Evolution of tropical savannas

Tropical savannas cover about one fifth of the landmass of the earth, are home to the majority of the remaining macro-fauna and closely linked to human evolution. In Africa the spread of savannas during climatic dry phases at the expense of forests has been hypothesized as a major cause for extinction and biodiversity loss in the Pleistocene.  I am interested in the effect of grass savannas on biodiversity on a longer evolutionary time-scale. In particular I am trying to understand if the rise of grass savannas and the shift of rain forest species into these habitats might be linked to increased speciation rates due to adaptive radiations.