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Using new tools (boosted regression trees) in predictive biogeography, with extensive spatial 23 distribution data for >19 000 species, we developed predictive models for South African plant species richness patterns. Further, biome level analysis explored possible functional determinants of country-wide regional species richness. Finally, to test model reliability independently, we predicted potential alien invasive plant species richness with an independent dataset. Amongst the different hypotheses generally invoked to explain species 30 diversity (energy, favorableness, topographic heterogeneity, irregularity and seasonality), results revealed topographic heterogeneity as the most powerful single explanatory variable for indigenous South African plant species richness. Some biome-specific responses were observed, i.e. two of the five analyzed biomes (Fynbos and Grassland) had richness best explained by the 'species-favorableness' hypothesis, but even in this case, topographic heterogeneity was also a primary predictor. This analysis, the largest conducted on an almost exhaustive species sample in a species-rich region, demonstrates the preeminence of topographic heterogeneity in shaping the spatial pattern of regional plant species richness. Model reliability was confirmed by the considerable predictive power for alien invasive species richness. It thus appears that topographic heterogeneity controls species richness in two main ways: firstly, by providing an abundance of ecological niches in contemporary space (revealed by alien invasive species richness relationships) and secondly, by facilitating the persistence of ecological niches through time. The extraordinary richness of the South African Fynbos biome, a world-renowned hotspot of biodiversity with the steepest environmental gradients in South Africa, may thus have arisen through both mechanisms. Comparisons with similar regions of the world outside South Africa are needed to confirm the generality of topographic heterogeneity and favorableness as predictors of plant richness.