Final fraction of cooperators as a function of initial fraction of cooperators with different .

<p>According to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0088412#pone.0088412.e164" target="_blank">Eq. (8)</a>, we obtain that when , the analytical results of respectively, which are marked out by arrows in the plot. For all the three line in the plot, we set , , , , , , , , , and . The simulation results show that the initial frequency of cooperators increases with increasing of . Large narrows the attraction basin of cooperation, which makes the flourishing of cooperation difficult.