In the vast majority of primate species, males routinely dominate females. In a few, like our near relations the bonobos, or distant ones like ringtailed lemurs, females are clearly the dominant sex. In some more monogamous species, the sexes are co-dominant. Hrdy begins her book by pointing out that males' attempts to control female reproduction began in pre-human times and show no sign of abating. Primate females don't just deal with males, they compete with each other directly over food.
Dominant females leave more surviving young on average than subordinate ones.
Women, Hrdy argues, still have every incentive to be ambitious - ambition to gain social status is in their genes. This does not mean that every woman is ambitious all the time. No lineage has ever been perpetually dominant, or not for long enough to breed a line of blue-blooded snobs with secure places at the top of the female hierarchy. What has been bred in is the ability to work the social system - knowing how to deal with life as a subordinate, and when ambition will pay off in making a bid for social power. Mammalian females go for quality offspring, more than quantity.