Recent IPCC projections suggest that Africa will be subject to particularly severe changes in atmospheric conditions. How the vegetation of Africa and particularly the grassland–savanna–forest complex will respond to these changes has rarely been investigated. Most studies on global carbon cycles use vegetation models that do not adequately account for the complexity of the interactions that shape the distribution of tropical grasslands, savannas and forests. This casts doubt on their ability to reliably simulate the future vegetation of Africa. We present a new vegetation model, the adaptive dynamic global vegetation model (aDGVM) that was specifically developed for tropical vegetation. The aDGVM combines established components from existing DGVMs with novel process-based and adaptive modules for phenology, carbon allocation and fire within an individual-based framework. Thus, the model allows vegetation to adapt phenology, allocation and physiology to changing environmental conditions and disturbances in a way not possible in models based on fixed functional types. We used the model to simulate the current vegetation patterns of Africa and found good agreement between model projections and vegetation maps. We simulated vegetation in absence of fire and found that fire suppression strongly influences tree dominance at the regional scale while at a continental scale fire suppression increases biomass in vegetation by a more modest 13%. Simulations under elevated temperature and atmospheric CO2 concentrations predicted longer growing periods, higher allocation to roots, higher fecundity, more biomass and a dramatic shift toward tree dominated biomes. Our analyses suggest that the CO2 fertilization effect is not saturated at ambient CO2 levels and will strongly increase in response to further increases in CO2 levels. The model provides a general and flexible framework for describing vegetation response to the interactive effects of climate and disturbances.