In past centuries exposure to infectious disease and malnutrition caused high mortality rates in children. Those who survived did so with a greater burden of various forms of low-level biological damage. Degenerative aging is caused by an accumulation of damage and thus remaining life expectancy is reduced. Researchers here dig up historical demographic data that supports this view, showing that people who survived high childhood mortality went on to live shorter lives on average:

Early environmental influences on later life health and mortality are well recognized in the doubling of life expectancy since 1800. To further define these relationships, we analyzed the associations between early life mortality with both the estimated mortality level at age 40 and the exponential acceleration in mortality rates with age characterized by the Gompertz model.

Using mortality data from 630 cohorts born throughout the 19th and early 20th century in nine European countries, we developed a multilevel model that accounts for cohort and period effects in later life mortality. We show that early life mortality, which is linked to exposure to infection and poor nutrition, predicts both the estimated cohort mortality level at age 40 and the subsequent Gompertz rate of mortality acceleration during aging.

After controlling for effects of country and period, the model accounts for the majority of variance in the Gompertz parameters (about 90% of variation in estimated level of mortality at age 40 and about 78% of variation in Gompertz slope). The gains in cohort survival to older ages are entirely due to large declines in adult mortality level, because the rates of mortality acceleration at older ages became faster.

Link: http://www.ncbi.nlm.nih.gov/pubmed/23626899

Source:
http://www.fightaging.org/archives/2013/05/early-mortality-rates-predict-late-mortality-rates.php