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              <p>The global phenomenon of biotic homogenization is threatening biodiversity worldwide. To explain homogenization, multiple frameworks based on different classifications of introduction and extinction events have been proposed. However, comprehensive and generalized approaches are still lacking. Using mathematical derivation, we present a single comprehensive formula, which demonstrates that similarity changes can be precisely determined by the frequencies of six event types, initial similarity, and total number of species. The formula also shows that the effect directions for all events are type-dependent, while their effect magnitudes generally covary with initial similarity and decrease with increasing species numbers. We argue that future empirical and/or predictive studies of biotic homogenization should pay more attention to these direct factors for a deep understanding of community similarity changes.</p>
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