The Sharpe‐Lotka continuous time deterministic model of population growth is developed to take account of some possible forms of mother‐daughter fertility association, characterised here by a bivariable measure, A. This leads to a linear double integral equation for which, subject to certain conditions, a finite time solution can be found by Laplace transform methods and thus also model specific results relating the intergenerational fertility effect to the long term population growth rate and magnitude are established. The quantitative implications of the theory are illustrated by a consideration of a general bilinear form of A and in this context numerical results illustrating the finite time growth and also the long term distribution of fertility levels in the stable female population are obtained. In particular, it is shown that different fertility specific subpopulations can coexist indefinitely.

中文翻译：

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家庭规模可变的人口增长

Sharpe-Lotka 人口增长连续时间确定性模型的开发考虑了母女生育关联的一些可能形式，这里以双变量度量 A 为特征。条件下，可以通过拉普拉斯变换方法找到有限时间解，因此还建立了与代际生育率效应与长期人口增长率和幅度相关的模型特定结果。该理论的定量含义通过考虑 A 的一般双线性形式来说明，在这种情况下，数值结果说明了有限时间增长以及稳定女性人口中生育水平的长期分布。特别是，