Species richness, species-area curves and Simpson's paradox

A key issue in ecology is how patterns of species diversity differ as a fun ction of scale. The scaling function is the species-area curve. The form of the species-area curve results from patterns of environmental heterogeneit y and species dispersal, and may be system-specific. A central concern is h ow, for a given set of species, the species-area curve varies with respect to a third variable, such as latitude or productivity. Critical is whether the relationship is scale-invariant (i.e. the species-area curves for diffe rent levels of the third variable are parallel), rank-invariant (i.e. the c urves are non-parallel, but non-crossing within the scales of interest) or neither, in which case the qualitative relationship is scale-dependent. Thi s recognition is critical for the development and testing of theories expla ining patterns of species richness because different theories have mechanis tic bases at different scales of action. Scale includes four attributes: sa mple-unit, grain, focus and extent. Focus is newly defined here. Distinguis hing among these attributes is a key step in identifying the probable scale (s) at which ecological processes determine patterns.