Positive effects of habitat patch size on biodiversity are often extrapolated to infer negative effects of habitat fragmentation on biodiversity at landscape scales. However, such cross-scale extrapolations typically fail. A recent, landmark, patch-scale analysis (Chase et al., 2020, Nature 584, 238-243) demonstrates positive patch size effects on biodiversity, that is, 'ecosystem decay' in small patches. Other authors have already extrapolated this result to infer negative fragmentation effects, that is, higher biodiversity in a few large than many small patches of the same cumulative habitat area. We test whether this extrapolation is valid. We find that landscape-scale patterns are opposite to their analogous patch-scale patterns: for sets of patches with equal total habitat area, species richness and evenness decrease with increasing mean size of the patches comprising that area, even when considering only species of conservation concern. Preserving small habitat patches will, therefore, be key to sustain biodiversity amidst ongoing environmental crises.