Abstract Background The relationship between the environmental (ED) or habitat (HD) diversity of a landscape and its species richness (S) is of global interest. The standard linear relationship tested is that total S rises with an increase in variability of environmental properties. Findings We recognize three basic S − ED patterns: convex, unimodal, and concave. These are shown to be based on three underlying species − area (S − A) curves: power, logarithmic, and sigmoid. From these, we find that the standard linear relationship lacks theoretical support. There are two sets of circumstances that can lead to a humped relationship: a particular type of S-A curve (logarithmic), and the operation of negative secondary effects as habitats become smaller and more isolated. The preponderance of positive linear and dearth of unimodal S − ED and S − HD relationships reported so far can be attributed to six causes. These include: only testing for linear relationships; limited data sets that exclude small, unique, or isolated habitats; regressions against non-causal variables; and/or use of biased data that have not been ground-truthed. Conclusions Informed by the underlying S − A curves and the level of negative biotic effects at high ED, one can predict the numerous shapes of the S − ED curve. Hump-backed S − ED curves should apply widely in regions with species-rich biotas and where the environmental range is large and numerous isolated habitats are present.