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1. Scaling theory predicts that organisms respond to different scales of resource patchiness in relation to their own size. We tested the hypothesis that the scale of nutrient patchiness mediates resource partitioning between large trees and small grasses in a semi-arid savanna. 2. In a factorial field experiment, Colophospermum mopane trees and associated grasses were fertilized at either a fine or coarse scale of patchiness with nitrogen (N), phosphorus (P) or N + P. The growth of marked tree shoots, herbaceous biomass and leaf N and P concentrations were monitored for 2 years following fertilization. 3. Responses of trees were partly scale dependent. Tree leaf N concentration and shoot length relatively increased with fertilization at a coarse scale. Tree leaf mass decreased when P was supplied at a fine scale of patchiness, suggesting intensified grass competition. 4. Phosphorus fertilization increased leaf P concentrations more in grasses than trees, whereas N fertilization increased leaf N concentration moderately in both trees and grasses. Herbaceous above-ground biomass around focal trees was negatively correlated with tree size when fertilized with N, suggesting intensified tree competition. 5. Synthesis. Our results support the hypothesis that trees benefit more from nutrients supplied at a relatively coarse scale of patchiness. No direct responses of grasses to scale were detected. In trees, the scale effect was surpassed by the effect of sample year, when rainfall varied.