Turnover and Dependency Are Minimized when Population Growth Is Negative

Joshua R. Goldstein, University of California, Berkeley

The sum of the birth rate and death rates is a measure of population turnover. It is also a measure of the care-giving needs – an alternative to the dependency ratio – since it tells the fraction of the population that is close to birth or close to death. Here I show that the minimum turnover for stable populations is obtained when the population growth rate is slightly negative, exemplifying a case when negative population growth can be optimal. An approximation of r*, the population growth rate that minimizes turnover, shows that lower values of life expectancy and/or greater coefficients of variation of age at death make r* more negative.