Abstract. Does the shape of a biogeographical region influence its spatial patterns of species richness? A complete answer must include careful distinction between the distribution of a species, which is a complex geometric object, and the range of a species, which is relatively simple, especially when reduced to one dimension. We consider range‐based models of species richness, in particular range overlap counts in one dimension, for which we give a unified mathematical treatment via the joint probability P(m,l) of midpoints and lengths of ranges. We discuss a number of difficulties, in practice and in principle, using range‐based models, and show that the so‐called mid‐domain effect, a proposed null model for the effect of geometric constraint, is qualitatively a property of all biologically realistic models based on range overlap counts. As such, range‐based models provide little insight into understanding or explaining biogeographical patterns in species richness. We characterize the quantitative null model for range overlap counts in one dimension, for which we give a simple and direct field test based on P(m,l). We apply this test to a large clade in a complete bioregion (the Proteaceae of the Cape Floristic Region): geometric constraint does not explain the spatial pattern in this case. We show that any geometric constraint on species richness, including range overlap counts, must act via edge effects. Thus, to understand biogeographical patterns, an understanding of the effects and consequences of edges is fundamental.

The basal area of indigenous forest plots containing large canopy individuals appears to be larger than plots without them. One explanation for this effect is the avoidance of competition for light due to these large individuals emerging above the rest of the canopy and thus casting relatively little shade. In this way the basal area of these emergent individuals becomes 'additive' to that of the 'rest' of the individuals on a plot. The 'additive basal area' phenomenon was tested for in the Knysna Forest, South Africa by regressing the basal area of focal species versus the total basal area of 0.04-ha plots, as well as against the basal area of the 'rest'. Regression analysis suggested weak competition and a stronger additive effect. However, no emergent individuals occurred in the study taxa. A strong impact of the size of the largest individual on total plot basal area was found. It is suggested that the reason for this is that large individuals overcome spatial and packing limitations in forests.

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We report a novel pattern in species richness, complementary to the well‐known species–area relationship. We show that, as sample area increases, the variation in relative richness decreases among otherwise comparable spatial units. This pattern holds for southern African birds, French birds, Cape Proteaceae and the trees of Barro Colorado Island. We propose a scale‐free method for quantifying this pattern by measuring the multifractal intensity of species richness, which is the multi‐scale tendency of adjacent patches with the same area to differ in richness. By this measure, spatial variability is strongest for Cape Proteaceae and weakest for Barro Colorado Island trees. Our results have implications for area‐dependent estimates of species‐richness, for example in reserve planning and in simulation‐based studies. They imply that such estimates are most accurate for large areas, and will be subject to substantial uncertainty when the multifractal intensity is high and the area is small. For comparative purposes, multifractal intensity may be used as a supplement or as an alternative to mean richness, as well as for other ecological densities, such as biomass distribution and local abundance.

Abstract. Neither conventional niche theory nor current lottery models offer a satisfactory theoretical scope for modelling coexistence of species with disjoint generations. South‐African fynbos and Australian kwongan include many species which are killed by, and recruit only after, fire. We propose a density‐dependent lottery model which accommodates the unusual demographics of these species. We show that coexistence requires density dependence in recruitment. The result applies to a wider class of populations than the one considered here. It is applied to non‐resprouting species in fynbos and kwongan. We show that the lottery assumption of recruitment in proportion to propagules is often satisfied, while the production of such propagules is often density‐dependent, and we discuss some evidence of mechanisms whereby this may occur.