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 function R=aMb, where R is respiration (metabolic) rate, a is a constant, M is body mass, and b is 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); and Type IV: nonlinear, ontogenetic shift from positively 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.

The scaling of metabolic rate with body mass has long been a controversial topic. Some workers have claimed that the slope of log-log metabolic scaling relationships typically obeys a universal 3/4-power law resulting from the geometry of resource-transport networks. Others have attempted to explain the broad diversity of metabolic scaling relationships. Although several potentially useful models have been proposed, at present none successfully predicts the entire range of scaling relationships seen among both physiological states and taxonomic groups of animals and plants. Here I argue that our understanding may be aided by three shifts in focus: from explaining average tendencies to explaining variation between extreme boundary limits, from explaining the slope and elevation (metabolic level) of scaling relationships separately to showing how and why they are interrelated, and from focusing primarily on internal factors (e.g. body design) to a more balanced consideration of both internal and external (ecological) factors. By incorporating all of these shifts in focus, the recently proposed metabolic-level boundaries hypothesis appears to provide a useful way of explaining both taxonomic and physiological variation in metabolic scaling relationships. This hypothesis correctly predicts that the scaling slope should vary mostly between 2/3 and 1 and that it should be related to metabolic (activity) level according to an approximately U-shaped function. It also implies that the scaling of other energy-dependent biological processes should be related to the metabolic level of the organisms being examined. Some data are presented that support this implication, but further research is needed.

Metabolic energy fuels all biological processes, and therefore theories that explain the scaling of metabolic rate with body mass potentially have great predictive power in ecology. A new model, that could improve this predictive power, postulates that the metabolic scaling exponent (b) varies between 2/3 and 1, and is inversely related to the elevation of the intraspecific scaling relationship (metabolic level, L), which in turn varies systematically among species in response to various ecological factors. We test these predictions by examining the effects of lifestyle, swimming mode and temperature on intraspecific scaling of resting metabolic rate among 89 species of teleost fish. As predicted, b decreased as L increased with temperature, and with shifts in lifestyle from bathyal and benthic to benthopelagic to pelagic. This effect of lifestyle on b may be related to varying amounts of energetically expensive tissues associated with different capacities for swimming during predator-prey interactions.

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

A common, long-held belief is that metabolic rate drives the rates of various biological, ecological and evolutionary processes. Although this metabolic pacemaker view (as assumed by the recent, influential 'metabolic theory of ecology') may be true in at least some situations (e.g. those involving moderate temperature effects or physiological processes closely linked to metabolism, such as heartbeat and breathing rate), it suffers from several major limitations, including: (i) it is supported chiefly by indirect, correlational evidence (e.g. similarities between the body-size and temperature scaling of metabolic rate and that of other biological processes, which are not always observed) - direct, mechanistic or experimental support is scarce and much needed; (ii) it is contradicted by abundant evidence showing that various intrinsic and extrinsic factors (e.g. hormonal action and temperature changes) can dissociate the rates of metabolism, growth, development and other biological processes; (iii) there are many examples where metabolic rate appears to respond to, rather than drive the rates of various other biological processes (e.g. ontogenetic growth, food intake and locomotor activity); (iv) there are additional examples where metabolic rate appears to be unrelated to the rate of a biological process (e.g. ageing, circadian rhythms, and molecular evolution); and (v) the theoretical foundation for the metabolic pacemaker view focuses only on the energetic control of biological processes, while ignoring the importance of informational control, as mediated by various genetic, cellular, and neuroendocrine regulatory systems. I argue that a comprehensive understanding of the pace of life must include how biological activities depend on both energy and information and their environmentally sensitive interaction. This conclusion is supported by extensive evidence showing that hormones and other regulatory factors and signalling systems coordinate the processes of growth, metabolism and food intake in adaptive ways that are responsive to an organism's internal and external conditions. Metabolic rate does not merely dictate growth rate, but is coadjusted with it. Energy and information use are intimately intertwined in living systems: biological signalling pathways both control and respond to the energetic state of an organism. This review also reveals that we have much to learn about the temporal structure of the pace of life. Are its component processes highly integrated and synchronized, or are they loosely connected and often discordant? And what causes the level of coordination that we see? These questions are of great theoretical and practical importance.

Rates of aerobic metabolism vary considerably across evolutionary lineages, but little is known about the proximate and ultimate factors that generate and maintain this variability.Using data for 131 teleost fish species, we performed a large-scale phylogenetic comparative analysis of how interspecific variation in resting and maximum metabolic rates (RMR and MMR, respectively) is related to several ecological and morphological variables. Mass-and temperature-adjusted RMR and MMR are highly correlated along a continuum spanning a 30-to 40-fold range. Phylogenetic generalized least squares models suggest RMR and MMR are higher in pelagic species and that species with higher trophic levels exhibit elevated MMR. This variation is mirrored at various levels of structural organization: gill surface area, muscle protein content, and caudal fin aspect ratio (a proxy for activity) are positively related with aerobic capacity. Muscle protein content and caudal fin aspect ratio are also positively correlated with RMR. Hypoxia-tolerant lineages fall at the lower end of the metabolic continuum. Different ecological lifestyles are associated with contrasting levels of aerobic capacity, possibly reflecting the interplay between selection for increased locomotor performance on one hand and tolerance to low resource availability, particularly oxygen, on the other. These results support the aerobic capacity model of the evolution of endothermy, suggesting elevated body temperatures evolved as correlated responses to selection for high activity levels.

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 coldinduced 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.

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