Claude Hagège hypothesizes a monogenetic origin of a faculty for speech but a polygenetic origin of human languages (The Dialogic Species: A Linguistic Contribution to the Social Sciences, trans. Sharon L. Shelley, Columbia University Press, Second Edition, 1990). I'm not certain the radical critique of universal grammar requires an evolutionary argument (in fact I reckon Hagège's radical critique is born of patient, close study of diverse living languages), but here is one:
We have seen that all evidence indicates virtual simultaneity of the birth of the species and the ancient migrations. Moreover, we can better sketch this vast adventure if we keep in mind the difference between the notions of speech faculty (langage) and language (langue). Through a continuing series of improvements, the first more or less coded stammerings became regular formations; their repertories extended as the aptitude to symbolize became enriched with the more specific faculty of articulating thought in ordered signs expressed by combinations of sounds. But such an evolution itself assumes a considerable period of time and thus cannot have produced human languages in the contemporary sense of the term, until after the great migrations. Thus, in all likelihood, this process took place in several different geographical areas. The ecological milieu, nature and its sounds, vegetable and animal species as well as the sound phenomena they produced, were therefore quite diverse. Diverse also, in each living biocenosis (or community of interdependent beings), were the nuclei of social organization which were constituted, and, consequently, the first languages themselves. For, from the beginning, they were closely affiliated with these social organizations, although it is true that this relationship was gradually obscured by the progressive and arbitrary conventions that separate words and phrase structures from their original sources.
For Hagège the origination of languages is closely tied to a capacity for thought; articulating abstract thought through vocal signs is a vital function of language above and beyond any residue of its sensory-motor aspects. He presents the view that the neocortical elaboration of Homo and of sapiens in particular precedes the development of languages. (Reportedly the neocortex ratio for humans "is about 50% larger than the maximum value for any other primate species" (Robin Dunbar, Coevolution of Neocortical Size, Group Size and Language in Humans.); of course the encephalization quotient of sapiens is also remarkably high; see the lecture notes of Bill Sellers, Primate Brains).