Time and trajectory of convergence to population stationarity with immigration and low fertility.

"Recent research aimed at extending classical stable population theory to include immigration has shown that a stationary population is the long-term equilibrium outcome if, starting from any initial configuration, a population is projected forward under conditions of constant below-replacement fertility, constant mortality, and a constant annual number of immigrants whose age-sex composition is also fixed. This paper addresses two related questions: (1) What path does the projected population follow on its way to a long-term stationary population equilibrium? and (2) How long does it take for a stationary population to be achieved? To answer these questions a formal theory of population dynamics in the below replacement case is developed and then illustrated with a projection of the 1980 U.S. population."