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Most of the Earth's biodiversity resides in the tropics. However, a comprehensive understanding of which factors control range limits of tropical species is still lacking. Climate is often thought to be the predominant range-determining mechanism at large spatial scales. Alternatively, species’ ranges may be controlled by soil or other environmental factors, or by non-environmental factors such as biotic interactions, dispersal barriers, intrinsic population dynamics, or time-limited expansion from place of origin or past refugia. How species ranges are controlled is of key importance for predicting their responses to future global change. Here, we use a novel implementation of species distribution modelling (SDM) to assess the degree to which African continental-scale species distributions in a keystone tropical group, the palms (Arecaceae), are controlled by climate, non-climatic environmental factors, or non-environmental spatial constraints. A comprehensive data set on African palm species occurrences was assembled and analysed using the SDM algorithm Maxent in combination with climatic and non-climatic environmental predictors (habitat, human impact), as well as spatial eigenvector mapping (spatial filters). The best performing models always included spatial filters, suggesting that palm species distributions are always to some extent limited by non-environmental constraints. Models which included climate provided significantly better predictions than models that included only non-climatic environmental predictors, the latter having no discernible effect beyond the climatic control. Hence, at the continental scale, climate constitutes the only strong environmental control of palm species distributions in Africa. With regard to the most important climatic predictors of African palm distributions, water-related factors were most important for 25 of the 29 species analysed. The strong response of palm distributions to climate in combination with the importance of non-environmental spatial constraints suggests that African palms will be sensitive to future climate changes, but that their ability to track suitable climatic conditions will be spatially constrained.