IDEA AND PERSPECTIVE The quest for a null model for macroecological patterns: geometry of species distributions at multiple spatial scales David Storch, 1,2 * Arnos ˇt L. S ˇ izling, 1,3 Jir ˇı ´ Reif, 2 Jitka Polechova ´, 1,4 Eva S ˇ izlingova ´ 5 and Kevin J. Gaston 3 1 Center for Theoretical Study, Charles University, Jilska ´ 1, 110 00 Praha 1, Czech Republic 2 Department of Ecology, Faculty of Science, Charles University, Vinic ˇna ´ 7, 128 44 Praha 2, Czech Republic 3 Biodiversity & Macroecology Group, Department of Animal & Plant Sciences, University of Sheffield, Sheffield S10 2TN, UK 4 Biomathematics & Statistics Scotland, University of Edinburgh, JCMB, The KingÕs Buildings, Edinburgh EH9 3JZ, UK 5 Department of Philosophy and History of Science, Faculty of Science, Charles University, Vinic ˇna ´ 7, 128 44 Praha 2, Czech Republic *Correspondence: E-mail: storch@cts.cuni.cz Abstract There have been several attempts to build a unified framework for macroecological patterns. However, these have mostly been based either on questionable assumptions or have had to be parameterized to obtain realistic predictions. Here, we propose a new model explicitly considering patterns of aggregated species distributions on multiple spatial scales, the property which lies behind all spatial macroecological patterns, using the idea we term Ôgeneralized fractalsÕ. SpeciesÕ spatial distributions were modelled by a random hierarchical process in which the original ÔhabitatÕ patches were randomly replaced by sets of smaller patches nested within them, and the statistical properties of modelled species assemblages were compared with macroecological patterns in observed bird data. Without parameterization based on observed patterns, this simple model predicts realistic patterns of species abundance, distribution and diversity, including fractal-like spatial distributions, the frequency distribution of species occupancies ⁄ abun- dances and the species–area relationship. Although observed macroecological patterns may differ in some quantitative properties, our concept of random hierarchical aggregation can be considered as an appropriate null model of fundamental macroecological patterns which can potentially be modified to accommodate ecologically important variables. Keywords Biodiversity, biogeography, generalized fractals, HubbellÕs neutral theory, macroecology, null models, scale, species spatial aggregation, species-abundance distribution, species– area relationship. Ecology Letters (2008) 11: 771–784 INTRODUCTION Several patterns in ecology that concern species richness, the abundances of species and the spatial distribution of individuals, seem to be near universal regardless of taxon and spatial scale. Macroecology has been defined as the study of such statistical regularities (Brown 1995; Maurer 1999). In the course of the exploration of the details of these patterns, the field has generated a multitude of hypotheses trying to explain each of them individually (for reviews see Gaston & Blackburn 2000; Storch & Gaston 2004; Gaston et al. 2008) but, since many different processes can lead to very similar patterns, these are often difficult to test. Moreover, the ubiquity of major macroecological patterns suggests that there are some more general principles behind particular biological processes which go beyond the intricacies of a given taxon or environment, and whose nature is essentially mathematical or statistical (see Nekola & Brown 2007). During the last two decades, it has become clear that many macroecological patterns are tightly connected, and can often be mathematically derived from each other. Some of these connections are deterministic, and particular patterns can be considered as simple by-products of other patterns. For example, the species–area relationship can be derived exactly from knowledge of the relationship between area and the probability of occurrence of individual species (hereafter the P–area relationship; Coleman 1981; S ˇ izling & Storch 2004), and the slope of the species–area relationship is in turn related to patterns of species spatial turnover (Harte & Kinzig 1997) and to the relationship between local and regional species richness (Rosenzweig & Ziv 1999; Ecology Letters, (2008) 11: 771–784 doi: 10.1111/j.1461-0248.2008.01206.x Ó 2008 Blackwell Publishing Ltd/CNRS