Postmenopausal longevity may have evolved in our lineage when ancestral grandmothers
subsidized their daughters' fertility by provisioning grandchildren, but the verbal
hypothesis has lacked mathematical support until now. Here, we present a formal simulation
in which life spans similar to those of modern chimpanzees lengthen into the modern
human range as a consequence of grandmother effects. Greater longevity raises the
chance of living through the fertile years but is opposed by costs that differ for
the sexes. Our grandmother assumptions are restrictive. Only females who are no longer
fertile themselves are eligible, and female fertility extends to age 45 years. Initially,
there are very few eligible grandmothers and effects are small. Grandmothers can support
only one dependent at a time and do not care selectively for their daughters' offspring.
They must take the oldest juveniles still relying on mothers; and infants under the
age of 2 years are never eligible for subsidy. Our model includes no assumptions about
brains, learning or pair bonds. Grandmother effects alone are sufficient to propel
the doubling of life spans in less than sixty thousand years.