Though we have other distinguishing characteristics (walking on two legs, for instance, and relative hairlessness), the brain and the behavior it produces are what truly set us apart from the other apes and primates. And how this three-pound organ composed of water, fat, and protein turned a mammal species into the dominant animal on earth today is the story John S. Allen seeks to tell.

Adopting what he calls a "bottom-up" approach to the evolution of human behavior, Allen considers the brain as a biological organ; a collection of genes, cells, and tissues that grows, eats, and ages,...