The theory of metabolic ecology predicts specific relationships among tree stem diameter, biomass, height, growth and mortality. As demographic rates are important to estimates of carbon fluxes in forests, this theory might offer important insights into the global carbon budget, and deserves careful assessment. We assembled data from 10 oldgrowth tropical forests encompassing censuses of 367 ha and > 1.7 million trees to test the theory's predictions. We also developed a set of alternative predictions that retained some assumptions of metabolic ecology while also considering how availability of a key limiting resource, light, changes with tree size. Our results show that there are no universal scaling relationships of growth or mortality with size among trees in tropical forests. Observed patterns were consistent with our alternative model in the one site where we had the data necessary to evaluate it, and were inconsistent with the predictions of metabolic ecology in all forests.

Summary The relationship between species richness and ecosystem function, as measured by productivity or biomass, is of long‐standing theoretical and practical interest in ecology. This is especially true for forests, which represent a majority of global biomass, productivity and biodiversity. Here, we conduct an analysis of relationships between tree species richness, biomass and productivity in 25 forest plots of area 8–50 ha from across the world. The data were collected using standardized protocols, obviating the need to correct for methodological differences that plague many studies on this topic. We found that at very small spatial grains (0.04 ha) species richness was generally positively related to productivity and biomass within plots, with a doubling of species richness corresponding to an average 48% increase in productivity and 53% increase in biomass. At larger spatial grains (0.25 ha, 1 ha), results were mixed, with negative relationships becoming more common. The results were qualitatively similar but much weaker when we controlled for stem density: at the 0.04 ha spatial grain, a doubling of species richness corresponded to a 5% increase in productivity and 7% increase in biomass. Productivity and biomass were themselves almost always positively related at all spatial grains. Synthesis. This is the first cross‐site study of the effect of tree species richness on forest biomass and productivity that systematically varies spatial grain within a controlled methodology. The scale‐dependent results are consistent with theoretical models in which sampling effects and niche complementarity dominate at small scales, while environmental gradients drive patterns at large scales. Our study shows that the relationship of tree species richness with biomass and productivity changes qualitatively when moving from scales typical of forest surveys (0.04 ha) to slightly larger scales (0.25 and 1 ha). This needs to be recognized in forest conservation policy and management.

Tropical forests vary substantially in the densities of trees of different sizes and thus in above-ground biomass and carbon stores. However, these tree size distributions show fundamental similarities suggestive of underlying general principles. The theory of metabolic ecology predicts that tree abundances will scale as the )2 power of diameter. Demographic equilibrium theory explains tree abundances in terms of the scaling of growth and mortality. We use demographic equilibrium theory to derive analytic predictions for tree size distributions corresponding to different growth and mortality functions. We test both sets of predictions using data from 14 large-scale tropical forest plots encompassing censuses of 473 ha and > 2 million trees. The data are uniformly inconsistent with the predictions of metabolic ecology. In most forests, size distributions are much closer to the predictions of demographic equilibrium, and thus, intersite variation in size distributions is explained partly by intersite variation in growth and mortality.

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...