Cooperation is crucial to overcome some of the most pressing social challenges of our times, such as the spreading of infectious diseases, corruption and environmental conservation. Yet, how cooperation emerges and persists is still a puzzle for social scientists. Since human cooperation is individually costly, cooperative attitudes should have been eliminated by natural selection in favour of selfishness. Yet, cooperation is common in human societies, so there must be some features which make it evolutionarily advantageous. Using a cognitive inspired model of human cooperation, recent work Realpe-Gómez (2018) has reported signatures of criticality in human cooperative groups. Theoretical evidence suggests that being poised at a critical point provides evolutionary advantages to groups by enhancing responsiveness of these systems to external attacks. After showing that signatures of criticality can be detected in human cooperative groups composed by Moody Conditional Cooperators, in this work we show that being poised close to a turning point enhances the fitness and make individuals more resistant to invasions by free riders.