Species–area relationships (SARs) are a key tool for understanding patterns of species diversity. A framework for the interpretation of SARs and their prediction under different landscape configurations remains elusive, however. This article addresses one of these configurations: how species’ minimum-area requirements affect the shape of island or other isolate Species–area curves. We distinguish between two classes of SARs: sample-area curves, compiled entirely within larger contiguous areas, and isolate curves, compiled between isolated areas. We develop this conceptual and graphic model in order to illuminate landscape-scale diversity patterns, to discuss how various landscape and species characteristics affect outcomes, and to investigate the dynamics of local extinction under conditions of habitat fragmentation. Minimum-area effects on actual islands and other isolates predictably cause Species–area curves either to be sigmoid in arithmetic space or to be lowered for smaller areas. In order to illustrate the inherent shape of isolate curves, this study fits convex and sigmoid regression models to empirical isolate (island) data sets that cover the small scales expected to include inflection points.