Parent-preferred dispersal promotes cooperation in structured populations.

Dispersal is a key process for the emergence of social and biological behaviours. Yet, little attention has been paid to dispersal's effects on the evolution of cooperative behaviour in structured populations. To address this issue, we propose two new dispersal modes, parent-preferred and offspring-preferred dispersal, incorporate them into the birth-death update rule, and consider the resultant strategy evolution in the prisoner's dilemma on random-regular, small-world, and scale-free networks, respectively. We find that parent-preferred dispersal favours the evolution of cooperation in these different types of population structures, while offspring-preferred dispersal inhibits the evolution of cooperation in homogeneous populations. On scale-free networks when the strength of parent-preferred dispersal is weak, cooperation can be enhanced at intermediate strengths of offspring-preferred dispersal, and cooperators can coexist with defectors at high strengths of offspring-preferred dispersal. Moreover, our theoretical analysis based on the pair-approximation method corroborates the evolutionary outcomes on random-regular networks. We also incorporate the two new dispersal modes into three other update rules (death-birth, imitation, and pairwise comparison updating), and find that similar results about the effects of parent-preferred and offspring-preferred dispersal can again be observed in the aforementioned different types of population structures. Our work, thus, unveils robust effects of preferential dispersal modes on the evolution of cooperation in different interactive environments.