The biodiversity scaling metrics widely studied in macroecology include the species-area relationship (SAR), the scale-dependent species-abundance distribution (SAD), the distribution of masses or metabolic energies of individuals within and across species, the abundance-energy or abundance-mass relationship across species, and the species-level occupancy distributions across space. We propose a theoretical framework for predicting the scaling forms of these and other metrics based on the state-variable concept and an analytical method derived from information theory. In statistical physics, a method of inference based on information entropy results in a complete macro-scale description of classical thermodynamic systems in terms of the state variables volume, temperature, and number of molecules. In analogy, we take the state variables of an ecosystem to be its total area, the total number of species within any specified taxonomic group in that area, the total number of individuals across those species, and the summed metabolic energy rate for all those individuals. In terms solely of ratios of those state variables, and without invoking any specific ecological mechanisms, we show that realistic functional forms for the macroecological metrics listed above are inferred based on information entropy. The Fisher log series SAD emerges naturally from the theory. The SAR is predicted to have negative curvature on a log-log plot, but as the ratio of the number of species to the number of individuals decreases, the SAR becomes better and better approximated by a power law, with the predicted slope z in the range of 0.14-0.20. Using the 3/4 power mass-metabolism scaling relation to relate energy requirements and measured body sizes, the Damuth scaling rule relating mass and abundance is also predicted by the theory. We argue that the predicted forms of the macroecological metrics are in reasonable agreement with the patterns observed from plant census data across habitats and spatial scales. While this is encouraging, given the absence of adjustable fitting parameters in the theory, we further argue that even small discrepancies between data and predictions can help identify ecological mechanisms that influence macroecological patterns.

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...