Inherited frailty and longevity.

The life spans of parents and children appear only weakly related, even though parents affect their children's longevity through both genetic and environmental influences. These influences can be summarized as a correlation between parents' and children's frailty. It is shown that even if children perfectly inherit their frailty from their parents, parents' life spans explain little of the variance in children's life spans, because the variance in life expectancies among people with different frailties is small compared with the variance in life spans among people at the same level of frailty. By interpreting frailty as a relative risk in a proportional-hazard model, longevity as a duration or waiting time, and inheritance as an invariance in relative risk over time, one can extend this result to repeatable events involving fertility, migration, marriage, unemployment, and so forth.