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A central tenet of ecology and biogeography is that the broad outlines of species ranges are determined by climate, whereas the effects of biotic interactions are manifested at local scales. While the first proposition is supported by ample evidence, the second is still a matter of controversy. To address this question, we develop a mathematical model that predicts the spatial overlap, i.e., co-occurrence, between pairs of species subject to all possible types of interactions. We then identify the scale in which predicted range overlaps are lost. We found that co-occurrence arising from positive interactions, such as mutualism (+/+) and commensalism (+/0), are manifested across scales of resolution. Negative interactions, such as competition (-/-) and amensalism (-/0), generate checkerboard-type co-occurrence patterns that are discernible at finer resolutions. Scale dependence in consumer-resource interactions (+/-) depends on the strength of positive dependencies between species. Our results challenge the widely held view that climate alone is sufficient to characterize species distributions at broad scales, but also demonstrate that the spatial signature of competition is unlikely to be discernible beyond local and regional scales.