Our response takes advantage of the wide-ranging commentary to clarify some aspects of our original proposal and augment others. We argue against the generative critics of our coevolutionary program for the language sciences, defend the use of close-to-surface models as minimizing cross-linguistic data distortion, and stress the growing role of stochastic simulations in making generalized historical accounts testable. These methods lead the search for general principles away from idealized representations and towards selective processes. Putting cultural evolution central in understanding language diversity makes learning fundamental in the cognition of language: increasingly powerful models of general learning, paired with channelled caregiver input, seem set to manage language acquisition without recourse to any innate universal grammar. Understanding why human language has no clear parallels in the animal world requires a cross-species perspective: crucial ingredients are vocal learning (for which there are clear non-primate parallels) and an intention-attributing cognitive infrastructure that provides a universal base for language evolution. We conclude by situating linguistic diversity within a broader trend towards understanding human cognition through the study of variation in, for example, human genetics, neurocognition, and psycholinguistic processing.