The diversification of life involved enormous increases in size and complexity. The evolutionary transitions from prokaryotes to unicellular eukaryotes to metazoans were accompanied by major innovations in metabolic design. Here we show that the scalings of metabolic rate, population growth rate, and production efficiency with body size have changed across the evolutionary transitions. Metabolic rate scales with body mass superlinearly in prokaryotes, linearly in protists, and sublinearly in metazoans, so Kleiber's 3/4 power scaling law does not apply universally across organisms. The scaling of maximum population growth rate shifts from positive in prokaryotes to negative in protists and metazoans, and the efficiency of production declines across these groups. Major changes in metabolic processes during the early evolution of life overcame existing constraints, exploited new opportunities, and imposed new constraints.energetic constraints | production efficiency | r max | endosymbiosis | multicellularity T he 3.5 billion year history of life on earth was characterized by dramatic increases in the size, complexity, and diversity of living things. The first organisms were microbes with relatively simple body plans and metabolic networks. A few major transitions in form and function occurred during the subsequent evolution of life (1). The resulting diversity of contemporary organisms ranges from minute, relatively simple unicellular prokaryotes to giant, complex animals and plants containing multiple differentiated organelles, cells, tissues, and organs.Two of the largest transitions were from simple prokaryotic to complex eukaryotic cells, and from unicellular to multicellular eukaryotes. Each transition required the integration of multiple individual organisms into a new higher-level unit of organization and selection (1, 2). These transitions involved dramatic changes in structure and function, and several orders of magnitude increase in body size (3). As all organisms share a common set of molecules and biochemical reactions (4, 5), the increases in size and organizational complexity were accomplished by assembling these universal components in new ways (6). Major changes in genetic systems made these transitions possible (1, 2), and complementary changes in metabolic systems supplied the energy and materials to grow larger and support more complex morphologies and physiologies (7,8).Scaling relations offer powerful insights into the fundamental processes that constrain and regulate biological structure and function. Nearly all characteristics of organisms, from use of energy to the population growth it fuels, vary with body size. Most of the variation can be described by allometric equations or power functions of the following form:where Y is the trait of interest, Y 0 is a normalization constant, M is body mass, and α is the scaling exponent. There is a large and longstanding literature on these biological scaling relations in plants and animals but that are fewer focused on unicellular prokaryotes and prot...

It has been known for decades that the metabolic rate of animals scales with body mass with an exponent that is almost always <1, >2/3, and often very close to 3/4. The 3/4 exponent emerges naturally from two models of resource distribution networks, radial explosion and hierarchically branched, which incorporate a minimum of specific details. Both models show that the exponent is 2/3 if velocity of flow remains constant, but can attain a maximum value of 3/4 if velocity scales with its maximum exponent, 1/12. Quarterpower scaling can arise even when there is no underlying fractality. The canonical "fourth dimension" in biological scaling relations can result from matching the velocity of flow through the network to the linear dimension of the terminal "service volume" where resources are consumed. These models have broad applicability for the optimal design of biological and engineered systems where energy, materials, or information are distributed from a single source.A llometric scaling laws reflect changes in biological structure and function as animals diversified to span >12 orders of magnitude in body size. Since the seminal work of Kleiber in 1932, it has been known that the metabolic rate, B, or rate of energy use in most animals and plants scales as approximately the 3/4 power of body mass, M (1-8), and this B ∼ M 3/4 scaling has come to be known as Kleiber's rule. Most other biological rates and times, such as heart rates, reproductive rates, blood circulation times, and life times, scale with characteristic quarter powers, as M −1/4 and M 1/4 , respectively (4-9). This unusual fourth dimension came as a surprise to biologists, who expected that heat dissipation would cause metabolic rate to scale the same as body surface area and hence geometrically as the 2/3 power of volume or mass. Quarter-power scaling lacked a unified theoretical explanation until 1997, when West et al. (WBE) (10) produced a model based on optimizing resource supply and minimizing hydrodynamic resistance in the supply network.The WBE model stimulated a resurgence of interest in allometric scaling in biology. It initiated a lively debate about the empirical generality of 3/4-power metabolic scaling and its theoretical explanation (11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26). A recent study revived the case for geometric scaling by showing that simple models of distribution networks generate metabolic scaling exponents of 2/3 (25). Nevertheless, the increasing number of empirical studies repeatedly finds exponents >2/3, <1, and often very close to 3/4 (14, 24, 26, 28-30). Here we show that an exponent of 3/4 emerges naturally as an upper bound for the scaling of metabolic rate in two simple models of vascular networks. Furthermore, quarter power scaling is shown to hold even when there is no underlying fractal network. A unique prediction of our models is that blood velocity scales as the 1/12 power of animal mass. These models have broad application to biological and human-engineered systems where resources ar...

Energy Uptake and Allocation During Ontogeny www.sciencemag.org (this information is current as of January 22, 2009 ):The following resources related to this article are available online at http All organisms face the problem of how to fuel ontogenetic growth. We present a model, empirically grounded in data from birds and mammals, that correctly predicts how growing animals allocate food energy between synthesis of new biomass and maintenance of existing biomass. Previous energy budget models have typically had their bases in rates of either food consumption or metabolic energy expenditure. Our model provides a framework that reconciles these two approaches and highlights the fundamental principles that determine rates of food assimilation and rates of energy allocation to maintenance, biosynthesis, activity, and storage. The model predicts that growth and assimilation rates for all animals should cluster closely around two universal curves. Data for mammals and birds of diverse body sizes and taxa support these predictions.

The temperature size rule (TSR) is the tendency for ectotherms to develop faster but mature at smaller body sizes at higher temperatures. It can be explained by a simple model in which the rate of growth or biomass accumulation and the rate of development have different temperature dependence. The model accounts for both TSR and the less frequently observed reverse-TSR, predicts the fraction of energy allocated to maintenance and synthesis over the course of development, and also predicts that less total energy is expended when developing at warmer temperatures for TSR and vice versa for reverse-TSR. It has important implications for effects of climate change on ectothermic animals.Keywords: development rate; ectotherm development; energy budget; growth rate; temperature size rule The rates of ontogenetic growth and development are not exceptions. Ectothermic animals develop faster at warmer temperatures [1], and they usually mature at smaller body sizes-as much as 20 per cent smaller for a 108C temperature increase. This phenomenon has been called the 'temperature size rule' (TSR) [2]. Like most biological 'rules', however, there are exceptions, including welldocumented cases of the reverse-TSR, where the mature body sizes are larger at higher temperatures. Different compilations give about 15 per cent (13-17%) of reverse-TSR cases [2,3].Here, we develop a simple model for the effects of temperature on ontogenetic development of ectothermic animals. The model extends an earlier model for allocation of energy and biomass to growth on endotherms [4] by explicitly incorporating the temperature dependence of the rate of development and the rate of somatic growth. Any imbalance in these two rates results in either the TSR or reverse-TSR, depending on which process is more sensitive to temperature. The model predicts the fractions of energy allocated to maintenance and biomass synthesis at a given developmental stage, including the total quantity of energy expended during

Just as the cardiovascular network distributes energy and materials to cells in an organism, urban road networks distribute energy, materials and people to locations in cities. Understanding the topology of urban networks that connect people and places leads to insights into how cities are organized. is paper proposes a statistical approach to determine features of urban road networks that affect accessibility. Statistics of road networks and traffic patterns across 425 U.S. cities show that urban road networks are much less centralized than biological vascular networks. As a result, per capita road capacity is independent of the spatial extent of cities. In contrast, driving distances depend on city area, although not as much as is predicted by a completely centralized model. is intermediate pattern between centralized and decentralized extremes may reflect a mixture of different travel behaviors. e approach presented here offers a novel macroscopic perspective on the differences between small and large cities and on how road infrastructure and traffic might change as cities grow.

The ontogenetic growth model (OGM) of West et al. provides a general description of how metabolic energy is allocated between production of new biomass and maintenance of existing biomass during ontogeny. Here, we reexamine the OGM, make some minor modifications and corrections, and further evaluate its ability to account for empirical variation on rates of metabolism and biomass in vertebrates both during ontogeny and across species of varying adult body size. We show that the updated version of the model is internally consistent and is consistent with other predictions of metabolic scaling theory and empirical data. The OGM predicts not only the near universal sigmoidal form of growth curves but also the M(1/4) scaling of the characteristic times of ontogenetic stages in addition to the curvilinear decline in growth efficiency described by Brody. Additionally, the OGM relates the M(3/4) scaling across adults of different species to the scaling of metabolic rate across ontogeny within species. In providing a simple, quantitative description of how energy is allocated to growth, the OGM calls attention to unexplained variation, unanswered questions, and opportunities for future research.

In a 1966 American Naturalist article, G. C. Williams initiated the study of reproductive effort (RE) with the prediction that longer-lived organisms ought to expend less in reproduction per unit of time. We can multiply RE, often measured in fractions of adult body mass committed to reproduction per unit time, by the average adult life span to get lifetime reproductive effort (LRE). Williams's hypothesis (across species, RE decreases as life span increases) can then be refined to read "LRE will be approximately constant for similar organisms." Here we show that LRE is a key component of fitness in nongrowing populations, and thus its value is central to understanding life-history evolution. We then develop metabolic life-history theory to predict that LRE ought to be approximately 1.4 across organisms despite extreme differences in production and growth rates. We estimate LRE for mammals and lizards that differ in growth and production by five- to tenfold. The distributions are approximately normal with means of 1.43 and 1.41 for lizards and mammals, respectively (95% confidence intervals: 1.3-1.5 and 1.2-1.6). Ultimately, therefore, a female can only produce a mass of offspring approximately equal to 1.4 times her own body mass during the course of her life.

Effective search strategies have evolved in many biological systems, including the immune system. T cells are key effectors of the immune response, required for clearance of pathogenic infection. T cell activation requires that T cells encounter antigen-bearing dendritic cells within lymph nodes, thus, T cell search patterns within lymph nodes may be a crucial determinant of how quickly a T cell immune response can be initiated. Previous work suggests that T cell motion in the lymph node is similar to a Brownian random walk, however, no detailed analysis has definitively shown whether T cell movement is consistent with Brownian motion. Here, we provide a precise description of T cell motility in lymph nodes and a computational model that demonstrates how motility impacts T cell search efficiency. We find that both Brownian and Lévy walks fail to capture the complexity of T cell motion. Instead, T cell movement is better described as a correlated random walk with a heavy-tailed distribution of step lengths. Using computer simulations, we identify three distinct factors that contribute to increasing T cell search efficiency: 1) a lognormal distribution of step lengths, 2) motion that is directionally persistent over short time scales, and 3) heterogeneity in movement patterns. Furthermore, we show that T cells move differently in specific frequently visited locations that we call “hotspots” within lymph nodes, suggesting that T cells change their movement in response to the lymph node environment. Our results show that like foraging animals, T cells adapt to environmental cues, suggesting that adaption is a fundamental feature of biological search.