Oscillatory dynamics in the coevolution of cooperation and mobility.

Although cooperation is a fundamental aspect of our society, it has been a longstanding puzzle in biological and social sciences because cooperation is often costly to those who practice it while others benefit. Recent studies have shown that natural selection favors cooperation when cooperators are more likely to interact with each other than with defectors, an effect called positive assortment. It might be that, in the real world, mobility makes positive assortment possible. However, to our knowledge, the coevolutionary dynamics of cooperation and mobility remains poorly understood. In this study, using an individual-based model where both cooperativeness and mobility are evolved under natural selection, we demonstrate that the coevolutionary dynamics results in the oscillation of the frequency of cooperation as long as the benefit-to-cost ratio of cooperation is large. This finding suggests that natural selection favors or fine-tunes a mobility rate by which cooperation can be maintained dynamically in the form of an oscillation without any other high cognitive abilities such as individual identification or memory of the past actions of other individuals.