Pachter, L.

We introduce a spectral existence criterion for the evolution of cooperation in the form of the inequality {lambda}max b > c, where {lambda}max is the leading eigenvalue of an interaction operator encoding population structure, and b and c represent benefit and cost tradeoffs, respectively. Nowak's five rules for the evolution of cooperation correspond to cases in which the cooperation condition reduces to a scalar assortment coefficient. These results follow from the Price equation, which sheds light on a long-standing debate on the role of inclusive fitness and evolutionary dynamics in explaining the evolution of cooperation.