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The mechanisms leading to structure in local assemblages are controversial. On the one hand, assemblage structure is thought to be the outcome of local interactions determined by the properties of species and their responses to the local environment. Alternatively, this structure has been shown to be an emergent property of assemblages of identical individuals or of random sampling of a regional assemblage. In ants at baits, a combination of environmental stress and interspecific competition is widely held to lead to a unimodal relationship between the abundance of dominant ants and species richness. It is thought that in comparatively adverse environments, both abundance and richness are low. As habitats become more favorable, abundance increases until the abundance of dominant ants is so high that they exclude those that are subordinate and so depress richness. Here we demonstrate empirically that this relationship is remarkably similar across three continents. Using a null model approach, we then show that the ascending part of the relationship is largely constrained to take this form not simply as a consequence of stress but also as a result of the shape of abundance frequency distributions. While the form of the species-abundance frequency distribution can also produce the descending part of the relationship, interspecific competition might lead to it too. Scatter about the relationship, which is generally not discussed in the literature, may well be a consequence of resource availability and environmental patchiness. Our results draw attention to the significance of regional processes in structuring ant assemblages. [ABSTRACT FROM AUTHOR]