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The relationship between levels of dominance and species richness is highly contentious, especially in ant communities. The dominance-impoverishment rule states that high levels of dominance only occur in species-poor communities, but there appear to be many cases of high levels of dominance in highly diverse communities. The extent to which dominant species limit local richness through competitive exclusion remains unclear, but such exclusion appears more apparent for non-native rather than native dominant species. Here we perform the first global analysis of the relationship between behavioral dominance and species richness. We used data from 1,293 local assemblages of ground-dwelling ants distributed across five continents to document the generality of the dominance-impoverishment rule, and to identify the biotic and abiotic conditions under which it does and does not apply. We found that the behavioral dominance-diversity relationship varies greatly, and depends on whether dominant species are native or non-native, whether dominance is considered as occurrence or relative abundance, and on variation in mean annual temperature. There were declines in diversity with increasing dominance in invaded communities, but diversity increased with increasing dominance in native communities. These patterns occur along the global temperature gradient. However, positive and negative relationships are strongest in the hottest sites. We also found that climate regulates the degree of behavioral dominance, but differently from how it shapes species richness. Our findings imply that, despite strong competitive interactions among ants, competitive exclusion is not a major driver of local richness in native ant communities. Although the dominance-impoverishment rule applies to invaded communities, we propose an alternative dominance-diversification rule for native communities.