Distinguishing punishing costly signals from nonpunishing costly signals can facilitate the emergence of altruistic punishment.

Altruistic punishment is regarded as a solution for the social dilemma, yet the fact that altruistic punishment itself is a type of public good raises the second-order social dilemma. Previous studies have typically explained the emergence of altruistic punishment by recouping punishers with other public goods or altruistic behaviors, but introducing new public goods would then raise the n-order social dilemma. Costly signaling theory (CST), by viewing public goods as costly signaling, is a potential approach to explain the evolution of cooperation without introducing other public goods because partnering altruistic signalers is not necessarily an altruistic behavior. However, previous studies based on CST have rarely distinguished altruistic punishment as the distinctive costly signal from a nonpunishing contribution. In this study, we explore the rules of transforming payoffs into fitness by differentiating punishing costly signals from nonpunishing costly signals. The results show that, under the condition that the efficacy of costly signaling is incomplete, altruistic punishment can only emerge in the population with transforming rules in which individuals regard altruistic punishment as a distinctive costly signal rather than a nonpunishing contribution.