of counteracting the spontaneous trends. The result is even more striking for the age distribution: the proportion aged under 60 is 18% in the Académie des Sciences but below 10% in the other three. The difference is even greater for the under-70s: 47% in the Académie des Sciences, 13-23% elsewhere.

37In all these academies, the number of regular members is small (40-130) relative to those of the two leading foreign scientific academies: the British Royal Society, founded in 1660, has 1,230 Fellows ; the U.S. National Academy of Sciences, founded in 1863, has 1,860 active (U.S.-resident) members. Allowing for the fact that the U.S. population is about five times that of France, and the fact that the NAS covers a broader range of disciplines than the Académie des Sciences, the latter should have between 300 and 350 members to be comparable in size to the NAS. The 2002 reform will bring the Academy closer to that target, with 250 regular Members aged under 75 (not counting the present Corresponding Members), and a total membership of 300 in 20 years. The context is different for the Royal Society: France and the U.K. have roughly the same population, but the Royal Society Fellows are co-opted from all the countries of the Commonwealth, including notably Canada, Australia, India, and Pakistan. On balance, however, the “strictly domestic” membership of the Royal Society is probably much larger than that of the Académie des Sciences [6]. Moreover, the rule governing change at the Royal Society is by number of new Fellows elected per year: this is currently 42 (whereas deaths numbered only 22 in 2002), as opposed to about 15 for the Académie des Sciences when the new system becomes permanent. This situation arguably reflects the fact that the Royal Society is not constrained by the need to pay its members, unlike the Institut de France. On the contrary, Fellows pay annual dues (£150 in 1999). In addition, the Fellows deceased in 2002 had an average age at election of under 50 (compared with 55 for the new members of the Académie des Sciences under the new system), and had served more than 31 years.

38It can be added that most of the major industrialized countries also have academies specializing in technology: the Royal Society of Engineering in the U.K. (1,300 members), the National Academy of Engineering in the U.S. (1,880 active national members), and now the Académie des Technologies in France (122 regular members and 55 emeritus members). The latter replaced, at the end of 2001, the Conseil pour les Applications de l’Académie des Sciences (CADAS), which included members appointed by the Académie des Sciences and members elected directly by CADAS.

III – Dynamics of a learned body: Application to the Académie des Sciences

39After describing the situations and actual changes in various academies, let us return to the broader issue of the dynamics of this type of population. A classic result, in demography as in epidemiology, establishes the connection between the size of a population and the entry rate and length of stay, when entry and exit conditions are unvarying. If the total size stays constant, the population is in a stationary state and the relation is written:

41where P is the population size, N the number of annual entries (here: of elections), D the length of stay equal to AS – AE, AE being the mean age at entry (i.e. at election) and AS the mean age at exit (i.e. in most cases, at death) [7].

42The mean age of current members (Am) is approximately equal to the mean of AS and AE, which, strictly speaking, would be true only for a linear distribution of lengths of stay:

44These very simple relations enable us to understand the equilibrium mechanisms involved. First, the basic process: if AS increases (simply by an increase in the life expectancy), and if P and AE do not change, the mean age of current members increases and N decreases. To clarify this, let us assume the mean age at death rises from 72.5 to 85, with the age at entry remaining close to 60. This will mechanically result in an increase of 6.25 years in the mean age of the membership, and a halving of the annual intake (when AS – AE rises from 12.5 to 25 years, N must fall by half).

45If the institution decides to lower the age at entry (AE) to slow the rise in the group’s mean age, the length of stay (D) will increase further, causing an additional decline in annual intake (N) — again, assuming an unchanged population size. The renewal of the population will be slower.

46Since (fortunately!) age at death cannot be controlled, one solution is to set a mandatory leaving age through accession to “emeritus“ or “honorary” membership. With AS now constant, there is no longer any need to change AE. In practice, as the academy can choose a leaving age substantially below the (current) mean age at death, it can even lower the age at entry and thus rejuvenate its membership definitively. If, for example, the academy sets a compulsory leaving age 10 years below the current age at death, it can lower the mean age at entry by the same number of years. The effect will be passed on in full to the mean age of the population, which will also fall by 10 years.

47An increase in the total population P creates a new regime, in which the number of entrants N increases in the same proportion as P if the other parameters stay unchanged. Moreover, it can produce an appreciable rejuvenation in the short term, if the mean age of the additional members elected the first year is markedly lower than the mean age of incumbent members.

48The reconstruction charted in Figure 1 showed that, for the Académie des Sciences, the conditions of stationarity hold over long periods — from 1666 to 1793, from 1795 to 1913, and from 1914 to 1965, with the in-between dates corresponding to sharp discontinuities. We shall therefore assume that the 2002 reform marks the start of a new stationary period and, on the basis of this assumption, examine the consequences of various possible changes in the Academy’s statutes.

49Our main focus here will be on the goal of rejuvenating the institution. This requires inventing a rule by which to counteract the natural aging resulting from the steady rise in longevity. It will be recalled that the 1987 reform had imposed a twin restriction: the Academy had to include 110 members aged under 80, of whom at least 30 were aged under 60. The first requirement was not difficult to implement, since it merely defined the age of exit from the reference population, i.e. the age when the seat is declared vacant. The second was more awkward: all that could be done was to register, at a given moment, that the number of under-60s had fallen below 30, thus triggering the obligation to elect only candidates under 60. That was indeed the purpose of the rule defined (to force the introduction of younger members), but its implementation depended on the random variations in the overall age distribution of the group. In 2002, the Academy instead opted for a further lowering of the exit age, to 75, and for stipulating that at least half of the annual intake should be of candidates under 55. These rules were set after an analysis of the impact of the various possible alternatives in a stationary population regime, and after simulating the changes in the group on the basis of the initial age distribution (these are the findings reported in this and the next sections). Lastly, the reference population (i.e. members under 75) was set at 250, a figure to be reached in five or six years.

50Table 3 gives some results of “stationary” regimes obtained with the formulas shown above, on the basis of a population of 250 members.

Table 3

Alternative stationary regimes

Table 3
Reference population P Mean age at entry AE Mean age at exit AS Length of tenure AS – AE Mean age of reference population Am Mean annual intake N Hypothesis 1 Present conditions (1995-1999), without 80-year age limit 250 60.0 85.0 25.0 72.50 10.0 Hypothesis 2 Same as Hypothesis 1 with 25-yr projection of mortality trend (AS = 87.5 yrs) 250 60.0 87.5 27.5 73.80 9.1 Hypothesis 2b AS = 87.5 yrs, AE = 55 yrs (–5 yrs) 250 55.0 87.5 32.5 71.25 7.7 Hypothesis 3 AS = 80 yrs (ER limit)* (AE unchanged = 60 yrs) 250 60.0 80.0 20.0 70.00 12.5 Hypothesis 4 AS = 75 yrs (ER limit) (AE unchanged = 60 yrs) 250 60.0 75.0 15.0 67.50 16.7 Hypothesis 5 AS = 75 yrs (ER limit) AE = 55 yrs (–5 yrs) 250 55.0 75.0 20.0 65.00 12.5 Hypothesis 5b AS = 75 yrs (ER limit) AE = 50 yrs (–10 yrs) 250 50.0 75.0 25.0 62.50 10.0 Hypothesis 6 AS = 70 yrs (ER limit) AE = 55 yrs (–5 yrs) 250 55.0 70.0 15.0 62.50 16.7 Hypothesis 6b AS = 70 yrs (ER limit) AE = 50 yrs (–10 yrs) 250 50.0 70.0 20.0 60.00 12.5 * ER limit = exit from reference population.

Alternative stationary regimes

51Hypothesis 1 corresponds roughly to the present situation, assuming a mean age at election of 60 but without defining a reference population. Hypothesis 2 simply assumes a change in the mortality function in line with present trends (25-year projection), while Hypothesis 3 allows for the notion of reference population as it existed until 2001.

52Hypotheses 4-6 explore the consequences of a lowering of the age limit for the reference population to 75 or 70, combined or not with a reduction of the maximum age at entry to 60, 55 or 50. One of the main findings is that the mean age does not fall significantly except with an exit age of about 75 or less. Once this exit age is chosen, a compromise has to be reached between two contradictory goals: a major rejuvenation of the intake, and the preservation of a high rate of intake. As we shall see, the hypothesis of a mean age at election of 55 is entirely realistic within the context of a future single-category institution, and in the end the Academy chose option 5.

IV – Projections

1 – The principles of the 2002 reform

53The policy implemented by the Académie des Sciences from 1965 onward was backed up by a heavy “investment” in Corresponding Members. Not only was their number raised to 180 (aged under 70) in 1987, but the Academy sought (1) to diversify the disciplines they represented, (2) to elect them at a considerably younger age than regular Members (5 years younger on average, in recent years), and (3) to involve them in almost all the Academy’s activities, except for electing Members and amending the statutes. This policy has unquestionably borne fruit, but has also shown its limits: if the same services are expected from a Corresponding Member as from a regular Member, how can the existence of two distinct categories be justified? This explains the emergence of a plan that became one of the main provisions of the 2002 reform: a substantial increase in membership, the abolition of the Corresponding Member category, and the introduction of new rules to preserve the advantages of the earlier situation. Another objective, as has been noted, was to lower the mean age of the group (1) by introducing an age for leaving the “reference population” (leavers would lose no rights apart from that of voting in elections for new members, but their seats would become vacant), and (2) by stipulating that half of the new entrants had to be under 55.

2 – Transition to 250 members: method of calculation

54The preceding analyses only describe the situation in a permanent regime, when all parameters are kept constant. But the rapid shift to a membership of 250 poses a transition problem, which cannot be addressed except through a detailed simulation of the evolution of the population year by year.

55For this purpose, we define for each year n a “reference population” (REFn), set exogenously on the basis of the new vacancies created in the transitional phase [8]. A member enters the population by election and leaves it by dying or by reaching the age limit (E) set for the reference population.

56Different rules may apply to the initial population (incumbent members at 1 January 2000, whatever their age: POPI) and to those elected later (new members: POPN). The new rules will not apply to members already serving on the date of the statute change. The decomposition of the age-X group in year n is thus:

58We have a mortality function, defined by the probabilities QMOR(X). We can make these probabilities time-dependent — to allow for the decline in mortality — by multiplying them each year by a coefficient K.

59For the year n, we compute the number of deaths (NDECn) leading to vacancies. This is equal to the total number of deaths occurring before the age limit E in either group, plus the deaths after that age in the first group. The number of members reaching the age limit in year n, NEMEn(X), determines a number of additional vacancies to be filled.

60Hence the number of potential members to be elected (after summing over all ages X < E):

62if the reference population changes between the two consecutive years, as will happen during the transitional period.

63The age distribution of elected members follows aREPEL(X) law (with ? REPEL(X) = 1):

65The populations POPI and POPN ultimately evolve as follows:

3 – Choice of parameters

68The initial age distribution is that of the 143 incumbent members at 1 January 1999 (of whom 28 were aged over 80).

69The age-specific mortality rates were determined by studying the populations of two academies (Académie des Sciences and Académie de Médecine) over the period 1969-1999. Their life expectancy at 60 is almost 23 years, or 3-4 years more than the current French male population. Next, we assumed an annual life-expectancy gain of 0.1 years (at age 60), which leads to multiplying the age-specific probabilities of death by 0.99 per year. Over the last 10 years the mean annual gain in the French population at the same age was 1.3 years: our value is thus slightly lower, which may be justified by the fact that the life expectancy of academicians already exceeds the French average.

70The age distribution of entrants is a crucial element. After analysing the ages at election of current regular Members and Corresponding Members, we chose a distribution centred on 55 years, ranging from 40 to 70 years.

71Figure 5a shows that the model chosen reflects quite closely the distribution of ages at election of the 137 current members elected after 1970, with a mean age of 56.3, which is still substantially higher than the ages at election of the Corresponding Members (200 aged under 75 in 2001), whose mean age was 51.7. If we combine the two distributions, in the scenario of a future single-category membership, we see (Figure 5b) that the chosen model remains on average slightly higher than the combined group. It is therefore a realistic hypothesis ; by contrast, it would be harder to reduce the mean age to 50. The advantage of this hypothesis is that it can be easily translated into a statutory requirement: one-half of the intake aged under 55, one-half over (a similar rule formerly applied to Corresponding Members, with age 50 as the dividing line).

Figure 5a

Actual age distributions of regular Members and Corresponding Members of Académie des Sciences (1970-1998) and distribution specified for scenarios A and B

Figure 5a

Actual age distributions of regular Members and Corresponding Members of Académie des Sciences (1970-1998) and distribution specified for scenarios A and B

Source: Author’s reconstruction based on biographical indexes and yearbooks published by Institut de France ; author’s computations.
Figure 5b

Actual distribution of ages at election for regular Members and Corresponding Members combined (1970-1998) and distribution specified for scenarios A and B

Figure 5b

Actual distribution of ages at election for regular Members and Corresponding Members combined (1970-1998) and distribution specified for scenarios A and B

Source: author’s reconstruction based on biographical indexes and yearbooks published by Institut de France ; author’s computations.

Scenario A: Trend projection, with one-half of the intake aged under 55

72On these bases, we conducted a series of simulations, of which only two are described here. The simulation period was 30 years — the time needed to reach a practically stationary regime. The simulations were performed age by age (from 40 to 100), and year by year (from year 0, just before the application of the reform, to year 30).

73The first scenario must serve as the reference: it describes the spontaneous change in the population, with no changes to the rules. The assumptions are as follows:

  • number of members under age 80 (= REF) kept at 120 ;
  • mortality changes as described earlier (choice of parameters) ;
  • intake follows the distribution defined above, which is, it will be recalled, younger than that of the ages at election of current members (we therefore admit a “spontaneous” rejuvenation of the intake), and without seeking to comply with the requirement that at least 30 members should be aged under 60.
The main results are reported in Figures 6a and 6b. With a mean age at entry of 55:
  • the (overall) mean age falls from 71 to 69.5, then rises back to 71 ;
  • the mean age of the reference population (under 80) falls from 66.5 to 64, then rises back to 66 ;
  • the annual intake fluctuates between 3 and 8, stabilizing at around 6 ;
  • the total population reaches 153 in 15 years, and 165 in 30 years [not shown] ;
  • the number aged under 60 rises immediately to 30, fluctuates between 32 and 36 for 10 years, then falls back to 26-29 in years 11-24: this pattern therefore confirms the current situation, in which elections of members aged over 60 are blocked, since the requirement that 30 members should be under 60 cannot be met “spontaneously”, even with a rule that half of the new entrants must be aged under 55.

Figure 6

Projection of selected characteristics of Académie des Sciences membership: scenario A (trend)

Figure 6

Projection of selected characteristics of Académie des Sciences membership: scenario A (trend)

Source: author’s computations.

Scenario B: New regime, with a single-category membership of 250, exit from reference population at 75 for new members only, and smoothing of transition

74This scenario incorporates the main provisions of the 2002 reform ; it also approximates to the stationary regime 5 described in Table 3.

75The assumptions are as follows:
  • transition to a “reference” population of 250, with a 75-year age limit for new members only ;
  • trend in mortality as above ;
  • election of 100 members in 6 years (15+15+20+20+15+15) [9] ;
  • reference population equal each year to sum of all incumbent members (POPI) and new members aged under 75 (POPN) ;
  • to facilitate the transition (most notably on the assumption that current Corresponding Members will be the main source of new members), the mean age at entry is set at 60 in the first year (lagging the model defined above), 59 in the second year,…. and 55 in the sixth and all following years (these decrements were ultimately not included in the reform).
Figures 7a and 7b show that sharp fluctuations will occur:
  • the mean age of the total membership falls from 71 to 66.5 in 8 years, but then rises again and is back at 69 after 30 years ; for the reference population, the upturn lasts only 1 year and the mean age then falls quickly (with the exit of members elected before 2002): it drops below 66 after 30 years ; the pattern is similar for the mean age of the under-75s, but the initial value (63) is reached again after 30 years ;
  • after the wave of special elections (capped at 15-20 per year), the number of elections per annum falls to 7, returns to 15 in about 15 years, then settles at about 13 ;
  • the proportion of under-60s (in the reference population) rises from 20% to 30% in the first few years, drops back to 22% after 15 years, then stabilizes at around 30% ;
  • because the initial rate of intake is slightly too low, the reference population is still only 193 after 5 years, 223 after 8 years, and 244 after 11 years [not shown] ; to the 100 planned elections, we should add those to fill normal vacancies, equivalent to approximately 30 during the period ;
  • the total membership stays close to the reference population in the first 10 years, then grows more quickly, reaching 343 after 30 years.
Figure 7

Projection of selected characteristics of Académie des Sciences membership: scenario B (with reform)

Figure 7

Projection of selected characteristics of Académie des Sciences membership: scenario B (with reform)

Source: author’s computations.
The benefits of the reform will therefore be marked for the mean age of members in the reference population: it will have fallen below 67 in 10 years, and below 66 in the longer run. The proportion of under-60s in the total will come close to 30% — a value that will also be that of the final stabilized situation. The rate of intake will also benefit from the increase in the total membership, rising from 5 to 14 per year, or by more than one per year and per Section in the system as currently organized.

76A further comment: if, in Figure 7a, the mean age of the reference population remains — after 30 years — substantially higher than that of the under-75s (at 65.3 versus 62.9), it is because the reference population still contains approximately 10% of members from the population present in 1999, whose mean age would be approaching 90 at the end of the simulation period.


77In a context of rising life expectancy, especially when the gains are concentrated at ages over 60, the mean age of the population of an academy whose membership is held constant can only increase. Of course, academicians of a given age are in better health today than those of the same age in the past, as is true for the general population (academicians probably even enjoy a specific advantage in this respect). The problem posed by the aging of the group is that of contact with the realities of the world of research, education, and economic activity in general, if the age at which the members have formally left it is unchanged.

78To counteract the spontaneous trend to aging in the institution, while retaining the principle of “perpetuity” for each member, new members would have to be elected at increasingly young ages year after year, which would have the drawback of reducing the rate of population replacement. Another solution, if it could be accepted, would be a continuous increase in membership: an annual growth of 2%, causing the population to double every 35 years, would lower the mean age relative to the initial stationary population by about 2 years ; an annual growth of 5%, doubling the population every 14 years, would lower the mean age by 4 years. It should be noted that this advantage would be secured once and for all: the mean age of a stable population — i.e. a population with a fixed rate of increase — remains constant.

79If we discard the hypothesis of a continuous increase in the number of members, the first effective “remedy” is to decide on a fixed age of exit from the Academy, via emeritus or honorary membership that frees seats without necessarily severing all ties with the institution. A second solution involves regulating the age at entry, with the simplest arrangement being to set a quota below a given age. The optimal solution is to combine both measures.

80That is what the Académie des Sciences managed to do from the mid-1960s, first by setting an age requirement for newly elected members, then by defining a “reference population” in 1987. The mean age at election consequently fell by 10 years and the mean age of members by 5 years ; if we restrict attention to the under-80s (reference population between 1987 and 2001), the mean age has declined to about 65-66.

81The 2002 reform will allow this new trend to be consolidated, in a context of an appreciable growth in membership. This type of reform always introduces a discontinuity that is reflected in more or less unmanageable fluctuations. Initially, the reform has a radical effect on the mean age of members, since the population is suddenly swollen by an influx of persons younger than the average of the members. These newcomers then age, while the rate of intake stabilizes at the normal rate of the new regime: the mean age therefore rises again, and the fluctuations are slow to become smoothed out. It is better to be aware of the phenomenon beforehand so as not to worry when it occurs.

82Overall, the Académie des Sciences will have been among the first to have controlled its natural evolution successfully. While the mean age of members of other institutions will often exceed 80, in the Academy it should very quickly return to 63 for members aged under 75 (who will form the reference population), and to 69 for the total membership, up to 2030. This change is accompanied by a large increase in the number of members, which seems essential if the Academy is to incorporate the new fields of scientific research and accomplish what one hopes will be increasingly numerous and useful tasks.

83What broader lessons can we draw from this historical reconstruction and the projection exercise? The results of section III obviously have a general relevance when the group (or even the rank) examined forms a stationary population. Unlike in many demographic studies of professional bodies, we are dealing here with a “single-rank” organization. In fact, since a proportion of the regular Members of the Academy are co-opted from among the Corresponding Members (formerly: from the Pupils, Adjunct Members, or Associate Members), the members of both categories could be studied together. We have not done so here because (for the moment) the necessary data are not all available: our data file does not include the Corresponding Members who did not become regular Members. It can be noted, however, that between 1705 and 1793, nearly all new regular Members had previously held another position in the Academy ; the proportion was subsequently fairly small, given the small number of Corresponding Members and the contradictory residence requirements for the two categories. Since 1985, by contrast, nearly three-quarters of the new regular Members had already been elected Corresponding Members, at a mean age of 51. Also, as noted earlier, the election of Corresponding Members stopped with the 2002 reform.

84Our projections provide further corroboration of the early analyses by Louis Henry: large-scale recruitment campaigns invariably cause sharp fluctuations, while the purpose of such initiatives is usually to correct an evolution judged to be harmful. It is important, therefore, to be vigilant and to optimize the size of the additional intake and the ages of new entrants, so as to minimize the negative effects of the resulting discontinuity.

85There is a sense in which the present article also explores the “demography of seniors”. The population aged over 65 is going to grow rapidly in the years ahead. Its age distribution will also change dramatically, as life-expectancy gains are larger at higher ages. At the same time, however, because the state of health — at a given age — is set to improve, too sharp a separation between the economically active population and the retired population will become increasingly hard to justify.


Age distribution of members of the Académie des Sciences at selected dates

Figure 8

Age distribution of members of the Académie des Sciences at selected dates

Source: Author’s reconstruction based on biographical indexes and yearbooks published by Institut de France.


  • [*]
    Institut National d’Études Démographiques and Institut National de la Santé et de la Recherche Médicale (U569, IFR69), Paris.
    Translated by Jonathan Mandelbaum.
  • [1]
    Also Maury, 1864 ; Institut de France, 1967 ; Brian, 1995 ; Brian and Demeulenaere-Douyère, 1996 ; Académie des Sciences, 2002.
  • [2]
    The Secretaries will be called “perpetual” from 1803 on. The origin of the term “perpetual” is the following. The Academy’s first “heads” were co-opted or appointed by the King for a year’s term. When it was decided that the Secretary would not have to comply with this requirement, but would be elected without a term limit, his position was described as “perpetual”. Today, Perpetual Secretaries retire at 75.
  • [3]
    Members of the French academies have traditionally been referred to as “les immortels” [Translator’s note].
  • [4]
    In 1795, the Directory established a 36-member Class for “moral and political sciences” in the Institut National des Arts et des Sciences. It was abolished in 1803 and restored in 1832, with 30 regular Members and 5 Unaffiliated Academicians.
  • [5]
    Jacques Véron (1985) has previously studied the Académie Française. In a related field, Jacques Houdaille (1989) has examined the population of Nobel prize-winners.
  • [6]
    A quick sampling of the 2003 directory of the Fellows of the Royal Society, which simply lists place of residence (and not nationality), shows that 11% reside in the U.S. (most of these are presumably British nationals) and 12% in another country, mainly Australia and Canada (these are probably not British nationals).
  • [7]
    In the reconstruction presented earlier, we were able to compute the actual lengths of stay from individual records. Many studies simply calculate the difference between the mean age of year n leavers and that of members elected in the same year. This does not necessarily correspond to the mean length of stay of the leavers or to the future mean length of stay of the newly elected members, as the conditions of stationarity are not always met.
  • [8]
    As the Academy’s total membership on 1 January 1999 stood at 143, 100 additional seats were allocated to move toward the goal of 250 members: the new population comprised only those aged under 75.
  • [9]
    The values shown on chart 7b do not exactly match these whole values, as the projection uses fractional numbers to take mortality into account.


Most academies are closed societies: members are admitted by election and remain until their death, and the total population usually remains constant over a given period. The demography of a closed body of this kind is simple: the annual intake is strictly determined by the annual “exits”, i.e. deaths, which is an exogenous variable. As a result, the rate of intake and the length of service in the institution are fully related, and also depend on age at election. In a context where the length of life is increasing (via the fall in mortality at ages above 60), the mean age of the population can only rise — unless the Academy elects ever younger members, which, in turn, reduces the rate of renewal. A more efficient solution is to set an age at which a seat is declared vacant.
This article begins with a summary of the main mechanisms at work in a stationary population. We then provide a brief overview of the history of the Académie des Sciences between 1666 and 2001 and a reconstruction of the evolution of its population (1,039 members over this period). After some comparisons with other academies, we conclude with the results of 30-year projections based on different hypotheses for changes in entry and exit rules — in particular the changes resulting from the amendments to the statutes adopted in 2002.



Une académie constitue généralement une société fermée : on y entre par élection, on en reste membre jusqu’à son décès, et l’effectif total demeure le plus souvent immuable sur une certaine période. La démographie d’un tel corps fermé est simple : le nombre annuel des entrées est conditionné strictement par celui des « sorties », c’est-à-dire des décès, qui est une donnée exogène. Il en résulte que le rythme des entrées et la durée de présence dans le corps sont complètement liés, et qu’ils dépendent aussi de l’âge à l’élection. Dans un contexte d’augmentation de la durée de vie (grâce à la baisse de la mortalité au-delà de 60 ans), l’âge moyen de la population ne peut qu’augmenter, sauf à recruter des membres de plus en plus jeunes et à réduire, ipso facto, le taux de renouvellement. Une solution plus efficace consiste à fixer un âge à partir duquel le poste est déclaré vacant.
Dans le présent article, nous rappelons d’abord les principaux mécanismes en jeu dans une population stationnaire. Nous proposons ensuite un bref historique de l’Académie des sciences, de 1666 à 2001, ainsi qu’une reconstitution de l’évolution de sa population (1039 membres au cours de cette période). Après quelques comparaisons avec d’autres académies, nous présentons finalement des résultats de projections effectuées à horizon de 30 ans, sur la base de diverses hypothèses d’évolution des règles de recrutement et de sortie, en particulier celles résultant des changements statutaires décidés en 2002.



Normalmente, una academia constituye una sociedad cerrada: se entra en ella por elección, se es miembro vitalicio y el efectivo total de miembros permanece inmutable durante un cierto tiempo. La demografía de tal ente cerrado es simple: el número anual de entradas está estrictamente condicionado por el de “salidas”, es decir de muertes, que es una variable exógena. Como consecuencia, el ritmo de entradas y la duración de presencia en la academia están en relación directa y dependen de la edad de los miembros en el momento de su elección. En un contexto de aumento de la esperanza de vida (gracias a la disminución de la mortalidad por encima de los 60 años), la edad media de la población va a ir en aumento a menos que se acepten miembros cada vez más jóvenes y que se reduzca ipso facto la tasa de renovación. Una solución más eficaz consiste en fijar una edad a partir de la cual el puesto se declara vacante.
En este artículo recordamos, para empezar, los mecanismos principales que intervienen en el seno de una población estacionaria. A continuación proponemos una breve historia de la Academia de Ciencias, de 1666 al 2001, y reconstituimos la evolución de su población (1039 miembros durante este periodo). Después de realizar algunas comparaciones con otras academias, presentamos los resultados de proyecciones llevadas a cabo a un horizonte de 30 años en base a varias hipótesis sobre la evolución de las reglas de entrada y de salida, especialmente las que resultan de los cambios estatutarios acordados en el 2002.


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Henri Leridon [*]
Henri Leridon, Unité mixte INED-INSERM “Épidémiologie, démographie et sciences sociales : santé reproductive, sexualité et infection à VIH” (U569), Hôpital de Bicêtre, 82 rue du Général Leclerc, 94276 Le Kremlin-Bicêtre, France, Phone: 33 (0)1 45 21 23 31, Fax: 33 (0)1 45 21 20 75
  • [*]
    Institut National d’Études Démographiques and Institut National de la Santé et de la Recherche Médicale (U569, IFR69), Paris.
    Translated by Jonathan Mandelbaum.
Translated by
Jonathan Mandelbaum
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