Describing and ultimately understanding species distribution and biodiversity patterns is undoubtedly one of the major goals in ecology (Gaston, 2000). Spatial scale is an extremely important issue here, and the topic is deservedly now getting more attention than hitherto (for example, Lomolino, 2000; Whittaker, Willis & Field, 2001). There is considerable interest in applying fractal and related cross-scale analytical methods to species distribution patterns, with a view to describing these patterns parsimoniously, connecting cross-scale species incidence with emergent properties such as the species–area relationship (Harte & Kinzig, 1997; Harte, Kinzig & Green, 1999; Plotkin et al., 2000; Harte, Blackburn & Ostling, 2001; Šizling & Storch, 2004; Kunin & Lennon, 2005), predicting abundance at fine scales from coarse scale information (Kunin, 1998; He & Gaston, 2000; Kunin, Hartley & Lennon, 2000; Gaston, 2003), identifying scaling regions and breakpoints (see Hartley et al., 2004) and detecting scale invariance in populations (Keitt et al., 2002). Although the roots of these cross-scale ideas lie partly in more familiar ecological pattern-analysis methods (for a good summary see Dale, 1998; Fortin & Dale, 2005), they offer exciting new ways of describing and thinking about species distribution patterns that may, ultimately, lead to a much better understanding of the ecological processes involved in their generation.
Despite this large and growing body of work, on the whole surprisingly little is known about the scaling properties of species distribution patterns.