Abstract. Metabolism provides a basis for using first principles of physics, chemistry, and biology to link the biology of individual organisms to the ecology of populations, communities, and ecosystems. Metabolic rate, the rate at which organisms take up, transform, and expend energy and materials, is the most fundamental biological rate. We have developed a quantitative theory for how metabolic rate varies with body size and temperature. Metabolic theory predicts how metabolic rate, by setting the rates of resource uptake from the environment and resource allocation to survival, growth, and reproduction, controls ecological processes at all levels of organization from individuals to the biosphere. Examples include: (1) life history attributes, including development rate, mortality rate, age at maturity, life span, and population growth rate; (2) population interactions, including carrying capacity, rates of competition and predation, and patterns of species diversity; and (3) ecosystem processes, including rates of biomass production and respiration and patterns of trophic dynamics.Data compiled from the ecological literature strongly support the theoretical predictions. Eventually, metabolic theory may provide a conceptual foundation for much of ecology, just as genetic theory provides a foundation for much of evolutionary biology.

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.

We derive a general model, based on principles of biochemical kinetics and allometry, that characterizes the effects of temperature and body mass on metabolic rate. The model fits metabolic rates of microbes, ectotherms, endotherms (including those in hibernation), and plants in temperatures ranging from 0 degrees to 40 degrees C. Mass- and temperature-compensated resting metabolic rates of all organisms are similar: The lowest (for unicellular organisms and plants) is separated from the highest (for endothermic vertebrates) by a factor of about 20. Temperature and body size are primary determinants of biological time and ecological roles.

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We review the biogeography of microorganisms in light of the biogeography of macroorganisms. A large body of research supports the idea that free-living microbial taxa exhibit biogeographic patterns. Current evidence confirms that, as proposed by the Baas-Becking hypothesis, 'the environment selects' and is, in part, responsible for spatial variation in microbial diversity. However, recent studies also dispute the idea that 'everything is everywhere'. We also consider how the processes that generate and maintain biogeographic patterns in macroorganisms could operate in the microbial world.

Abstract. Demographic and genetic contributions from conspecific immigrants tend to reduce extinction rates of insular populations. The MacArthur-Wilson model of island biogeography is modified to provide for this effect of immigration on extinction, which we call the rescue effect. This new model predicts that when immigration rates are high relative to extinction rates, turnover rate is directly related to the distance between an island and the source of colonizing species. A field study of the distribution of arthropods among isolated plants supports the model.

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.

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.