Much linguistic research suggests that the structure of human language is determined to a large degree by the structure of an innate language faculty. This has led many researchers to examine the role of natural selection in explaining the origins of language. In this paper, however, we extend recent work that suggests that some of the fundamental properties of language are not directly determined by the learning mechanism but instead emerge from the dynamics arising from cultural selection.

We employ a computational methodology termed the "iterated learning model" to explore the relation between learning biases and cultural stability of languages. In this model, information is transfered solely via cultural rather than genetic transmission. Cultural transmission is modelled using a mathematically sound approach to learning based on Kolmogorov complexity. We view language as a complex adaptive system, and note that only stable languages will survive. Stability results when a language is learnable from sparse exposure, but is nevertheless expressive.

We argue that the emergence of compositional syntax (the property of human language where the meaning of a signal is a function of the meaning of its parts) occurs under specific conditions of preadaptation. A compositionally structured language only has a cultural stability payoff when:

1. An agent must frequently express meanings for which no pertinent signal has been observed. This phenomenon is known as the poverty of stimulus.
2. The cognitive apparatus of the agent is such that meanings are represented with a high dimensionality.