Age structured populations with fixed size

The logic of population dynamics implies that in a human population closed to migration the only alternative is growing or ageing (ruling out early death). Additionally excluding sustained population growth, a continuing trend towards top-heavy age pyramids is unavoidable. Subpopulations such as learned societies are no exception to this rule. One striking feature of academies of sciences is their increasing "over-ageing". Faced with rising life expectancy, particularly for older persons, the average age of academy members has increased conspicuously. This trend of over-ageing is enforced by an increase in the age at election. A first objective of the current project is the comparative study of age dynamics of learned societies. We want to assess the impact of longevity and intake, size, and retirement policies (or of the lack thereof) on the age composition and size of these societies. A comparative study of this sort will permit us to decompose the interplay of recruitment policies and external conditions (e.g., survival) and assess their influence on the future development of the academies. To counteract the spontaneous trends in ageing in the institution, new members would have to be elected at increasingly young ages, which would have the drawback of reducing the rate of population replacement under fixed-size or moderate growth policies. The second main objective of the proposal is thus to derive the optimal strategy of recruiting new members - assuming alternative objective functions. We intend to investigate the optimal trade-off between the average age of the members of an academy and the number of newly selected members in every time period. Moreover, the members` productivity measured by publications, scientific and organisational activities will be included as an additional efficiency indicator. The resulting optimal recruitment strategies will be compared with historical developments and provide a basis to design future scenarios. In addition, a further interesting optimal control problem arises through a common practice of learned societies - as the Austrian Academy of Sciences - to recruit their full members from the pool of corresponding members. This creates an interesting two-stage recruitment/promotion problem. Questions as `how long is the expected waiting time to become a full member` and `how big is the chance to be promoted` are crucial in this context. The third objective of the project is to apply the optimal control framework developed in the second part of the proposal to the topics of migration and personnel management. Models of age-specific recruitment with prescribed population sequences and structure play an important role in the design of efficient age-oriented immigration policies. How many migrants, and at what ages, would have to immigrate in order to achieve a certain goal (e.g., zero growth or fiscal balance in the pension system of the receiving country) or how age-specific immigration in a sub-replacement population would influence its overall dependency ratio. In addition, similar problems as the two- stage optimisation problem of recruitment/promotion arise in the era of over-tenured universities. Faced with a period of retrenchment, how should a university reduce its tenure ratio? To put it in more general terms: to what extent do the career prospects for members of an organisation decrease in stagnation periods after a growth phase? Note that such problems can be studied from both the point of view of the organisation as a whole and in the context of individual career planning.

Almost all parts of the world are faced with aging societies. These demographic developments are a major challenge to policy and science.The causes of the changes in the age pyramid are low birth rates and decreasing mortality at older ages. Consequently, we live in increasingly old populations and many subpopulations, as for example learned societies are no exceptions.The first part of the project was devoted to the analysis of the demographic development of various European learned societies. Academies of Sciences thereby form interesting case studies of subpopulations, which face rapid aging problems. On the one hand, members of learned societies have a remarkable high longevity, which contributes to aging in the upper age groups. On the other hand, the aging of the Academies of Sciences is even increased through the election of old members. Our results indicate that scholars show a remarkable high longevity, especially in the 20th Century. They prove to have not only a higher life expectancy than any particular national population, but also higher than other social groups with low mortality profiles (e.g. higher social classes, tertiary educated population) in the respective countries.A young age structure and a high number of vacant positions represent conflicting objectives. The second part of our project was dedicated exactly to this trade-off. Using methods of dynamic optimization, we have shown that it is optimal to choose a mix of young and old recruits. This astonishing result corresponds in no way to the current election policies, such as practiced in the OEAW.In the third part of this project, the age-specific immigration profile was determined that minimizes the dependency ratio of a population facing below-replacement fertility. It should be noted that the size and age structure of the population depend very much on the age of the immigrants. Under very general assumptions on fertility and mortality in the population, we showed that the optimal age of immigrants lies in the mid-30s. Earlier work claimed that this age is at 20. The shift to higher ages is due to the higher number of expected offspring of a 20-year-old.