Using a simple empirical approach, we analyze world and regional‐level cohort replacement as determined by the key components of population dynamics, i.e. fertility, survival, and migration, for 1950–2010, using UN data. We define two kinds of homeostatic relationships among these components: fertility responses to mortality change (type I) and migration responses to changes in net reproduction (type II), and show that both can be observed to some degree in this period. We examine the extent of cohort replacement embodied in the medium‐variant UN population projections over 2010–2100 and consider how the international migration assumptions made in such projections would be affected by a homeostatic perspective.