Summary 1.This article reviews the application of some summary statistics from current theory of spatial point processes for extracting information from spatial patterns of plants. Theoretical measures and issues connected with their estimation are described. Results are illustrated in the context of specific ecological questions about spatial patterns of trees in two forests. 2. The pair correlation function, related to Ripley's K function, provides a formal measure of the density of neighbouring plants and makes precise the general notion of a 'plant's-eye' view of a community. The pair correlation function can also be used to describe spatial relationships of neighbouring plants with different qualitative properties, such as species identity and size class. 3. The mark correlation function can be used to describe the spatial relationships of quantitative measures (e.g. biomass). We discuss two types of correlation function for quantitative marks. Applying these functions to the distribution of biomass in a temperate forest, it is shown that the spatial pattern of biomass is uncoupled from the spatial pattern of plant locations. 4. The inhomogeneous pair correlation function enables first-order heterogeneity in the environment to be removed from second-order spatial statistics. We illustrate this for a tree species in a forest of high topographic heterogeneity and show that spatial aggregation remains after allowing for spatial variation in density. An alternative method, the master function, takes a weighted average of homogeneous pair correlation functions computed in subareas; when applied to the same data and compared with the former method, the spatial aggregations are smaller in size. 5. Synthesis. These spatial statistics, especially those derived from pair densities, will help ecologists to extract important ecological information from intricate spatially correlated plants in populations and communities.

A persistent challenge in ecology is to explain the high diversity of tree species in tropical forests. Although the role of species characteristics in maintaining tree diversity in tropical forests has been the subject of theory and debate for decades, spatial patterns in local diversity have not been analyzed from the viewpoint of individual species. To measure scale-dependent local diversity structures around individual species, we propose individual speciesarea relationships (ISAR), a spatial statistic that marries common species-area relationships with Ripley's K to measure the expected ␣ diversity in circular neighborhoods with variable radius around an arbitrary individual of a target species. We use ISAR to investigate if and at which spatial scales individual species increase in tropical forests' local diversity (accumulators), decrease local diversity (repellers), or behave neutrally. Our analyses of data from Barro Colorado Island (Panama) and Sinharaja (Sri Lanka) reveal that individual species leave identifiable signatures on spatial diversity, but only on small spatial scales. Most species showed neutral behavior outside neighborhoods of 20 m. At short scales (<20 m), we observed, depending on the forest type, two strongly different roles of species: diversity repellers dominated at Barro Colorado Island and accumulators at Sinharaja. Nevertheless, we find that the two tropical forests lacked any key species structuring species diversity at larger scales, suggesting that ''balanced'' species-species interactions may be a characteristic of these speciesrich forests. We anticipate our analysis method will be a starting point for more powerful investigations of spatial structures in diversity to promote a better understanding of biodiversity in tropical forests.biodiversity ͉ spatial patterns ͉ spatial statistic ͉ species-area relationship S ince the establishment of large permanent sampling plots where all stems Ͼ1 cm in diameter at breast height (dbh) are identified, measured, and mapped (1, 2), substantial progress has been made in explaining the high local diversity of tree species in tropical forests; however, ecologists are still far from having a definitive answer. Several competing hypotheses on processes promoting species coexistence have been developed and tested, but these efforts have yielded contrasting results (3-5). Neutral theory (6-8) suggested that species-specific differences are unimportant for certain community attributes, whereas niche theory outlines the importance of species characteristics and trade-offs (9, 10). It is also clear that species-specific differences affect the spatial distribution of populations (11-16). Surprisingly, although plant-plant interactions should play a major role in structuring tropical forests, the resulting spatial patterns in diversity have not been analyzed from the viewpoint of individual species. However, strong differences in species traits and in species interactions should create clearly identifiable nonrandom spatial structures in diversity...

Theory predicts that higher biodiversity in the tropics is maintained by specialized interactions among plants and their natural enemies that result in conspecific negative density dependence (CNDD). By using more than 3000 species and nearly 2.4 million trees across 24 forest plots worldwide, we show that global patterns in tree species diversity reflect not only stronger CNDD at tropical versus temperate latitudes but also a latitudinal shift in the relationship between CNDD and species abundance. CNDD was stronger for rare species at tropical versus temperate latitudes, potentially causing the persistence of greater numbers of rare species in the tropics. Our study reveals fundamental differences in the nature of local-scale biotic interactions that contribute to the maintenance of species diversity across temperate and tropical communities.

Most ecological hypotheses about species coexistence hinge on species differences, but quantifying trait differences across species in diverse communities is often unfeasible. We examined the variation of demographic traits using a global tropical forest data set covering 4500 species in 10 large-scale tree inventories. With a hierarchical Bayesian approach, we quantified the distribution of mortality and growth rates of all tree species at each site. This allowed us to test the prediction that demographic differences facilitate species richness, as suggested by the theory that a tradeoff between high growth and high survival allows species to coexist. Contrary to the prediction, the most diverse forests had the least demographic variation. Although demographic differences may foster coexistence, they do not explain any of the 16-fold variation in tree species richness observed across the tropics. C omparative studies of tree demography typically consider the entire community as a unit, ignoring species differences (1), simply because most tree inventories include small samples of many species (2, 3). Comparative studies show that tropical forests typically have higher turnover than do temperate forests (4) and that higher tree turnover associates with higher tree diversity (5). These studies cannot, however, test ecological hypotheses about diversity, coexistence, and demography (6-10).A tradeoff between rapid growth and long life span permits species coexistence and can foster diversity: Species reproducing early in life persist despite poor competitive ability by growing rapidly on disturbed sites where resources are abundant. Long-lived species coexist by outliving the weedy invaders, persisting where resources are scarce. This is a familiar and widely known tradeoff in plant and animal communities (9-11) called the successionalniche hypothesis (7,12). At a deterministic equilibrium, an indefinite number of species can coexist by this mechanism, each differing from all others along a continuum from short life span (with high growth) to long life span (and low growth). With stochastic demography, however, there is limiting similarity and the equilibrium species richness is finite (11, 13). This hypothesis is widely quoted as an explanation for tropical forest diversity (14-16). Here, we ask whether species differences along a demographic axis explain why some tropical forests have many more species than others.If demographic niches are a key force controlling forest diversity, then more diverse forests have more demographic niches. More niches could come about either by spreading demographic rates over a wider range or packing more in the same range. Here, we focus on the first prediction: Tropical forests gain diversity by having a wider range of demographic niches, as reflected by the range of mortality and growth rates across species.We provide a direct test by quantifying mortality and growth of 4500 tree species in 10 different forests in America, Asia, and Africa (17). The 10 sites form a large-scale ob...