species are very abundant; 3,248 species (29.0%) have >10⁶ individuals in the Brazilian Amazon, and 4,575 species (40.8%) have >10⁵ individuals >10 cm DBH. At the other end of the relative-abundance spectrum, we estimate that more than a third of all species (3,981, or 35.5%) in the Brazilian Amazon each have (or had) total population sizes <10³ individuals. The remaining quarter of tree species in the Brazilian Amazon have estimated abundances between 10³ and 10⁵ individuals >10 cm DBH.

Many common Amazonian tree species must have extremely large range sizes. In the fertile-soil, aseasonal-climate, high-diversity forests of western Amazonia, many of the same species are found in tree communities separated by thousands of kilometers north and south along the eastern side of the Andes (ter Steege et al., 2006; Condit et al., 2002). One can calculate the probability that two trees randomly sampled from geographically separated tree communities are the same species from existing plot data in western Amazonia. After decreasing rapidly over short distances (<100 m), this probability decays very slowly over large distances (Condit et al., 2002). However, there is much higher turnover of species and genera when one traverses the Amazon Basin over the seasonality gradient from the northwest (aseasonal) to southeast (highly seasonal) and on the soil-fertility gradient from the southwest (high fertility) to the northeast (low fertility) (ter Steege et al., 2006).

Extremely common, widespread species with >10⁶ adults constitute between a quarter and a third of the total number of Amazonian tree species, and these species are expected to have broad ranges over the Amazon. But what are the range sizes for the many rare to very rare species in the Amazon Basin? By rare in the present context, we mean that the global population size of a given species is small irrespective of the spatial distribution and density of the individual plants of the species. To estimate range size, we need to know the relationship between population size and the area it occupies. If we assume that local population densities of common and rare species are approximately of the same order of magnitude (e.g., because of similar order-of-magnitude seed-dispersal distances), then it follows that rare species will generally have smaller range sizes than common species. This generalization could be violated if rare species are systematically more likely to have a fragmented metapopulation structure than common species.

Whatever the spatial structure of tropical tree populations, however, we can take an empirical approach to this question using the mapped 50-ha plots. We can ask: How does the average distance from a focal tree to a conspecific neighbor change with increasing rank of neighbor, i.e., the