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A fundamental goal of ecology is to reveal generalities in the myriad types of interactions among species, such as competition, mutualism and predation. Another goal is to explain the enormous differences in species richness among groups of organisms. Here, we show how these two goals are intertwined: we find that different types of species interactions have predictable impacts on rates of species diversification, which underlie richness patterns. On the basis of a systematic review, we show that interactions with positive fitness effects for individuals of a clade (e.g. insect pollination for plants) generally increase that clade’s diversification rates. Conversely, we find that interactions with negative fitness effects (e.g. predation for prey, competition) generally decrease diversification rates. The sampled clades incorporate all animals and land plants, encompassing 90% of all described species across life. Overall, we show that different types of local‐scale species interactions can predictably impact large‐scale patterns of diversification and richness.