Effects of fertility and mortality on extinction of family and number of living children.

A model is developed to study the effects of fertility and mortality on number of living children and on extinction of family. Numerical illustrations are provided by applying the model to three different populations differing in fertility and mortality. It is found that a combination of a high birth rate and a low death rate is required to assure a reasonable probability that the family will not ultimately become extinct. A moderate to high birth rate and a low death rate are necessary to assure that there will be at least one surviving son in the parents' old age. This finding implies that zero population growth is impossible as long as parents depend on children for old age security. Thus, alternate old age security measures must be adopted by societies attempting to reduce their birth rate to the replacement level.