Scheiner, S. M., S. B. Cox, M. Willig, G. G. Mittelbach, C. Osenberg, and M. Kaspari. 2000. Species richness, species-area curves and Simpson's paradox. Evolutionary Ecology Research 2:791-802.

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A key issue in ecology is how patterns of species diversity differ as a function of scale. The scaling function is the species-area curve. The form of the species-area curve results from patterns of environmental heterogeneity and species dispersal, and may be system-specific. A central concern is how, 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 different levels of the third variable are parallel), rank-invariant (i.e. the curves are non-parallel, but non-crossing within the scales of interest) or neither, in which case the qualitative relationship is scale-dependent. This recognition is critical for the development and testing of theories explaining patterns of species richness because different theories have mechanistic bases at different scales of action. Scale includes four attributes: sample-unit, grain, focus and extent. Focus is newly defined here. Distinguishing among these attributes is a key step in identifying the probable scale(s) at which ecological processes determine patterns.

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