West, Brown and Enquist's model of allometric scaling again: the same questions remain

Thermal Impact and the Relevance of Body Size and Activity on the Oxygen Consumption of a Terrestrial Snail, Theba pisana (Helicidae) at High Ambient Temperatures

Metabolism, mainly driven by oxygen consumption, plays a key role in life, as it is one of the main ways to respond to extreme temperatures through internal processes. Theba pisana, a widespread Mediterranean land snail, is exposed to a wide range of ambient temperature. In this species the oxygen consumption was tested as a response variable by multiple regression modelling on the "explanatory" variables shell-free mass, temperature, and relative humidity. Our results show that the oxygen consumption of T. pisana can be well described (73.1%) by these three parameters. In the temperature range from 23 °C to 35 °C the oxygen consumption decreased with increasing temperature. Relative humidity, in the range of 67% to 100%, had the opposite effect: if it increases, oxygen consumption will increase as well. Metabolism is proportional to an individual's mass to the power of the allometric scaling exponent α, which is between 0.62 and 0.77 in the mentioned temperature range. CT scans of shells and gravimetry revealed the shell-free mass to be calculated by multiplying the shell diameter to the third power by 0.2105. Data were compared to metabolic scaling exponents for other snails reported in the literature.

What is complex allometry?

Complex allometry describes a smooth, curvilinear relationship between logarithmic transformations of a biological variable and a corresponding measure for body size when the observations are displayed on a bivariate graph with linear scaling. The curvature in such a display is commonly captured by fitting a quadratic equation to the distribution; and the quadratic term is typically interpreted, in turn, to mean that the mathematically equivalent equation for describing the arithmetic distribution is a two-parameter power equation with an exponent that changes with body size. A power equation with an exponent that is itself a function of body size is virtually uninterpretable, yet numerous attempts have been made in recent years to incorporate such an exponent into theoretical models for the evolution of form and function in both plants and animals. However, the curvature that is described by a quadratic equation fitted to logarithms usually means that an explicit, non-zero intercept is required in the power equation describing the untransformed distribution - not that the exponent in the power equation varies with body size. Misperceptions that commonly accompany reports of complex allometry can be avoided by using nonlinear regression to examine untransformed data.

How and Why Does Metabolism Scale with Body Mass?

Most explanations for the relationship between body size and metabolism invoke physical constraints; such explanations are evolutionarily inert, limiting their predictive capacity. Contemporary approaches to metabolic rate and life history lack the pluralism of foundational work. Here, we call for reforging of the lost links between optimization approaches and physiology.

The Relevance of Time in Biological Scaling

Various phenotypic traits relate to the size of a living system in regular but often disproportionate (allometric) ways. These "biological scaling" relationships have been studied by biologists for over a century, but their causes remain hotly debated. Here, I focus on the patterns and possible causes of the body-mass scaling of the rates/durations of various biological processes and life-history events, i.e., the "pace of life". Many biologists have regarded the rate of metabolism or energy use as the master driver of the "pace of life" and its scaling with body size. Although this "energy perspective" has provided valuable insight, here I argue that a "time perspective" may be equally or even more important. I evaluate various major ways that time may be relevant in biological scaling, including as (1) an independent "fourth dimension" in biological dimensional analyses, (2) a universal "biological clock" that synchronizes various biological rates/durations, (3) a scaling method that uses various biological time periods (allochrony) as scaling metrics, rather than various measures of physical size (allometry), as traditionally performed, (4) an ultimate body-size-related constraint on the rates/timing of biological processes/events that is set by the inevitability of death, and (5) a geological "deep time" approach for viewing the evolution of biological scaling patterns. Although previously proposed universal four-dimensional space-time and "biological clock" views of biological scaling are problematic, novel approaches using allochronic analyses and time perspectives based on size-related rates of individual mortality and species origination/extinction may provide new valuable insights.

Evolutionary scaling of maximum growth rate with organism size

Data from nearly 1000 species reveal the upper bound to rates of biomass production achievable by natural selection across the Tree of Life. For heterotrophs, maximum growth rates scale positively with organism size in bacteria but negatively in eukaryotes, whereas for phototrophs, the scaling is negligible for cyanobacteria and weakly negative for eukaryotes. These results have significant implications for understanding the bioenergetic consequences of the transition from prokaryotes to eukaryotes, and of the expansion of some groups of the latter into multicellularity. The magnitudes of the scaling coefficients for eukaryotes are significantly lower than expected under any proposed physical-constraint model. Supported by genomic, bioenergetic, and population-genetic data and theory, an alternative hypothesis for the observed negative scaling in eukaryotes postulates that growth-diminishing mutations with small effects passively accumulate with increasing organism size as a consequence of associated increases in the power of random genetic drift. In contrast, conditional on the structural and functional features of ribosomes, natural selection has been able to promote bacteria with the fastest possible growth rates, implying minimal conflicts with both bioenergetic constraints and random genetic drift. If this extension of the drift-barrier hypothesis is correct, the interpretations of comparative studies of biological traits that have traditionally ignored differences in population-genetic environments will require revisiting.

Variable metabolic scaling breaks the law: from 'Newtonian' to 'Darwinian' approaches

Life's size and tempo are intimately linked. The rate of metabolism varies with body mass in remarkably regular ways that can often be described by a simple power function, where the scaling exponent (b, slope in a log-linear plot) is typically less than 1. Traditional theory based on physical constraints has assumed that b is 2/3 or 3/4, following natural law, but hundreds of studies have documented extensive, systematic variation in b. This overwhelming, law-breaking, empirical evidence is causing a paradigm shift in metabolic scaling theory and methodology from ‘Newtonian’ to ‘Darwinian’ approaches. A new wave of studies focuses on the adaptable regulation and evolution of metabolic scaling, as influenced by diverse intrinsic and extrinsic factors, according to multiple context-dependent mechanisms, and within boundary limits set by physical constraints.

Metabolic Scaling in Birds and Mammals: How Taxon Divergence Time, Phylogeny, and Metabolic Rate Affect the Relationship between Scaling Exponents and Intercepts

Simple Summary

This study is based on a large dataset and re-evaluates data on the metabolic rate, providing new insights into the similarities and differences across different groups of birds and mammals. We compared six taxonomic groups of mammals and birds according to their energetic characteristics and the geological time of evolutionary origin. The overall metabolic rate of a taxonomic group increases with the geological time of evolutionary origin. The terrestrial mammals and flightless birds have almost equal metabolic levels. The higher the metabolic rate in a group, the less it increases within increasing body size in this group.

Abstract

Analysis of metabolic scaling in currently living endothermic animal species allowed us to show how the relationship between body mass and the basal metabolic rate (BMR) has evolved in the history of endothermic vertebrates. We compared six taxonomic groups according to their energetic characteristics and the time of evolutionary divergence. We transformed the slope of the regression lines to the common value and analyzed three criteria for comparing BMR of different taxa regardless of body size. Correlation between average field metabolic rate (FMR) of the group and its average BMR was shown. We evaluated the efficiency of self-maintenance in ordinary life (defined BMR/FMR) in six main groups of endotherms. Our study has shown that metabolic scaling in the main groups of endothermic animals correlates with their evolutionary age: the younger the group, the higher the metabolic rate, but the rate increases more slowly with increasing body weight. We found negative linear relationship for scaling exponents and the allometric coefficient in five groups of endotherms: in units of mL O₂/h per g, in relative units of allometric coefficients, and also in level or scaling elevation. Mammals that diverged from the main vertebrate stem earlier have a higher “b” exponent than later divergent birds. A new approach using three criteria for comparing BMR of different taxa regardless of body mass will be useful for many biological size-scaling relationships that follow the power function.

Anatomical features of inferior mesenteric and left colic arteries and surgery in colorectal cancer patients with persistent descending mesocolon

BACKGROUND

Persistent descending mesocolon (PDM) is a fetal abnormality in which the left-sided colon is not fused to the retroperitoneum, and it is often accompanied by the adhesion between the mesocolon and small bowel mesentery. Due to its rarity, whether PDM exhibits anatomical characteristics of the inferior mesenteric artery (IMA) and left colic artery (LCA), and how the anomaly affects laparoscopic surgery are largely unknown. We investigated the branches of these arteries and outcomes of patients who underwent laparoscopic surgery.

METHODS

Based on computed tomography (CT) and three-dimensional CT angiography, branching patterns of the IMA, LCA and branches originating from the LCA were analysed in 954 patients with left-sided colon or rectal cancer. PDM was diagnosed by preoperative CT colonography, and confirmed at time of surgery. The anatomical features of the vessels and short-term outcomes of laparoscopic surgery were compared between patient groups stratified by PDM.

RESULTS

Twelve patients (1.3%) were diagnosed with PDM. No branching pattern of the IMA specific to PDM was noted. On the other hand, patients with PDM had fewer branches (mean: 1.0) from the LCA than those without PDM (mean: 1.8, p = 0.009). In patients undergoing laparoscopic surgery, outcomes such as operative time, intraoperative blood loss, and number of harvested nodes were comparable between the two patient groups.

CONCLUSION

Few branches of the LCA characterize PDM. PDM does not complicate laparoscopic surgery of the left-sided colon and rectum. However, the above anatomical feature increases the risk of poor colonic perfusion when dividing the LCA.

Complications with body-size correction in comparative biology: possible solutions and an appeal for new approaches

The magnitude of many kinds of biological traits relates strongly to body size. Therefore, a first step in comparative studies frequently involves correcting for effects of body size on the variation of a phenotypic trait, so that the effects of other biological and ecological factors can be clearly distinguished. However, commonly used traditional methods for making these body-size adjustments ignore or do not completely separate the causal interactive effects of body size and other factors on trait variation. Various intrinsic and extrinsic factors may affect not only the variation of a trait, but also its covariation with body size, thus making it difficult to remove completely the effect of body size in comparative studies. These complications are illustrated by several examples of how body size interacts with diverse developmental, physiological, behavioral and ecological factors to affect variation in metabolic rate both within and across species. Such causal interactions are revealed by significant effects of these factors on the body-mass scaling slope of metabolic rate. I discuss five possible major kinds of methods for removing body-size effects that attempt to overcome these complications, at least in part, but I hope that my Review will encourage the development of other, hopefully better methods for doing so.

Allometric Scaling in Pharmacokinetic Studies in Anesthesiology

A clinical review is presented of basic allometric scaling theory and its application to pharmacokinetic models in anesthesia and other fields in the biologic sciences.

Recent advances in blood rheology: a review

Due to the potential impact on the diagnosis and treatment of various cardiovascular diseases, work on the rheology of blood has significantly expanded in the last decade, both experimentally and theoretically. Experimentally, blood has been confirmed to demonstrate a variety of non-Newtonian rheological characteristics, including pseudoplasticity, viscoelasticity, and thixotropy. New rheological experiments and the development of more controlled experimental protocols on more extensive, broadly physiologically characterized, human blood samples demonstrate the sensitivity of aspects of hemorheology to several physiological factors. For example, at high shear rates the red blood cells elastically deform, imparting viscoelasticity, while at low shear rates, they form "rouleaux" structures that impart additional, thixotropic behavior. In addition to the advances in experimental methods and validated data sets, significant advances have also been made in both microscopic simulations and macroscopic, continuum, modeling, as well as novel, multiscale approaches. We outline and evaluate the most promising of these recent developments. Although we primarily focus on human blood rheology, we also discuss recent observations on variations observed across some animal species that provide some indication on evolutionary effects.

Coevolution of body size and metabolic rate in vertebrates: a life-history perspective

Despite many decades of research, the allometric scaling of metabolic rates (MRs) remains poorly understood. Here, we argue that scaling exponents of these allometries do not themselves mirror one universal law of nature but instead statistically approximate the non-linearity of the relationship between MR and body mass. This 'statistical' view must be replaced with the life-history perspective that 'allows' organisms to evolve myriad different life strategies with distinct physiological features. We posit that the hypoallometric allometry of MRs (mass scaling with an exponent smaller than 1) is an indirect outcome of the selective pressure of ecological mortality on allocation 'decisions' that divide resources among growth, reproduction, and the basic metabolic costs of repair and maintenance reflected in the standard or basal metabolic rate (SMR or BMR), which are customarily subjected to allometric analyses. Those 'decisions' form a wealth of life-history variation that can be defined based on the axis dictated by ecological mortality and the axis governed by the efficiency of energy use. We link this variation as well as hypoallometric scaling to the mechanistic determinants of MR, such as metabolically inert component proportions, internal organ relative size and activity, cell size and cell membrane composition, and muscle contributions to dramatic metabolic shifts between the resting and active states. The multitude of mechanisms determining MR leads us to conclude that the quest for a single-cause explanation of the mass scaling of MRs is futile. We argue that an explanation based on the theory of life-history evolution is the best way forward.

An non-loglinear enzyme-driven law of photosynthetic scaling in two representative crop seedlings under different water conditions

The loglinear pattern of respiratory scaling has been studied for over a century, while an increasing number of non-loglinear patterns have been found in the plant kingdom. Several previous studies had attempted to reconcile conflicting patterns from the aspects of statistical approaches and developmental stages of the organisms. However, the underlying enzymatic mechanism was largely ignored. Here, we propose an enzyme-driven law of photosynthetic scaling and test it in typical crop seedlings under different water conditions. The results showed that the key enzyme activity, the relative photosynthetic assimilation and the relative growth rate were all constrained by the available water, and the relationship between these biological traits and the available water supported our predictions. The enzyme-driven law appears to be more suitable to explain the curvature of photosynthetic scaling than the well-established power law, since it provides insight into the biochemical origin of photosynthetic assimilation.

Plant respiration: Controlled by photosynthesis or biomass?

Two simplifying hypotheses have been proposed for whole-plant respiration. One links respiration to photosynthesis; the other to biomass. Using a first-principles carbon balance model with a prescribed live woody biomass turnover, applied at a forest research site where multidecadal measurements are available for comparison, we show that if turnover is fast the accumulation of respiring biomass is low and respiration depends primarily on photosynthesis; while if turnover is slow the accumulation of respiring biomass is high and respiration depends primarily on biomass. But the first scenario is inconsistent with evidence for substantial carry-over of fixed carbon between years, while the second implies far too great an increase in respiration during stand development-leading to depleted carbohydrate reserves and an unrealistically high mortality risk. These two mutually incompatible hypotheses are thus both incorrect. Respiration is not linearly related either to photosynthesis or to biomass, but it is more strongly controlled by recent photosynthates (and reserve availability) than by total biomass.

From Dendrochronology to Allometry

The contribution of tree-ring analysis to other fields of scientific inquiry with overlapping interests, such as forestry and plant population biology, is often hampered by the different parameters and methods that are used for measuring growth. Here I present relatively simple graphical, numerical, and mathematical considerations aimed at bridging these fields, highlighting the value of crossdating. Lack of temporal control prevents accurate identification of factors that drive wood formation, thus crossdating becomes crucial for any type of tree growth study at inter-annual and longer time scales. In particular, exactly dated tree rings, and their measurements, are crucial contributors to the testing and betterment of allometric relationships.

Axial anatomy of the leaf midrib provides new insights into the hydraulic architecture and cavitation patterns of Acer pseudoplatanus leaves

The structure of leaf veins is typically described by a hierarchical scheme (e.g. midrib, 1st order, 2nd order), which is used to predict variation in conduit diameter from one order to another whilst overlooking possible variation within the same order. We examined whether xylem conduit diameter changes within the same vein order, with resulting consequences for resistance to embolism. We measured the hydraulic diameter (Dh), and number of vessels (VN) along the midrib and petioles of leaves of Acer pseudoplatanus, and estimated the leaf area supplied (Aleaf-sup) at different points of the midrib and how variation in anatomical traits affected embolism resistance. We found that Dh scales with distance from the midrib tip (path length, L) with a power of 0.42, and that VN scales with Aleaf-sup with a power of 0.66. Total conductive area scales isometrically with Aleaf-sup. Embolism events along the midrib occurred first in the basipetal part and then at the leaf tip where vessels are narrower. The distance from the midrib tip is a good predictor of the variation in vessel diameter along the 1st order veins in A. pseudoplatanus leaves and this anatomical pattern seems to have an effect on hydraulic integrity since wider vessels at the leaf base embolize first.

Inferring vascular architecture of the wheat spikelet based on resource allocation in the branched headt (bht-A1) near isogenic lines

Substantial genetic and physiological efforts were made to understand the causal factors of floral abortion and grain filling problem in wheat. However, the vascular architecture during wheat spikelet development is surprisingly under-researched. We used the branched headt near-isogenic lines, FL-bht-A1-NILs, to visualise the dynamics of spikelet fertility and dry matter accumulation in spikelets sharing the same rachis node (henceforth Primary Spikelet, PSt, and Secondary Spikelet, SSt). The experiment was conducted after grouping FL-bht-A1-NILs into two groups, where tillers were consistently removed from one group. Our results show differential spikelet fertility and dry matter accumulation between the PSt and SSt, but also showed a concomitant improvement after de-tillering. This suggests a tight regulation of assimilate supply and dry matter accumulation in wheat spikelets. Since PSt and SSt share the same rachis node, the main vascular bundle in the rachis/rachilla is expected to bifurcate to connect each spikelet/floret to the vascular system. We postulate that the vascular structure in the wheat spikelet might even follow Murray's law, where the wide conduits assigned at the base of the spikelet feed the narrower conduits of the distal florets. We discuss our results based on the two modalities of the vascular network systems in plants.

Misconceptions and issues regarding allometric scaling during the drug development process

INTRODUCTION

Allometry is the study of size and its consequences. The simple hypothesis of allometric scaling is that all physiological parameters are proportional to body size or body mass. This review examines the development of theory-based allometry or fixed exponents (0.75 and 1.0 for basal metabolic rate and volume, respectively) and the evidence for or against the theory. The main focus of this report is to show the readers that there is enough evidence from experimental data that negate the concept of theory-based allometry in biology, physiology, and pharmacokinetics. Areas covered: In this review, the history of the development of theoretical allometry and the strong evidence against theory-based allometry demonstrated by experimental data is provided. During drug development, allometry is applied to both inter-species (from animals to humans) and intra-species (adults to children) scaling. These two forms of allometric scaling in the context of theory-based allometry are discussed and provide insight on scientific progress that refute theory-based allometry. Expert opinion: Theory-based allometry is a mere theory and experimental data and real-life observations strongly negate the existence of such a theory. Pharmacostatistical and physiological models based on theory-based allometry can be misleading and incorrect because the theory-based allometric exponent 0.75 is not universal. The exponents of allometry are data dependent and are not fixed in the universe.

Prediction of Clearance, Volume of distribution, and Half-life of Drugs in Extremely Low to Low Birth Weight Neonates: An Allometric Approach

BACKGROUND AND OBJECTIVES

More than 20 million infants worldwide (15.5 % of all births) are born with low birth weight. Low birth weight is associated with poor growth in childhood and a higher incidence of adult diseases, such as type 2 diabetes, hypertension and cardiovascular disease. The objective of this study was to evaluate the predictive performance of allometric models to predict clearance, volume of distribution, and half-life in extremely low to low birth weight neonates (<1 to 2.5 kg body weight).

METHODS

Several allometric models were used to predict clearance (4 models), volume of distribution (2 models), and half-life (2 models) in extremely low to low birth weight neonates. From the literature, clearance, volume of distribution, and half-life values for 16 drugs for these neonates were obtained. The predictive performance of these allometric models was evaluated by comparing the predicted values of the aforementioned pharmacokinetic parameters with the observed pharmacokinetic parameters in an individual neonate. For the evaluation of the predictive performance of these allometric models, there were 16 drugs with 36 (n = 279), 34 (n = 261), and 31 (n = 197) weight groups for clearance, volume of distribution, and half-life, respectively.

RESULTS

The prediction error of ≤50 % for mean clearance, volume of distribution, and half-life values were 69, 79, and 58 %, respectively, by proposed allometric models. The prediction error of ≤50 % for mean clearance, volume of distribution, and half-life values by theoretical allometric exponents were 0 % (exponent = 0.75), 71 % (exponent = 1.0), and 0 % (exponent = 0.25), respectively. In this analysis, out of 16 drugs, there were three drugs (ibuprofen, zidovudine, and buprenorphine) which are metabolized by glucuronidation and one drug (furosemide) is renally secreted. The predicted clearances of these four drugs were substantially higher by the proposed allometric methods. It seems that drugs of these physiological characteristics may require different method(s) to improve the prediction of clearance in the neonates.

CONCLUSIONS

Overall, the proposed allometric methods can predict mean pharmacokinetic parameters of drugs in extremely low to low birth weight neonates with reasonable accuracy and are of practical value during neonatal drug development.

On the thermodynamic origin of metabolic scaling

The origin and shape of metabolic scaling has been controversial since Kleiber found that basal metabolic rate of animals seemed to vary as a power law of their body mass with exponent 3/4, instead of 2/3, as a surface-to-volume argument predicts. The universality of exponent 3/4 -claimed in terms of the fractal properties of the nutrient network- has recently been challenged according to empirical evidence that observed a wealth of robust exponents deviating from 3/4. Here we present a conceptually simple thermodynamic framework, where the dependence of metabolic rate with body mass emerges from a trade-off between the energy dissipated as heat and the energy efficiently used by the organism to maintain its metabolism. This balance tunes the shape of an additive model from which different effective scalings can be recovered as particular cases, thereby reconciling previously inconsistent empirical evidence in mammals, birds, insects and even plants under a unified framework. This model is biologically motivated, fits remarkably well the data, and also explains additional features such as the relation between energy lost as heat and mass, the role and influence of different climatic environments or the difference found between endotherms and ectotherms.

The Evolution of Energetic Scaling across the Vertebrate Tree of Life

Metabolism is the link between ecology and physiology-it dictates the flow of energy through individuals and across trophic levels. Much of the predictive power of metabolic theories of ecology derives from the scaling relationship between organismal size and metabolic rate. There is growing evidence that this scaling relationship is not universal, but we have little knowledge of how it has evolved over macroevolutionary time. Here we develop a novel phylogenetic comparative method to investigate how often and in which clades the macroevolutionary dynamics of the metabolic scaling have changed. We find strong evidence that the metabolic scaling relationship has shifted multiple times across the vertebrate phylogeny. However, shifts are rare and otherwise strongly constrained. Importantly, both the estimated slope and intercept values vary widely across regimes, with slopes that spanned across theoretically predicted values such as 2/3 or 3/4. We further tested whether traits such as ecto-/endothermy, genome size, and quadratic curvature with body mass (i.e., energetic constraints at extreme body sizes) could explain the observed pattern of shifts. Though these factors help explain some of the variation in scaling parameters, much of the remaining variation remains elusive. Our results lay the groundwork for further exploration of the evolutionary and ecological drivers of major transitions in metabolic strategy and for harnessing this information to improve macroecological predictions.

Energy Homeostasis in Monotremes

In 1803, the French anatomist Étienne Geoffroy Saint-Hilaire decided that the newly described echidna and platypus should be placed in a separate order, the monotremes, intermediate between reptiles and mammals. The first physiological observations showed monotremes had low body temperatures and metabolic rates, and the consensus was that they were at a stage of physiological development intermediate between "higher mammals" and "lower vertebrates." Subsequent studies demonstrated that platypuses and echidnas are capable of close thermoregulation in the cold although less so under hot conditions. Because the short-beaked echidna Tachyglossus aculeatus, may show very large daily variations in body temperature, as well as seasonal hibernation, it has been suggested that it may provide a useful model of protoendotherm physiology. Such analysis is complicated by the very significant differences in thermal relations between echidnas from different climates. In all areas female echidnas regulate Tb within 1°C during egg incubation. The lactation period is considered to be the most energetically expensive time for most female mammals but lactating echidnas showed no measurable difference in field metabolic rate from non-lactating females, while the lactation period is more than 200 days for Kangaroo Island echidnas but only 150 days in Tasmania. In areas with mild winters echidnas show reduced activity and shallow torpor in autumn and early winter, but in areas with cold winters echidnas enter true hibernation with Tb falling as low as 4.5°C. Monotremes do not possess brown adipose tissue and maximum rates of rewarming from hibernation in echidnas were only half those of marmots of the same mass. Although echidnas show very large seasonal variations in fat stores associated with hibernation there is no relationship between plasma leptin and adiposity. Leptin levels are lowest during post-reproductive fattening, supporting suggestions that in evolutionary terms the anorectic effects of leptin preceded the adiposity signal. BMR of platypuses is twice that of echidnas although maximum metabolism is similar. High levels of thyroid hormones in platypuses may be driving metabolism limited by low body temperature. Monotremes show a mosaic of plesiomorphic and derived features but can still inform our understanding of the evolution of endothermy.

Mass scaling of metabolic rates in carabid beetles (Carabidae) – the importance of phylogeny, regression models and gas exchange patterns

The origin of the allometric relationship between standard metabolic rate (MR) and body mass (M), often described as MR=aMb, remains puzzling and interpretation of the mass-scaling exponent, b may depend on the methodological approach, shapes of residuals, coefficient of determination (r2) and sample size. We investigated the mass scaling of MRs within and between species of Carabidae beetles. We used ordinary least squares (OLS) regression, phylogenetically generalized least squares (PGLS) regression and standardized major axis (SMA) regression to explore the effects of different model-fitting methods and data clustering caused by phylogenetic clades (grade shift) and gas exchange patterns (discontinuous, cyclic and continuous). At the interspecific level, the relationship between MR and M was either negatively allometric (b&lt;1) or isometric (b=1), depending on the fitting method. At the intraspecific level, the relationship either did not exist or was isometric or positively allometric (b&gt;1), and the fit was significantly improved after the analysed dataset was split according to gas exchange patterns. The studied species originated from two distinct phylogenetic clades that had different intercepts but a common scaling exponent (OLS, 0.61) that was much shallower than the scaling exponent for the combined dataset for all species (OLS, 0.71). The best scaling exponent estimates were obtained by applying OLS while accounting for grade shifts or by applying PGLS. Overall, we show that allometry of MR in insects can depend heavily on the model fitting method, the structure of phylogenetic non-independence and ecological factors that elicit different modes of gas exchange.

A comparative perspective on longevity: the effect of body size dominates over ecology in moths

Both physiologically and ecologically based explanations have been proposed to account for among-species differences in lifespan, but they remain poorly tested. Phylogenetically explicit comparative analyses are still scarce and those that exist are biased towards homoeothermic vertebrates. Insect studies can significantly contribute as lifespan can feasibly be measured in a high number of species, and the selective forces that have shaped it may differ largely between species and from those acting on larger animals. We recorded adult lifespan in 98 species of geometrid moths. Phylogenetic comparative analyses were applied to study variation in species-specific values of lifespan and to reveal its ecological and life-history correlates. Among-species and between-gender differences in lifespan were found to be notably limited; there was also no evidence of phylogenetic signal in this trait. Larger moth species were found to live longer, with this result supporting a physiological rather than ecological explanation of this relationship. Species-specific lifespan values could not be explained by traits such as reproductive season and larval diet breadth, strengthening the evidence for the dominance of physiological determinants of longevity over ecological ones.

Kleiber's Law: How the Fire of Life ignited debate, fueled theory, and neglected plants as model organisms

Size is a key feature of any organism since it influences the rate at which resources are consumed and thus affects metabolic rates. In the 1930s, size-dependent relationships were codified as "allometry" and it was shown that most of these could be quantified using the slopes of log-log plots of any 2 variables of interest. During the decades that followed, physiologists explored how animal respiration rates varied as a function of body size across taxa. The expectation was that rates would scale as the 2/3 power of body size as a reflection of the Euclidean relationship between surface area and volume. However, the work of Max Kleiber (1893-1976) and others revealed that animal respiration rates apparently scale more closely as the 3/4 power of body size. This phenomenology, which is called "Kleiber's Law," has been described for a broad range of organisms, including some algae and plants. It has also been severely criticized on theoretical and empirical grounds. Here, we review the history of the analysis of metabolism, which originated with the works of Antoine L. Lavoisier (1743-1794) and Julius Sachs (1832-1897), and culminated in Kleiber's book The Fire of Life (1961; 2. ed. 1975). We then evaluate some of the criticisms that have been leveled against Kleiber's Law and some examples of the theories that have tried to explain it. We revive the speculation that intracellular exo- and endocytotic processes are resource delivery-systems, analogous to the supercellular systems in multicellular organisms. Finally, we present data that cast doubt on the existence of a single scaling relationship between growth and body size in plants.

Metabolic scaling in animals: methods, empirical results, and theoretical explanations

Life on earth spans a size range of around 21 orders of magnitude across species and can span a range of more than 6 orders of magnitude within species of animal. The effect of size on physiology is, therefore, enormous and is typically expressed by how physiological phenomena scale with mass(b). When b ≠ 1 a trait does not vary in direct proportion to mass and is said to scale allometrically. The study of allometric scaling goes back to at least the time of Galileo Galilei, and published scaling relationships are now available for hundreds of traits. Here, the methods of scaling analysis are reviewed, using examples for a range of traits with an emphasis on those related to metabolism in animals. Where necessary, new relationships have been generated from published data using modern phylogenetically informed techniques. During recent decades one of the most controversial scaling relationships has been that between metabolic rate and body mass and a number of explanations have been proposed for the scaling of this trait. Examples of these mechanistic explanations for metabolic scaling are reviewed, and suggestions made for comparing between them. Finally, the conceptual links between metabolic scaling and ecological patterns are examined, emphasizing the distinction between (1) the hypothesis that size- and temperature-dependent variation among species and individuals in metabolic rate influences ecological processes at levels of organization from individuals to the biosphere and (2) mechanistic explanations for metabolic rate that may explain the size- and temperature-dependence of this trait.

Prediction of drug clearance in children: an evaluation of the predictive performance of several models

The objective of this study is to evaluate the predictive performance of several models to predict drug clearance in children ≤5 years of age. Six models (allometric model (data-dependent exponent), fixed exponent of 0.75 model, maturation model, body weight-dependent model, segmented allometric model, and age-dependent exponent model) were evaluated in this study. From the literature, the clearance values for six drugs from neonates to adults were obtained. External data were used to evaluate the predictive performance of these models in children ≤5 years of age. With the exception of a fixed exponent of 0.75, the mean predicted clearance in most of the age groups was within ≤50% prediction error. Individual clearance prediction was erratic by all models and cannot be used reliably to predict individual clearance. Maturation, body weight-dependent, and segmented allometric models to predict clearances of drugs in children ≤5 years of age are of limited practical value during drug development due to the lack of availability of data. Age-dependent exponent model can be used for the selection of first-in-children dose during drug development.

Cellular metabolic rates from primary dermal fibroblast cells isolated from birds of different body masses

The rate of metabolism is the speed at which organisms use energy, an integration of energy transformations within the body; it governs biological processes that influence rates of growth and reproduction. Progress at understanding functional linkages between whole organism metabolic rate and underlying mechanisms that influence its magnitude has been slow despite the central role this issue plays in evolutionary and physiological ecology. Previous studies that have attempted to relate how cellular processes translate into whole-organism physiology have done so over a range of body masses of subjects. However, the data still remains controversial when observing metabolic rates at the cellular level. To bridge the gap between these ideas, we examined cellular metabolic rate of primary dermal fibroblasts isolated from 49 species of birds representing a 32,000-fold range in body masses to test the hypothesis that metabolic rate of cultured cells scales with body size. We used a Seahorse XF-96 Extracellular flux analyzer to measure cellular respiration in fibroblasts. Additionally, we measured fibroblast size and mitochondrial content. We found no significant correlation between cellular metabolic rate, cell size, or mitochondrial content and body mass. Additionally, there was a significant relationship between cellular basal metabolic rate and proton leak in these cells. We conclude that metabolic rate of cells isolated in culture does not scale with body mass, but cellular metabolic rate is correlated to growth rate in birds.

Scaling relationships between leaf mass and total plant mass across Chinese forests

Biomass partitioning is important for illustrating terrestrial ecosystem carbon flux. West, Brown and Enquist (WBE) model predicts that an optimal 3/4 allometric scaling of leaf mass and total biomass of individual plants will be applied in diverse communities. However, amount of scientific evidence suggests an involvement of some biological and environmental factors in interpreting the variation of scaling exponent observed in empirical studies. In this paper, biomass information of 1175 forested communities in China was collected and categorized into groups in terms of leaf form and function, as well as their locations to test whether the allocation pattern was conserved or variable with internal and/or environmental variations. Model Type II regression protocol was adopted to perform all the regressions. The results empirically showed that the slopes varied significantly across diverse forested biomes, between conifer and broadleaved forests, and between evergreen and deciduous forests. Based on the results, leaf form and function and their relations to environments play a significant role in the modification of the WBE model to explore more accurate laws in nature.

Thermodynamics constrains allometric scaling of optimal development time in insects

Development time is a critical life-history trait that has profound effects on organism fitness and on population growth rates. For ectotherms, development time is strongly influenced by temperature and is predicted to scale with body mass to the quarter power based on 1) the ontogenetic growth model of the metabolic theory of ecology which describes a bioenergetic balance between tissue maintenance and growth given the scaling relationship between metabolism and body size, and 2) numerous studies, primarily of vertebrate endotherms, that largely support this prediction. However, few studies have investigated the allometry of development time among invertebrates, including insects. Abundant data on development of diverse insects provides an ideal opportunity to better understand the scaling of development time in this ecologically and economically important group. Insects develop more quickly at warmer temperatures until reaching a minimum development time at some optimal temperature, after which development slows. We evaluated the allometry of insect development time by compiling estimates of minimum development time and optimal developmental temperature for 361 insect species from 16 orders with body mass varying over nearly 6 orders of magnitude. Allometric scaling exponents varied with the statistical approach: standardized major axis regression supported the predicted quarter-power scaling relationship, but ordinary and phylogenetic generalized least squares did not. Regardless of the statistical approach, body size alone explained less than 28% of the variation in development time. Models that also included optimal temperature explained over 50% of the variation in development time. Warm-adapted insects developed more quickly, regardless of body size, supporting the "hotter is better" hypothesis that posits that ectotherms have a limited ability to evolutionarily compensate for the depressing effects of low temperatures on rates of biological processes. The remaining unexplained variation in development time likely reflects additional ecological and evolutionary differences among insect species.

Morphological characteristics of blood cells in monitor lizards: is erythrocyte size linked to actual body size?

Blood cell morphology and count are not uniform across species. Recently, between-species comparisons revealed that the size of red blood cells is associated with body size in some lizard taxa, and this finding was interpreted in the context of the metabolic theory. In the present study, we examined the numbers and the size of blood cells in 2 species of monitor lizards, the mangrove-dwelling monitor (Varanus indicus) and the savannah monitor (V. exanthematicus), and we compared these traits in individuals of different body size. The results revealed that during the course of ontogeny, the size of red blood cells increases with body mass. Because the mass-specific metabolic rate decreases with body size and the cell volume-to-surface ratio decreases with the cell size, changes in the erythrocyte size might be the result of oxygen transport adjustment.

Roles of nucleation, denucleation, coarsening, and aggregation kinetics in nanoparticle preparations and neurological disease

Kinetic models for nucleation, denucleation, Ostwald ripening (OR), and nanoparticle (NP) aggregation are presented and discussed from a physicochemical standpoint, in terms of their role in current NP preparations. Each of the four solid-state mechanisms discussed predict a distinct time dependence for the evolution of the mean particle radius over time. Additionally, they each predict visually different particle size distributions (PSDs) under limiting steady-state (time-independent) conditions. While nucleation and denucleation represent phase transformation mechanisms, OR and NP aggregation do not. Thus, when modeling solid-state kinetics relevant to NP processing, either the time evolution of the mean particle radius or the fractional conversion data should be fit using appropriate models (discussed herein), without confusing/combining the two classes of models. Experimental data taken from the recent literature are used to demonstrate the usefulness of the models in real-world applications. Specifically, the following examples are discussed: the preparation of bismuth NPs, the synthesis of copper indium sulfide nanocrystals, and the aggregation of neurological proteins. Because the last process is found to obey reaction-limited colloid aggregation (RLCA) kinetics, potential connections between protein aggregation rates, the onset of neurological disease, and population lifespan dynamics are suggested by drawing a parallel between RLCA kinetics and Gompertz kinetics. The physical chemistry underpinning NP aggregation is investigated, and a detailed definition of the rate constant of aggregation, k(a), is put forth that provides insight into the origin of the activation energy barrier of aggregation. For the two nanocrystal preparations investigated, the initial kinetics are found to be well-described by the author's dispersive kinetic model for nucleation-and-growth, while the late-stage NP size evolution is dominated by OR. At intermediate times, it is thought that the two mechanisms both contribute to the NP growth, resulting in PSD focusing as discussed in a previous work [Skrdla, P. J. J. Phys. Chem. C2012, 116, 214-225]. On the basis of these two mechanisms, a synthetic procedure for obtaining monodisperse NP PSDs, of small and/or systematically targeted mean sizes, is proposed.