Language arises from the interaction of three complex adaptive systems — biological evolution, learning, and culture. We focus here on cultural evolution, and present an Iterated Learning Model of the emergence of compositionality, a fundamental structural property of language. Our main result is to show that the poverty of the stimulus available to language learners leads to a pressure for linguistic structure. When there is a bottleneck on cultural transmission, only a language which is generalizable from sparse input data is stable. Language itself evolves on a cultural time-scale, and compositionality is language’s adaptation to stimulus poverty.