When will the human population peak? In this article, we build on classical results by Ansley Coale, who showed that when fertility declines steadily, births reach their maximum before fertility reaches replacement level, and the decline in total population size does not occur until several decades after fertility has reached that level. We extend Coale's results by modeling longevity increases, net immigration, and a slowdown in fertility decline that resembles current projections. With these extensions, our models predict a typical lag between replacement-level fertility and population decline of about 35 to 40 years, consistent with projections by the United Nations and about 15 years longer than the lag predicted by Coale. Our analysis helps reveal underlying factors in the timing of peak population.

中文翻译：

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人口峰值的正式人口统计

人口何时达到顶峰？在本文中，我们以安斯利·科尔（Ansley Coale）的经典结果为基础，他表明，当生育率稳步下降时，出生率在生育率达到更替水平之前达到最高水平，并且总人口规模的下降直到生育率达到该水平几十年后才会发生。 。我们通过模拟寿命增加、净移民和生育率下降放缓（与当前预测类似）来扩展科尔的结果。通过这些扩展，我们的模型预测更替水平生育率和人口下降之间的典型滞后期约为 35 至 40 年，与联合国的预测一致，并且比 Coale 预测的滞后期长约 15 年。我们的分析有助于揭示人口高峰时间的潜在因素。