G. G. Simpson, one of the chief architects of evolutionary biology's modern synthesis, proposed that diversification occurs on a macroevolutionary adaptive landscape, but landscape models are seldom used to study adaptive divergence in large radiations. We show that for Caribbean Anolis lizards, diversification on similar Simpsonian landscapes leads to striking convergence of entire faunas on four islands. Parallel radiations unfolding at large temporal scales shed light on the process of adaptive diversification, indicating that the adaptive landscape may give rise to predictable evolutionary patterns in nature, that adaptive peaks may be stable over macroevolutionary time, and that available geographic area influences the ability of lineages to discover new adaptive peaks.