BACKGROUND:Evolution of cooperative behaviour is widely studied in different models where interaction is heterogeneous, although static among individuals. However, in nature individuals can often recognize each other and chose, besides to cooperate or not, to preferentially associate with or to avoid certain individuals.Here we consider a dynamical interaction graph, in contrast to a static one. We propose several rules of rejecting unwanted partners and seeking out new ones, and study the probability of emergence and maintenance of cooperation on these dynamic networks.RESULTS:Our simulations reveal that cooperation can evolve and be stable in the population if we introduce preferential linking, even if defectors can perform it too. The fixation of cooperation has higher probability than that of on static graphs, and this effect is more prevalent at high benefit to cost ratios. We also find an optimal number of partners, for which the fixation probability of cooperation shows a maximum.CONCLUSIONS:The ability to recognize, seek out or avoid interaction partners based on the outcome of past interactions has an important effect on the emergence of cooperation. Observations about the number of partners in natural cooperating groups are in concordance with the result of our model.