The Formal Demography of Peak Population

When will the human pop u la tion peak? In this arti cle, we build on clas si cal results by Ansley Coale, who showed that when fer til ity declines steadily, births reach their max i mum before fer til ity reaches replace ment level, and the decline in total pop u la tion size does not occur until sev eral decades after fer til ity has reached that level. We extend Coale's results by mod el ing lon gev ity increases, net immi gra tion, and a slow down in fer til ity decline that resem bles cur rent pro jec tions. With these exten sions, our models predict a typical lag between replacement level fertility and population decline of about 35 to 40 years, con sis tent with pro jec tions by the United Nations and about 15 years lon ger than the lag predicted by Coale. Our anal y sis helps reveal under ly ing fac tors in the tim ing of peak pop u la tion.