Understanding how and why cultural diversity changes in human populations remains a central topic of debate in cultural evolutionary studies. Due to the effects of drift, small and isolated populations face evolutionary challenges in the retention of richness and diversity of cultural information. Such variation, however, can have significant fitness consequences, particularly when environmental conditions change unpredictably, such that knowledge about past environments may be key to long-term persistence. Factors that can shape the outcomes of drift within a population include the semantics of the traits as well as spatially structured social networks. Here, we use cultural transmission simulations to explore how social network structure and interaction affect the rate of trait retention and extinction. Using Rapa Nui (Easter Island, Chile) as an example, we develop a model-based hypothesis for how the structural constraints of communities living in small, isolated populations had dramatic effects and likely led to preventing the loss of cultural information in both community patterning and technology.