While culture is widespread in the animal kingdom, human culture has been claimed to be special due to being cumulative. It is currently debated which cognitive abilities support cumulative culture, but behavior copying is one of the main abilities proposed. One important source of contention is the presence or absence of behavior copying in our closest living relatives, non-human great apes (apes) - especially given that their behavior does not show clear signs of cumulation. Those who claim that apes copy behavior often base this claim on the existence of stable ape cultures in the wild (Whiten et al. 1999; van Schaik et al. 2003). We developed an individual-based model to test whether ape cultural patterns can both emerge and stabilize in the entire absence of any behavior copying, but only allowing for a well-supported alternative social learning mechanism, namely socially-mediated reinnovation, where only the frequency of reinnovation is under social influence, but the form of the behavior is not. Our model reflects wild ape life conditions, including physiological and behavioral individual needs, demographic and spatial features, and the possible range of genetic and ecological variations between populations. Our results show that, under a wide range of realistic values of all model parameters, we fully reproduce the most defining features of wild ape cultural patterns (Whiten et al. 1999; van Schaik et al. 2003). Overall, our results show that ape cultures can both emerge and stabilize without behavior copying. Ape cultures are therefore unable to pinpoint behavior copying abilities, lending support to the notion that behavior copying is, among apes, unique in the human lineage.