The way children learn language sets the adaptive landscape on which languages evolve. This is acknowledged by many, but there are few connections between models of language acquisition and models of language Evolution (some exceptions include Yang (2002), Yu & Smith (2007) and Chater & Christiansen (2009)).
However, the chasm between the two fields may be getting smaller, as theories are defined as models which are both more interpretable to the more technically-minded Language Evolutionists and extendible into populations and generations.
Also, strangely, models of word learning have been getting simpler over time. This may reflect a move from attributing language acquisition to specific mechanisms towards a more general cognitive explanation. I review some older models here, and a recent publication by Fazly et al.