In this review I show that the ‘3/4‐power scaling law’ of metabolic rate is not universal, either within or among animal species. Significant variation in the scaling of metabolic rate with body mass is described mainly for animals, but also for unicells and plants. Much of this variation, which can be related to taxonomic, physiological, and/or environmental differences, is not adequately explained by existing theoretical models, which are also reviewed. As a result, synthetic explanatory schemes based on multiple boundary constraints and on the scaling of multiple energy‐using processes are advocated. It is also stressed that a complete understanding of metabolic scaling will require the identification of both proximate (functional)and ultimate (evolutionary)causes. Four major types of intraspecific metabolic scaling with body mass are recognized [based on the power functionR=aM^b, whereRis respiration (metabolic) rate,ais a constant,Mis body mass, andbis the scaling exponent]: Type I: linear, negatively allometric (b<1); Type II: linear, isometric (b=1); Type III: nonlinear, ontogenetic shift from isometric (b=1), or nearly isometric, to negatively allometric (b 1) to one or two later phases of negative allometry (b<1). Ontogenetic changes in the metabolic intensity of four component processes (i.e.growth, reproduction, locomotion, and heat production) appear to be important in these different patterns of metabolic scaling. These changes may, in turn, be shaped by age (size)‐specific patterns of mortality. In addition, major differences in interspecific metabolic scaling are described, especially with respect to mode of temperature regulation, body‐size range, and activity level. A‘metabolic‐level boundaries hypothesis’ focusing on two major constraints (surface‐area limits on resource/waste exchange processes and mass/volume limits on power production) can explain much, but not all of this variation. My analysis indicates that further empirical and theoretical work is needed to understand fully the physiological and ecological bases for the considerable variation in metabolic scaling that is observed both within and among species.Recommended approaches for doing this are discussed. I conclude that the scaling of metabolism is not the simple result of a physical law, but rather appears to be the more complex result of diverse adaptations evolved in the context of both physico‐chemical and ecological constraints.

In this review I show that four major kinds of theoretical approaches have been used to explain the scaling of metabolic rate in cells, organisms and groups of organisms in relation to system size. They include models focusing on surface-area related fluxes of resources and wastes (including heat), internal resource transport, system composition, and various processes affecting resource demand, all of which have been discussed extensively for nearly a century or more. I argue that, although each of these theoretical approaches has been applied to multiple levels of biological organization, none of them alone can fully explain the rich diversity of metabolic scaling relationships, including scaling exponents (log-log slopes) that vary from ~0 to >1. Furthermore, I demonstrate how a synthetic theory of metabolic scaling can be constructed by including the context-dependent action of each of the above modal effects. This “contextual multimodal theory” (CMT) posits that various modulating factors (including metabolic level, surface permeability, body shape, modes of thermoregulation and resource-transport, and other internal and external influences) affect the mechanistic expression of each theoretical module. By involving the contingent operation of several mechanisms, the “meta-mechanistic” CMT differs from most metabolic scaling theories that are deterministically mechanistic. The CMT embraces a systems view of life, and as such recognizes the open, dynamic nature and complex hierarchical and interactive organization of biological systems, and the importance of multiple (upward, downward and reciprocal) causation, biological regulation of resource supply and demand and their interaction, and contingent internal (system) and external (environmental) influences on metabolic scaling, all of which are discussed. I hope that my heuristic attempt at building a unifying theory of metabolic scaling will not only stimulate further testing of all of the various subtheories composing it, but also foster an appreciation that many current models are, at least in part, complementary or even synergistic, rather than antagonistic. Further exploration about how the scaling of the rates of metabolism and other biological processes are interrelated should also provide the groundwork for formulating a general metabolic theory of biology.

Metabolic rate is traditionally assumed to scale with body mass to the 3/4-power, but significant deviations from the ‘3/4-power law’ have been observed for several different taxa of animals and plants, and for different physiological states. The recently proposed ‘metabolic-level boundaries hypothesis’ represents one of the attempts to explain this variation. It predicts that the power (log–log slope) of metabolic scaling relationships should vary between 2/3 and 1, in a systematic way with metabolic level. Here, this hypothesis is tested using data from birds and mammals. As predicted, in both of these independently evolved endothermic taxa, the scaling slope approaches 1 at the lowest and highest metabolic levels (as observed during torpor and strenuous exercise, respectively), whereas it is near 2/3 at intermediate resting and cold-induced metabolic levels. Remarkably, both taxa show similar, approximately U-shaped relationships between the scaling slope and the metabolic (activity) level. These predictable patterns strongly support the view that variation of the scaling slope is not merely noise obscuring the signal of a universal scaling law, but rather is the result of multiple physical constraints whose relative influence depends on the metabolic state of the organisms being analysed.