On the dynamics of a population subject to slowly changing vital rates

Approximate closed-form expressions are given for the birth and death rates, the age-specific growth rates, and the age distribution of a population subject to slowly changing vital rates. The slower these rates have changed in the recent past, the better the approximations will be. These results, which are reminiscent of stable population theory, are tested by projecting the female population of the United States subject to realistically changing levels of fertility. The closed-form expressions yield quite accurate results and show that the dynamics of a population subject to slowly changing vital rates are to a large extent independent of the particular patterns of fertility. As in stable population theory, the asymptotic behavior of such a population is essentially determined by current survival rates and recent values of the intrinsic growth rate.