Threshold fertility for the avoidance of extinction under critical conditions.

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.