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The taxonomic, phylogenetic and trait dimensions of beta diversity each provide us unique insights into the importance of historical isolation and environmental conditions in shaping global diversity. These three dimensions should, in general, be positively correlated. However, if similar environmental conditions filter species with similar trait values, then assemblages located in similar environmental conditions, but separated by large dispersal barriers, may show high taxonomic, high phylogenetic, but low trait beta diversity. Conversely, we expect lower phylogenetic diversity, but higher trait biodiversity among assemblages that are connected but are in differing environmental conditions. We calculated all pairwise comparisons of approximately 110 x 110 km grid cells across the globe for more than 5000 mammal species (approx. 70 million comparisons). We considered realms as units representing geographical distance and historical isolation and biomes as units with similar environmental conditions. While beta diversity dimensions were generally correlated, we highlight geographical regions of decoupling among beta diversity dimensions. Our analysis shows that assemblages from tropical forests in different realms had low trait dissimilarity while phylogenetic beta diversity was significantly higher than expected, suggesting potential convergent evolution. Low trait beta diversity was surprisingly not found between isolated deserts, despite harsh environmental conditions. Overall, our results provide evidence for parallel assemblage structure of mammal assemblages driven by environmental conditions at a global scale.