The mathematics of ageing:

Abstract

Abstract Age is a crucial variable in social sciences and particularly in population dynamics. In this paper, we link methods from formal demography and Operations Research to investigate age-structured models to study the greying of academia. As scientific productivity is usually found to decrease at advanced ages, there was a vivid discussion on the ageing among tenured professors and faculty staff of universities. We investigate population ageing in academia from two perspectives. First, we propose a two-state optimal control model to explain the substantial variations of scientific production over the life cycle of researchers. We identify conditions under which typical hump-shaped age-specific patterns of scientific production turn out to be optimal for individual researchers. The second part of the paper deals with the dynamics of the age structure of scientific institutions. Similar to the university professors, many European learned societies experienced a rapid ageing of their member population, where they face the dilemma that keeping young, i.e. electing young entrants, has the drawback of reducing the replacement rate of members. It turns out that electing a mix of young and old members delivers the optimal solution of the problem, i.e. guaranteeing a young age structure, while ensuring a high recruitment rate.

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