Introduction

Arguably, the most important development in ecology in the past few decades has been the discovery of space. The spatial structure of populations and their interactions has become increasingly central to our understanding of ecological dynamics, revolutionizing many areas of both theory and application (e.g. Tilman & Kareiva, 1997). While this is true of all organisms, spatial aspects of population biology are particularly apparent in sessile organisms such as plants. Plant populations are spatially complex, with individuals typically clustered within patches that are themselves aggregated in habitats that are patchily distributed in space. Despite attempts to define the “natural” scale of patchiness (reviewed in Dale, 1999), most populations I know of appear aggregated at virtually any spatial scale. This greatly complicates the description of the abundance and distribution of species, as most of the useful measures are intrinsically scale bound. Indeed, many different aspects of abundance can be reflected by grid occupancy at some appropriate scale of resolution (Kunin, 1998). Thus the extent of a species' geographic range reflects its coarse-scale distribution, whereas population size or cover reflects fine-scale abundance, with factors such as the number of discrete subpopulations or habitat specialization being reflected at intermediate scales.

In an attempt to summarize such spatially complex patterns, the area occupied by a species may be plotted at multiple spatial scales on logarithmic axes, into a “scale area curve” that could summarize abundance scaling.

Introduction

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.