16. Ageing in the Wild, Residual Demography and Discovery of a Stationary Population Equality

In the late 1990s while exploring methods for estimating population age structure using the post-capture longevity of fruit flies sampled from the wild (referred to as residual demography) I discovered an identity in which the fraction of individuals x days old in a stationary population equals the fraction that die x days later. I co-authored a paper containing this identity in 2004 as part of a larger publication with my biodemography colleagues where we extended the concept for practical application. In 2009 demographer James Vaupel published a proof of this identity and referred to it using the eponym Carey’s Equality. The Vaupel paper was then followed six years later (2015) by a surprise—the identity had been published in French 30 years earlier in the gray literature by demographer Nicolas Brouard. Remarkably the identity had never been cited in either the searchable (journal) literature or in any of the mainstream demography texts, treatises, encyclopedias or reference books. Here I tell the story of how I discovered this identity, why it is important, implications for human demography, and lessons learned along the way.