A non‐linear model of fertility is described, which was derived from data for more than a century from England and Wales, New Zealand, and the U.S.A. The demographic transition is modelled with a logistic function, and age‐specific fertility rates are estimated using lognormal distributions. The stepwise inclusion of a partner availability estimate in the model showed that it accounts for twenty‐nine percent of otherwise unexplained variance. Projected future births stabilise in sustained or limit cycles with periods a little longer than 40 years, and amplitudes at least 7% of the mean. The necessary conditions for cycle persistence are outlined on a graph of maximum and minimum fertility parameters.

中文翻译：

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三个国家的出生人数模型，具有持续的 40 年周期

描述了一个非线性的生育率模型，该模型源自英格兰和威尔士、新西兰和美国一个多世纪以来的数据。人口转变用逻辑函数建模，年龄别生育率估计使用对数正态分布。模型中逐步包含合作伙伴可用性估计表明它占其他原因无法解释的方差的 29%。预计的未来出生人数稳定在持续或有限周期内，周期略长于 40 年，幅度至少为平均值的 7%。循环持续性的必要条件在最大和最小生育参数图上进行了概述。