Fig. 4: The intrinsic bursty behaviour in human interactions suppresses the maintenance of cooperation.

For each dataset, we show the difference \(f_{\mathrm{c}}^{{\mathrm{RPTRE}}} - f_{\mathrm{c}}^{{\mathrm{ORI}}}\) between the frequency of cooperators \(f_{\mathrm{c}}^{{\mathrm{RPTRE}}}\) in temporal networks generated from each datsaset after randomly permuting both the timestamps and edges (RPTRE) which erases the burstiness inherent to human interaction data (see Methods), and \(f_{\mathrm{c}}^{{\mathrm{ORI}}}\) over the original scenarios. By construction, at any fixed value of \(b\), each curve here sums to at most \(1\) with the corresponding curve in Fig. 2 from a–d. We see that the frequency of cooperators generally increases after the bursty behaviour is destroyed, suggesting that correlations in activity within a social network are antagonistic toward the formation of cooperation. Note that for clarity of presentation, we did not plot the case for \(g = 5000\). However, all results for each dataset after randomisations with different null models²⁹ can be found in Supplementary Figs. 11–14. Other parameters are the same as those in Fig. 2.