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Recent empirical studies suggest that heavy-tailed distributions of humanactivities are universal in real social dynamics [Muchnik, \emph{et al.}, Sci.Rep. \textbf{3}, 1783 (2013)]. On the other hand, community structure isubiquitous in biological and social networks [M.~E.~J. Newman, Nat. Phys.\textbf{8}, 25 (2012)]. Motivated by these facts, we here consider theevolutionary Prisoner's dilemma game taking place on top of a real socialnetwork to investigate how the community structure and the heterogeneity inactivity of individuals affect the evolution of cooperation. In particular, weaccount for a variation of the birth-death process (which can also be regardedas a proportional imitation rule from social point of view) for the strategyupdating under both weak- and strong-selection (meaning the payoffs harvestedfrom games contribute either slightly or heavily to the individuals'performance). By implementing comparative studies, where the players areselected either randomly or in terms of their actual activities to playinggames with their immediate neighbors, we figure out that heterogeneous activitybenefits the emergence of collective cooperation in harsh environment (theaction for cooperation is costly) under strong selection, while it impairs theformation of altruism under weak selection. Moreover, we find that theabundance of communities in the social network can evidently foster thefixation of cooperation under strong-selection, in contrast to the gamesevolving on the randomized counterparts. Our results are therefore helpful forus to better understand the evolution of cooperation in real social systems.

Community structure benefits the fixation of cooperation under strong selection