It seemed to be like that but it has recently been challenged: see paper of Tierney and deMenocal (Science, 2013), where they see an abrupt change in precipitation at the Horn of Africa. Their hypothesis is that there are regional precipitation regimes induced by oceanological changes (mainly sea surface temperature). Another look is that of Clausen et al. in a recent paper in Nature Geoscience (also 2013), where they consider that a globally gradual termination in changes in vegetation cover might still involve abrupt changes in distinct components of the vegetation system. So the answer is not that straigthforward anymore :)