Most previous studies involving public goods games are investigated under a simplifying assumption that participation is either compulsive or unidirectional optional in collective interactions. Nevertheless, how the mutual selection rule, a more realistic participation mode, affects the evolution of cooperation in structured populations is still unclear. Here we introduce a reputation-based mutual selection rule for constituting participant groups into spatial threshold public goods games, where the public goods game can be conducted only if the participant number is not less than the threshold parameter. Interestingly, we find that moderate tolerance range results in the best environment for cooperators viability. Also, we show that lower member threshold is favorable for the evolution of cooperation, and correspondingly provide some typical snapshots for defectors, "active" cooperators (cooperators on which the public goods games are successfully conducted), and "inactive" cooperators. Moreover, we investigate the effects of memory factor in individuals' reputation updating on the evolution of cooperation. Our work may provide an appropriate and alternative perspective in understanding the widespread cooperative behaviors in some realistic situations.
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