Cover; Scaling Biodiversity; Title; Copyright; Contents; Contributors; Foreword; References; Preface; CHAPTER ONE: Introduction: scaling biodiversity -- what is the problem?; Part I. Spatial scaling of species richness and distribution; Part II. Alternative measures of biodiversity: taxonomy, phylogeny, and turnover; Part III. Scaling of biological diversity with energy and the latitudinal biodiversity gradient; Part IV. Processes, perspectives, and syntheses; Concluding remarks; References; PART I: Spatial scaling of species richness and distribution.CHAPTER TWO: Species-area curves and the geometry of natureIntroduction; Gradient analysis; The geometry of heterogeneity and the species-area relationship; The fractal geometry of the landscape and species richness; Multiple gradients; The Environmental Texture Model of the triphasic species-area curve; Low D at fine scales; High D at intermediate scales; Low D at broad scales; Exceptions; The case of mountainous regions; Richness of North American vascular floras in mountainous regions; Conclusions; Acknowledgments; References.CHAPTER THREE: The distribution of species: occupancy, scale, and rarityIntroduction; Occupancy-area models; Testing the models; Random and fractal simulations; Species distributions at the local scale; Species distributions at the regional scale; Estimating occupancy at fine scales from the occupancy at coarse scales; Comparing the slope between rare and common species; Discussion; Acknowledgments; References; CHAPTER FOUR: Species distribution patterns, diversity scaling and testing for fractals in southern African birds; Introduction; Methods; The fractal model; The cross-scale model.Synthetic realizations of the cross-scale modelModel fitting: testing for fractal and cross-scale relationships; Maximum likelihood estimation; A comparison with the saturation model; Species distribution data; Species-area relationships; Results; Discussion; Conclusions; Acknowledgments; References; CHAPTER FIVE: Geometry of species distributions: random clustering and scale invariance; Introduction; Self-similarity and hierarchical aggregation; Fractals; Generalized fractals; Generating generalized fractals -- models of more or less random multiscale aggregation; M1 The fractal model.M2 The model of stable proportion of occupied area among levelsM3 The model of stable proportion of area within levels; M4 The random proportion model; M5 The area- and taxa-invariance model; Model properties and tests; The relationship between area and probability of occurrence; The species-area relationship; Frequency distribution of the occupied Euclidean area; Discussion and conclusions; Acknowledgments; Appendix 5.I: The area- and taxa-invariant distribution; Appendix 5. II: Calculating the distribution of occupied areas; M2 The model of stable proportion of occupied area between levels.