What do colon cancer, ant colonies, language and global warming have in common? This might sound like the front end of a joke, but in fact it’s a serious challenge to the standard view of evolution. Martin A. Nowak, the director of the Program for Evolutionary Dynamics at Harvard, has devoted a brilliant career to showing that Darwin, and particularly his followers, batted only two for three. Random mutation and natural selection have indeed been powerful motors for change in the natural world — the struggle for existence pitting the fit against the fitter in a hullabaloo of rivalry. But most of the great innovations of life on earth, Nowak argues, from genes to cells to societies, have been due to a third motor, and “master architect,” of evolution: cooperation.

“SuperCooperators” (written with Roger Highfield, editor of New Scientist magazine) is an absorbing, accessible book about the power of mathematics. Unlike Darwin with his brine bottles and pigeon coops, Nowak aims to tackle the mysteries of nature with paper, pencil and computer. By looking at phenomena as diverse as H.I.V. infection and English irregular verbs, he has formally defined five distinct mechanisms that have helped give rise to cooperative behavior, from the first molecules that joined to self-replicate, to the first cells that formed multicellular organisms, all the way to human societies, which exhibit a degree of cooperation unmatched in all creation. In Nowak’s view, figuring out how cooperation comes about and breaks down, as well as actively pursuing the “snuggle for existence,” is the key to our survival as a species.

At the heart of Nowak’s ideas is the haunting game of Prisoner’s Dilemma. The game involves two accomplices who are caught for a crime, interrogated separately and offered a deal. If one player incriminates the other, or “defects,” while the second remains silent, or “cooperates,” he will be given a sentence of one year, while the other player gets four. If both remain silent, they will be sentenced to only two years, but if both defect, they will receive three years. The rational choice for either prisoner is to defect, getting three years — though had both cooperated, they’d have been out in two. In the absence of trust, reason can be self-destructive.

In the 1990s, Nowak and Karl Sigmund, building on work by Robert Axelrod, showed that the Prisoner’s Dilemma, played over and over, could describe cycles of behavior in which strategies of selfishness (“Always Defect”) are beaten out by cooperation (“Tit for Tat”), then overtaken by even more cooperative behavior (“Generous Tit for Tat,” summarized as “Never forget a good turn, but occasionally forgive a bad one”), only to be invaded once more by egoists until the cycle begins anew. These “evolutionary dynamic” models, made more realistic by introducing an element of randomness, demonstrate that under the right conditions, competition can lead to teamwork. They also show how fragile that balance can be.