Differences in trait composition, or functional structure, of assemblages across spatial scales may stem from the ability to tolerate local conditions (environmental filters) and from assembly rules (biological filters). However, disentangling their respective roles has proven difficult, and limited generalities have emerged from research on the spatial scaling of functional structure. Here we quantify differences in trait composition among 679 spatially nested (i.e., paired regional pool and local community) bird and mammal assemblages worldwide. Among the regional pool, we identify species with trait combinations within the range observed locally as the ecological species pool. The ecological species pool has a trait structure that is generally different from that of the regional pool, consistent with the operation of environmental filters. In contrast, local species trait structure generally shows little difference from that of the ecological pool. We find notable deviations from expectations based on equiprobable draws from the ecological pool. However, these deviations vary little across scales and broad environmental gradients. For mammals, but not birds, this is consistent with assembly rules. Thus, by conceptualizing ecological pools, we demonstrate that functional structure is jointly determined by processes causing both low and high functional differences between scales and are able to quantify their relative importance.