Differential female longevity is so far unexplained in evolutionary te
rms. The theory of evolutionarily necessary aging which goes back to W
allace appears to be up to the task. In this theory, aging minimizes c
ompetition between forebear and offspring. The aging equation which is
implicit contains the well-known empirical Gompertz law as a special
case, Moreover, its parameters are automatically sex-specific. It is s
hown that the slower aging of the female members of two species of mam
mals, humans and sperm whales, can be 'predicted' on the basis of this
equation. A prediction of effective human monogamy under archaic cond
itions is obtained as a corollary. The analogous if opposite predictio
n for sperm whales (strong promiscuity) is empirically testable.