Natural languages vary widely in the degree to which they make use of nested compositional structure in their grammars. It has long been noted by linguists that the languages historically spoken in small communities develop much deeper levels of compositional embedding than those spoken by larger groups. Recently this observation has been confirmed by a robust statistical analysis of the World Atlas of Language Structures. In order to examine this connection mechanistically, we propose an agent-based model that accounts for key cultural evolutionary features of language transfer and language change. We identify transitivity as a physical parameter of social networks critical for the evolution of compositional structure, and the hierarchical patterning of scale-free distributions as inhibitory.Natural languages vary widely in grammatical structure, especially in the degree to which they make use of nested composition. A graduated divide in this typological space is the extent to which words themselves make use of compositional patterning. That is, the degree on average to which words possess internal structural hierarchies (morphological composition), beyond their arrangement in the phrasal hierarchy of a sentence (syntactic composition). In some languages, such as Chinese, morphological structure is virtually nonexistent, whereas others, like Lushootseed (an indigenous, Salishan language of North America), have so much morphological structure that entire utterances can be a single, highly complex word. It is not yet understood how such typological patterns emerge historically, and why natural languages vary in this property over time.Computational modeling researchers have proposed both symbolic (Smith et al., 2003) and neural architectures (Batali, 1998) to demonstrate that compositional language structure develops where cultural evolutionary forces are at * Equally contributing authors.