PLOS One Paper: "The fertility rate should exceed 2.7 to avoid extinction."
A 2025 Japanese paper suggests that may be underestimating the fertility goal needed to insure population survival.
While 2.1 is the number needed for mathematical survival, unexpected events (wars, plagues, etc) point to the need for a larger buffer for a given population, especially in regard to small populations and cultures.
The Shizuoka University paper, "Threshold fertility for the avoidance of extinction under critical conditions" (lead author Diane Carmeliza N. Cuaresma, April 30, 2025) argues that the required fertility rate to avoid eventual extinction should be 2.7, not 2.1.
The Abstract:
>The developed countries now face a low fertility crisis. The replacement level fertility (RLF) is conventionally considered to be 2.1 children per woman, in which demographic stochasticity arising from random variations in individual offspring numbers is ignored. However, the importance of demographic stochasticity casts doubts on the adequacy of the replacement level fertility of 2.1, especially in a small population. Here, we investigate the extinction threshold for the fertility rate of a sexually reproducing population caused by demographic stochasticity. The results indicate that the fertility rate should exceed 2.7 to avoid extinction. The extinction threshold is reduced by a female-biased sex ratio. We argue that the present results explain the observed phenomena of female-biased births under severe conditions as an effective way to avoid extinction. Furthermore, since fertility rates are below this threshold in developed countries, family lineages of almost all individuals are destined to go extinct eventually.
From the paper, a passage that caught my eye, which is of importance to those who especially value their family line:
>It should be remarked that this condition has already been met in developed countries. Extinction is not an immediate issue owing to the large population size in these countries. However, the present results have a profound implication from an individual perspective: The family lineages of almost all individuals are destined to go extinct, whereas very few exceptions may survive for many generations (Figs 3 and 4). Languages also face the risk of extinction, with at least 40% of more than 6,700 spoken languages in the world threatened to disappear within the next 100 years [39,40]. The extinction of a language results in the disappearance of a culture, art, music and oral traditions [39].