The concept of fitness is central to evolution, but it quantifies only the expected number of offspring an individual will produce. The actual number of offspring is also subject to demographic stochasticity-that is, randomness associated with birth and death processes. In nature, individuals who are more fecund tend to have greater variance in their offspring number. Here, we develop a model for the evolution of two types competing in a population of nonconstant size. The fitness of each type is determined by pairwise interactions in a prisoner's dilemma game, and the variance in offspring number depends upon its mean. Although defectors are preferred by natural selection in classical population models, since they always have greater fitness than cooperators, we show that sufficiently large offspring variance can reverse the direction of evolution and favor cooperation. Large offspring variance produces qualitatively new dynamics for other types of social interactions, as well, which cannot arise in populations with a fixed size or with a Poisson offspring distribution.
Keywords: cooperation; demographic stochasticity; evolutionary game theory; over-dispersion.