Allometric scaling relations, including the 3/4 power law for metabolic rates, are characteristic of all organisms and are here derived from a general model that describes how essential materials are transported through space-filling fractal networks of branching tubes. The model assumes that the energy dissipated is minimized and that the terminal tubes do not vary with body size. It provides a complete analysis of scaling relations for mammalian circulatory systems that are in agreement with data. More generally, the model predicts structural and functional properties of vertebrate cardiovascular and respiratory systems, plant vascular systems, insect tracheal tubes, and other distribution networks.

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Plant traits – the morphological, anatomical, physiological, biochemical and phenological characteristics of plants and their organs – determine how primary producers respond to environmental factors, affect other trophic levels, influence ecosystem processes and services and provide a link from species richness to ecosystem functional diversity. Trait data thus represent the raw material for a wide range of research from evolutionary biology, community and functional ecology to biogeography. Here we present the global database initiative named TRY, which has united a wide range of the plant trait research community worldwide and gained an unprecedented buy-in of trait data: so far 93 trait databases have been contributed. The data repository currently contains almost three million trait entries for 69 000 out of the world's 300 000 plant species, with a focus on 52 groups of traits characterizing the vegetative and regeneration stages of the plant life cycle, including growth, dispersal, establishment and persistence. A first data analysis shows that most plant traits are approximately log-normally distributed, with widely differing ranges of variation across traits. Most trait variation is between species (interspecific), but significant intraspecific variation is also documented, up to 40% of the overall variation. Plant functional types (PFTs), as commonly used in vegetation models, capture a substantial fraction of the observed variation – but for several traits most variation occurs within PFTs, up to 75% of the overall variation. In the context of vegetation models these traits would better be represented by state variables rather than fixed parameter values. The improved availability of plant trait data in the unified global database is expected to support a paradigm shift from species to trait-based ecology, offer new opportunities for synthetic plant trait research and enable a more realistic and empirically grounded representation of terrestrial vegetation in Earth system models.

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letters to nature 664 NATURE | VOL 400 | 12 AUGUST 1999 | www.nature.com point mutations on the performance of digital organisms. In all cases, the ®tness (replication rate) of each mutant was calculated in the same environment in which its simple or complex parent evolved, and the mutant's ®tness is expressed relative to the parent. The ®rst tool makes every possible one-step point mutant for a particular parent. The default set includes 28 different instructions; given a parent of genome length 80, for example, there are 80 3 28 2 1 2;160 different one-step point mutants. The mean ®tness of these mutants permits exact calculation of a in the decay test. The second tool produces a random sample of progeny that differ from their parent by two or more point mutations. For each parent, we generated between 10 5 and 10 7 progeny with two mutations, three mutations and so on, up to ten mutations. The third tool produces and analyses pairs of point mutations alone and in combination; for each two-step mutant, we have both corresponding one-step mutants. Having the single mutants allows us to compare a double mutant's actual ®tness with the exact value expected under the hypothesis that the mutations interact in a multiplicative manner. We ran the pair test on 10 4 and 10 5 mutational pairs for each complex and simple organism, respectively. Statistical methods. We performed the Wilcoxon signed-ranks test on the difference scores for all comparisons between complex and simple organisms 29 . This test re¯ects the evolutionary relationship between pairs of organisms; it is also non-parametric and thus insensitive to deviations from a normal distribution. To estimate b in the decay tests, we minimized the sum of squared deviations around the log-transformed mean ®tness values. We excluded samples with fewer than 100 viable mutants, in which case log mean ®tness was poorly estimated. By increasing sample size to 10 8 , we can obtain additional viable mutants; the exclusion of some values because of insuf®cient sampling appears to have no systematic effect on estimation of b.

Species abundance distributions (SADs) follow one of ecologyÕs oldest and most universal laws -every community shows a hollow curve or hyperbolic shape on a histogram with many rare species and just a few common species. Here, we review theoretical, empirical and statistical developments in the study of SADs. Several key points emerge. (i) Literally dozens of models have been proposed to explain the hollow curve. Unfortunately, very few models are ever rejected, primarily because few theories make any predictions beyond the hollow-curve SAD itself. (ii) Interesting work has been performed both empirically and theoretically, which goes beyond the hollow-curve prediction to provide a rich variety of information about how SADs behave. These include the study of SADs along environmental gradients and theories that integrate SADs with other biodiversity patterns. Central to this body of work is an effort to move beyond treating the SAD in isolation and to integrate the SAD into its ecological context to enable making many predictions. (iii) Moving forward will entail understanding how sampling and scale affect SADs and developing statistical tools for describing and comparing SADs. We are optimistic that SADs can provide significant insights into basic and applied ecological science.

Fractal-like networks effectively endow life with an additional fourth spatial dimension. This is the origin of quarter-power scaling that is so pervasive in biology. Organisms have evolved hierarchical branching networks that terminate in size-invariant units, such as capillaries, leaves, mitochondria, and oxidase molecules. Natural selection has tended to maximize both metabolic capacity, by maximizing the scaling of exchange surface areas, and internal efficiency, by minimizing the scaling of transport distances and times. These design principles are independent of detailed dynamics and explicit models and should apply to virtually all organisms.

Several equations have been proposed to describe ontogenetic growth trajectories for organisms justified primarily on the goodness of fit rather than on any biological mechanism. Here, we derive a general quantitative model based on fundamental principles for the allocation of metabolic energy between maintenance of existing tissue and the production of new biomass. We thus predict the parameters governing growth curves from basic cellular properties and derive a single parameterless universal curve that describes the growth of many diverse species. The model provides the basis for deriving allometric relationships for growth rates and the timing of life history events.