Fertility, birth, reproduction: Connecting formal demographic frameworks.

The conventional framework of fertility research conceptualizes childbirth from the mother's perspective. From her perspective, birth is an uncertain and potentially recurring event. In contrast, the Born once, die once (B1D1) framework conceptualizes birth as an event experienced by the child. From that perspective, birth is certain and, like death, occurs only once. As an advantage over the conventional approach, the new perspective allows for the use of density, survival, and hazard functions to study age patterns of birth at the macro level, using birth counts for all parities by maternal age. Here, we reformulate the B1D1 framework using fertility-rate notation. This allows us to extend the conventional fertility framework by analogous density, survival, and hazard functions. These functions can shed new light on differences in age patterns of fertility across populations and advance conventional fertility research, including by capturing fertility and mortality age patterns with common concepts and measures.