Compositionality, a unique and fundamental property of human language, emerges from the pressures placed on language as it is learnt and used by consecutive generations – the pressure for learnability, arising from the transmission process, and a pressure for expressivity imposed by the use of language to convey meaning. This study uses human diffusion chains to explore the contribution that learning and communication make to the cultural evolution of linguistic structure. Languages are exposed to either a learning pressure, a communication pressure, or both. The language in the communication chain became expressive and showed varying degrees of structure, in some cases deliberately introduced as an aid to comprehension. This puts the focus back on the cognitive processes of language users, and emphasises the role of recipient design in the emergence of structure in language. The languages in the learning conditions struggled to maintain a significant degree of structure, contrary to expectations. However, the development of the languages provides clues about the way that language adapts in response to the particular communicative and learning environment.