Transition dynamics in human populations
Population momentum is the ratio of a population's ultimate size after a demographic transition to its initial size before the transition. For an instantaneous drop to replacement fertility, Nathan Keyfitz found a simple expression $M_{K}$ for the momentum. However, as Keyfitz pointed out, `no one thinks that any country will drop immediately to stationary reproduction patterns'. I present exact analytical results developed jointly with Nan Li concerning the momentum of a population whose demographic transition completes within a finite time. I show that relatively simple formulae are accurate approximations to population momentum for transitions that take as long as 100 years. I show also that the speed of fertility decline makes a substantial difference to population momentum.

