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Body Size and Metabolism
Abstract
Benedict has shown that this law is already over ninety years old, Robiquet and Tillaye having formulated it quite clearly in 1839. The history of the surface law is given in the paper of (Harris and Benedict (1919)). We may here only briefly mention the different ways in which it has been found. The early writers derived the law from theoretical considerations on a rather small experimental basis, as did Bergmann, who in 1847 had already written a book on the subject. Respiration trials were carried out by Regnault and Reiset, and Rameaux based the surface law on measurements of the amount of air respired per minute by two thousand human beings of different sizes. (Rubner (1883)) demonstrated the law in accurate respiration trials on dogs and Richet rediscovered it empirically on rabbits. The latter writes (p. 223): “C’est aprèe coup seulement que je me suis avisé que la donnée surface était plus intéressante que la donnée poids.”
... where M is the individual fresh mass, Y is the individual respiration rate, F is an intercept and f is the scaling exponent (the slope of log-log coordinates) [1,[18][19][20][21][22]. Since Kleiber [18] empirically observed simple and robust allometry of f = 0.75, most theoretical work has focused on the value of f and has attempted to explain metabolic scaling relationships. ...
... where M is the individual fresh mass, Y is the individual respiration rate, F is an intercept and f is the scaling exponent (the slope of log-log coordinates) [1,[18][19][20][21][22]. Since Kleiber [18] empirically observed simple and robust allometry of f = 0.75, most theoretical work has focused on the value of f and has attempted to explain metabolic scaling relationships. West et al. [19] proposed a model unifying metabolic rates for plants and animals and predicted that f would converge to 0.75. ...
... In addition, herbaceous plants have higher mass-specific respiration rates than woody plants across a wide range of sizes, except for the smallest masses ( figure 3). These findings are largely consistent with previous reports that smaller organisms have higher mass-specific metabolic rates [18,56,57]. Woody plants decrease mass-specific respiration of stems and roots during ontogeny [27,28,53] because of their continuous secondary growth that accumulates metabolically inert tissues in stems and roots [26,31,[37][38][39]. ...
Woody and herbaceous plants are the main components of global terrestrial ecosystems, and their growth, adaptation and survival depend largely on the metabolism of shoots and roots. Therefore, understanding size-scaling of metabolic rates in woody and herbaceous plants, and in shoots and roots, is a fundamental issue in ecology. However, few empirical studies have examined metabolic scaling exponents across a wide range of plant sizes. Using whole-plant chamber systems, we measured respiration rates of entire root systems and shoots of 96 woody species (n = 1243) and 33 herbaceous species (n = 463) from various terrestrial biomes, with plant masses spanning nine orders of magnitude. Scaling exponents for relationships between respiration rates and fresh mass were greater in shoots than in roots, and both were greater in herbaceous plants than in woody plants. Furthermore, scaling of whole-plant respiration, including various species, converged separately for woody and herbaceous plants. These findings suggest some general physico-chemical constraints on energy use by shoots and roots of individual plants in various terrestrial biomes, including forests and grasslands. These data will advance our understanding of terrestrial ecosystem structure and function.
... An activity multiplier of 2 was used to estimate values of field metabolic rate. The scaling relationship (3.3 M 0.76 ;Fariña 2002), where M is body mass in kg, was originally derived from Kleiber (1932) and it was used to compare metabolic rates derived from a mammal of similar body size with the typical placental metabolism. (i.e., basal metabolic rate multiplied by a factor of 2 converted to kJ/hr − 1 ) by the same factor. ...
... Consistent trends of narrow thermoneutral zones resulting from sparse fur (0.07-8.5 hairs/cm 2 ) with lower critical temperature estimates higher than 10° C and upper critical temperature Fig. 4 Bar chart of estimated basal metabolic rate (BMR) and field metabolic rate (FMR) in ground sloths. Values in unit watts (W) calculated from the xenarthran metabolic scaling equation (White and Seymour 2004) are compared to those (right) based on a 'typical placental' metabolism (Kleiber 1932;Fariña 2002) was modeled to have no thermal stress with 10 mm fur during the warmest months of the year and also with 30 mm fur during the coldest months at northern and mid latitudes (Fig. 6). Both Mylodon at the southernmost extent of its range and Nothrotheriops across its entire geographic range were determined to have no heat stress with dense fur with a coat thickness of 50 mm. ...
... In addition to refined estimates of clade specific basal metabolic rates for ground sloths, numerous other environmental factors beyond ambient temperatures were input and modeled across the geographic distributions of each genus to determine more exact boundaries of thermal neutrality. The basal metabolic rate estimates derived from the xenarthran scaling equation (White and Seymour 2004) produced metabolic rates representing only 34-41% of those for mammals with typical placental metabolism as determined by the relationship of Kleiber (1932) (Fariña 2002). Substantially lower basal metabolic rates were predicted in the present study, thus producing markedly different results for thermal tolerance ranges across the various integument conditions tested compared with those already reported. ...
Remains of megatheres have been known since the 18th -century and were among the first megafaunal vertebrates to be studied. While several examples of preserved integument show a thick coverage of fur for smaller ground sloths living in cold climates such as Mylodon and Nothrotheriops, comparatively very little is known about megathere skin. Assuming a typical placental mammal metabolism, it was previously hypothesized that megatheres would have had little-to-no fur as they achieved giant body sizes. Here the “hairless model of integument” is tested using geochemical analyses to estimate body temperature to generate novel models of ground sloth metabolism, fur coverage, and paleoclimate with Niche Mapper software. The simulations assuming metabolic activity akin to those of modern xenarthrans suggest that sparse fur coverage would have resulted in cold stress across most latitudinal ranges inhabited by extinct ground sloths. Specifically, Eremotherium predominantly required dense 10 mm fur with implications for seasonal changes of coat depth in northernmost latitudes and sparse fur in the tropics; Megatherium required dense 30 mm fur year-round in its exclusive range of cooler, drier climates; Mylodon and Nothrotheriops required dense 10–50 mm fur to avoid thermal stress, matching the integument remains of both genera, and further implying the use of behavioral thermoregulation. Moreover, clumped isotope paleothermometry data from the preserved teeth of four genera of ground sloth yielded reconstructed body temperatures lower than those previously reported for large terrestrial mammals (29 ± 2°–32 ± 3° C). This combination of low metabolisms and thick fur allowed ground sloths to inhabit various environments.
... In the early 1930s, the Swiss biologist Max Kleiber expected a slope of approx. 2/3 when he plotted the measured basal metabolic rateĖ of mammals against their body mass m in a log-log plot [1] (Fig. 3). He suspected a size constraint due to Galileo's "surface law" [2] in connection with heat transfer. ...
... However, he noted: "The best-fitting unit of body size for comparing the metabolism of rat, man, and steer has been found to be m 3/4 ." [1]. Today, the empirical relationshipĖ ∝ m 3/4 (Eq. ...
Each mammal has a budget of approximately one billion heartbeats after birth. This is consistent with their heart rate and life span, which scale with their mass to the power -1/4 and 1/4 respectively, given a complex cardiovascular system. However, the underlying empirical law, i.e., Kleiber’s law, according to which the metabolic rate scales with the mass to the power of 3/4, applies to all animals: for instance, flatworms with a most simple vascular system and a size slightly above the diffusion limit on growth show the same metabolic scaling as mammals. To date, there is no concise theory that is consistent with cell metabolism and compatible with physiological laws, e.g., that the volume flow scales with the capillary diameter to the power of three (Murray’s law). In this paper’s we present how cell metabolism determines the scaling of the organism’s metabolic rate via the Metabolic Module (MM), a cylinder formed by the organism’s cells with a concentric capillary – sized and shaped with scarcity. Evolutionary changes from one taxonomic class to the next led to an unsteady increase in the number of MMs: the metabolism of protists and planarians, e.g., flatworms, is given by one MM only; for ectotherms, i.e., cold-blooded organisms, one thousand and for endotherms, i.e., warm-blooded organisms, nearly one hundred million MMs working together. Special cases, such as diffusion-limited metabolism and the 3/4 power law are asymptotes of the presented general theory. The presented general theory of metabolism offers valuable insights for the targeted development of artificial tissues.
... The relationship between body size and BMR, also often referred to as Kleiber's law, was published by Max Kleiber (Kleiber, 1932), who showed that energy requirements are correlated non-linearly with body mass (M b ) to the power of 0.75, commonly called the allometric scaling factor. There have been numerous publications that debate the value of the allometric scaling factor, but it remains frequently discussed, and it has been shown to vary with conditions such as diet and habitat/environment (He et al., 2023;McNab, 2008McNab, , 2009White, 2010;White et al., 2007). ...
... Several variables are known to alter metabolic rate, including digestion (called the heat increment of feeding or specific dynamic action) and thermoregulation in an environment with a temperature outside the thermoneutral zone (Metze, 2016;Secor, 2009). The definition of 'basal' metabolic rate restricts measurements to adult, non-pregnant and not lactating, postprandial animals that are inactive/resting, but not sleeping, and are in their thermoneutral range (Kleiber, 1932). Comparing metabolic rates between individuals or species that are not measured using the basal definition, therefore, increases variation and might lead to erroneous conclusions. ...
We measured the BASAL breathing frequency following an overnight fast in adult, non‐pregnant/non‐lactating, inactive mammals ranging in body mass from 15 to 5520 kg. The data included results from 338 individual animals from 34 species that were divided into terrestrial, semi‐aquatic (Otariidae and Phocidae) and aquatic mammals. Following attempts to limit the collection of breathing frequency using a basal definition and to correct the analysis phylogenetically, our results suggest that there are differences in the allometric mass‐exponent between terrestrial and aquatic/semi‐aquatic mammals. An allometric regression model, whereby both body mass and breathing frequency were transformed using log10, suggested that the allometric mass exponent for terrestrial mammals (−0.303) was different from both aquatic mammals (−0.124) and semi‐aquatic mammals (−0.091). For semi‐aquatic mammals, the breathing frequency was lower in water, but we detected no association between the breathing frequency and the temperature of the medium (water or air). We propose that allometric studies of cardiorespiratory function should, if possible, adhere to the basal definition during data collection, similar to that used for metabolic rate. Such data will provide valuable information for comparative medicine of large species that are difficult to study, for which controlled baseline data might be difficult to obtain.
... Overall, our results have several repercussions. The first opens a new avenue for exploring the molecular origin of scaling laws [59]. We shall mention in the Discussion how serious the remaining challenges are in proceeding with research toward that goal. ...
... We can verify from the data in Table 1 and Figure 2B that the (k cat /K m , ϕ/RT) points are close to the regression line for X/RT values around 10 and higher than 10. Figure 2B shows that the dissipation rate of enzymes, expressed as dissipation/RT, is proportional to their catalytic efficiency raised to a power of 0.73. This finding resembles the scaling law proposed by Max Kleiber nearly a century ago [59,103]. Kleiber concluded that "the mean, standard metabolic rate of mammals amounts to 70 times the 3/4 power of their body weight [103]". ...
The research literature presents divergent opinions regarding the role of dissipation in living systems, with views ranging from it being useless to it being essential for driving life. The implications of universal thermodynamic evolution are often overlooked or considered controversial. A higher rate of entropy production indicates faster thermodynamic evolution. We calculated enzyme-associated dissipation under steady-state conditions using minimalistic models of enzyme kinetics when all microscopic rate constants are known. We found that dissipation is roughly proportional to the turnover number, and a log-log power-law relationship exists between dissipation and the catalytic efficiency of enzymes. “Perfect” specialized enzymes exhibit the highest dissipation levels and represent the pinnacle of biological evolution. The examples that we analyzed suggested two key points: (a) more evolved enzymes excel in free-energy dissipation, and (b) the proposed evolutionary trajectory from generalist to specialized enzymes should involve increased dissipation for the latter. Introducing stochastic noise in the kinetics of individual enzymes may lead to optimal performance parameters that exceed the observed values. Our findings indicate that biological evolution has opened new channels for dissipation through specialized enzymes. We also discuss the implications of our results concerning scaling laws and the seamless coupling between thermodynamic and biological evolution in living systems immersed in out-of-equilibrium environments.
... These results may reflect differences in seasonal, sex-specific, and size-related ecological and behavioral patterns influencing caiman physiology (Dessauer 1970;Divers and Stahl 2019;Grigg and Kirshner 2015;Hill, Wyse, and Anderson 2016;Kleiber 1932). These patterns align with the seasonal and sexspecific variations in body condition discussed earlier, highlighting the interplay between ecological factors and physiological responses. ...
... Additionally, the concept of weight-specific metabolic rate provides further explanation for these differences. Smaller individuals exhibit higher specific metabolic rates, leading to faster depletion of energetic reserves compared to larger animals (Hill, Wyse, and Anderson 2016;Kleiber 1932). This could explain the lower levels of glucose and albumin observed in smaller caimans, as their elevated energy expenditure results in reduced reserves. ...
The Atlantic Forest broad‐snouted caiman ( Caiman latirostris ) inhabits regions within one of the world's most ecologically diverse ecosystems, yet few studies have explored the relationship between body condition, blood biochemistry, and environmental factors in the wild. Our study investigated the effects of sex, ontogeny, habitat, and environmental variables on the body condition and blood biochemistry of free‐ranging caimans from the state of Alagoas, Northeast Brazil. From 2020 to 2022, we captured 75 caimans across three sites in different seasons. Results revealed sex‐specific responses to seasonal and Interannual weather changes, with females showing higher body condition in the wet season, while males peaked in the dry season. Elevated glucose, total protein, albumin, triglycerides, and fructosamine were linked to higher body condition and larger individuals, while elevated aspartate aminotransferase to low body condition. Seasonal rainfall influenced blood parameters, with the dry season associated with higher creatinine, calcium, and alanine aminotransferase levels, and the wet season with higher total protein, sodium, and potassium. Differences in glucose, alkaline phosphatase, and gamma‐glutamyl transferase across sites pointed to physiological effects of human activities. Blood biochemical values varied widely, with some exceeding reported species ranges. These findings highlight the need to interpret physiological data within the context of local habitat and environmental conditions. Conservation strategies should go beyond species presence and habitat preservation, incorporating pollution control. Our study advances understanding of Caiman latirostris ecophysiology, offering valuable insights for the conservation and management of crocodilian populations in both wild and captive environments.
... The size-complexity rule states that complexity increases as a power-law of the size of a complex system [67]. This rule has been observed at all levels of cosmic evolution in physical (stellar evolution), chemical (autocatalytic cycles), biological (Kleiber's law) and social systems (cities, economies), with some explanation for the proposed origin [20,68,69,74,88]. We reproduce two graphs for real systems to compare with the results of this simulation, namely for stellar evolution Figure 46 and for the evolution of cities Figure 47. ...
... This is supported by many experimental and observational data on scaling relations by Geoffrey West, Bonner, Carneiro, and many others [20,[67][68][69]. The data coincide with Kleiber's law [88], and other similar laws, such as the area speciation rule in ecology and others. Most famously, Hegel wrote in 1812 about the quantity-quality transition [33] which was developed further [34]. ...
Self-organization in complex systems is a process associated with reduced internal entropy and the emergence of structures that may enable the system to function more effectively and robustly in its environment and in a more competitive way with other states of the system or with other systems. This phenomenon typically occurs in the presence of energy gradients, facilitating energy transfer and entropy production. As a dynamic process, self-organization is best studied using dynamic measures and principles. The principles of minimizing unit action, entropy, and information while maximizing their total values are proposed as some of the dynamic variational principles guiding self-organization. The least action principle (LAP) is the proposed driver for self-organization; however, it cannot operate in isolation; it requires the mechanism of feedback loops with the rest of the system’s characteristics to drive the process. Average action efficiency (AAE) is introduced as a potential quantitative measure of self-organization, reflecting the system’s efficiency as the ratio of events to total action per unit of time. Positive feedback loops link AAE to other system characteristics, potentially explaining power–law relationships, quantity–AAE transitions, and exponential growth patterns observed in complex systems. To explore this framework, we apply it to agent-based simulations of ants navigating between two locations on a 2D grid. The principles align with observed self-organization dynamics, and the results and comparisons with real-world data appear to support the model. By analyzing AAE, this study seeks to address fundamental questions about the nature of self-organization and system organization, such as “Why and how do complex systems self-organize? What is organization and how organized is a system?”. We present AAE for the discussed simulation and whenever no external forces act on the system. Given so many specific cases in nature, the method will need to be adapted to reflect their specific interactions. These findings suggest that the proposed models offer a useful perspective for understanding and potentially improving the design of complex systems.
... where MM expected is the expected value for a performance metric at the mean body mass for the experiment, MM actual is the known value of that performance metric for the individual, Mass actual is the known body mass of the individual, Mass mean is the mean body mass for that experiment and b is the mass scaling coefficient (−0.25; e.g. Gillooly et al., 2001;Kleiber, 1932). Mass scaling was computed within the Respirometry package in R v. 4.2.2 (Birk, 2024). ...
Warming ocean temperatures can increase the metabolic rates of fishes, potentially contributing to changes in their growth and survival to recruitment age. During prolonged marine heatwave conditions in the Gulf of Alaska between 2014 and 2019, Pacific Cod (Gadus macrocephalus) metabolic rates may have increased, but little is known about the relationship between metabolism and temperature for immature individuals of this species. We examined the effect of prolonged temperature exposure (~1 year) on the performance (standard, routine, and maximum metabolic rates; critical swimming speed; and aerobic scope) and swimming efficiency (cost of transport and optimal swimming speed) of age-1 Pacific Cod during two laboratory experiments across a range of temperatures (Expt. 1: 2°C, 4°C, 6°C and 8°C; Expt. 2: 6°C, 10°C and 14°C). We also explored relationships between performance and additional body state variables (e.g. condition and growth) and environmental variables (e.g. photoperiod and salinity). Temperature did not influence baseline metabolic performance (standard and routine metabolic rates) in either experiment. However, we observed significantly higher baseline metabolic rates in Expt. 2 compared to Expt. 1, even at the same temperatures. In contrast, maximum performance metrics (e.g. maximum metabolic rate and critical swimming speed) were significantly influenced by temperature. These patterns in performance were generally explained by differing costs of transport and rates of oxygen consumption during swimming trials between the two experiments. Further, body state variables and environmental variables were poorly correlated with performance, even when combined in a multivariate framework. Together, these findings suggest that other factors, such as season, oceanographic conditions early in life, year-class effects, or epigenetic effects, may influence Pacific Cod metabolism more than temperature or measured body state variables and environmental variables following prolonged thermal acclimation.
... Agricultural scientists Max Kleiber and Samuel Brody independently obtained an important empirical allometric relationship. They concluded in Kleiber (1932Kleiber ( , 1947Kleiber ( , 1961, Brody et al. (1932), andBrody (1945) that for warm-blooded animals like birds or domesticated cattle, the animal's basal metabolic rate B and body mass M are related by where B 0 is a normalization constant. Basal metabolic rate is the rate at which an organism expends energy, while in a resting state, in order to support basic life functions such as tissue maintenance. ...
... Kleiber 1932). Subsequent studies found that the increase of home range was higher than the hypothesis predicted (Schoener 1968;Swihart et al. 1988), which may suggest the efficiency of energy acquisition decreases as the size of the home range expands (Harestad and Bunnell 1979).Metabolic rate refers to the rate at which substrates are oxidized to produce energy. ...
Home range size limits the amount of resources an individual can access; hence, it often increases with energy demands. However, maintaining a large home range also requires more energy expenditure, and foraging over a larger area can decrease search efficiency, especially for central place foragers that travel frequently between a home base and food patches. So far, studies examining the relationship between home range size and individual energy management are limited. We investigated whether resting metabolic rate (RMR) was correlated with home range size in bush Karoo rats ( Otomys unisulcatus ). Using flow-through respirometry and mini-GPS dataloggers, we measured individual RMR and home range size of 25 female adult bush Karoo rats in the wild. No association was found between body mass and home range size, instead, RMR was positively associated with home range size. This indicates a larger home range provides sufficient energy to support increased RMR in female bush Karoo rats, supporting either greater body mass or to fuel energy-costly biological process, which feed back to the ability to utilize alarger home range.
... The author, however, has found additional evidence for organismal-like development of Earth. Consider, for example, the Kleiber's law, which states that an animal's metabolic rate scales to the 3/4 power of its mass (Kleiber, 1932). This was found to be valid for most plants as well. ...
By the conventional theories on planetary formation, major discontinuities in the interior of a planet should mainly be the result of compositional differentiation or phase change of material correlated with pressure/temperature gradients. Once the planet is formed and events impacting the planet are of significantly lower energy than its own mass, no significant changes in mantle layers are expected. Exchange and recycling of material between the interior and surface of a terrestrial planet like Earth is assumed to occur through mantle plumes and processes associated with plate tectonics. Although life on surface can certainly be affected by these processes, any correlation between mass extinctions of life on surface and mantle discontinuities is conventionally unexpected and would be hard to explain. Here it is argued that correlation between temporal distribution of major surface events and spatial distribution of internal discontinuities may not be surprising, and evidence is provided that such correlation indeed does exist.
... Also counter to our prediction (1b), body fat or mass did not help predict den entrance dates. Prior research in southcentral Alaska found that neither higher body fat nor body mass predicted longer denning periods ; however, we expected mass of bears living in the coldest environments to be more important because thermal loss ratios cause smaller bears to lose heat more rapidly (Kleiber 1932, Fowler et al. 2019. ...
Denning is a critical behavioral adaptation for brown bears Ursus arctos to cope with winter, a period of extended resource scarcity. Bears reduce their body temperature, heart rate, and metabolism during this time to minimize energy expenditures. The Arctic has among the most pronounced and longest period of resource scarcity. Thus, we predicted bears in the region would respond by having among the longest recorded denning periods. We used GPS data from brown bears to determine the den entry, den exit, and denning duration for a population living primarily above the Arctic Circle. On average, brown bears in the region denned for 206 days, the longest duration reported using GPS data of which we are aware. The longest denning duration for any individual bear was a remarkable 233 days (64% of the year), which is near the theoretical maximum of 241 days. We found that food availability in fall delayed den entrance, with bears that appeared to consume more salmon entering their dens later. Bears showed greater synchrony in den exiting than den entrance, and female bears with cubs exited their dens more than a week after other bears. Later snow melt out in spring was also associated with later den exits. Climate change has the potential to affect the denning ecology of Arctic brown bears by altering the availability of food, ambient temperature, and precipitation, all of which can alter the costs and benefits of hibernation for brown bears.
... Both intrinsic and extrinsic (environmental) factors have been proposed to explain variation in BMR, with hypotheses ranging from the subcellular to the habitat level (Careau et al., 2014). Body size and taxonomic affiliation (because many taxa are distinguished by their ecological and behavioral characteristics; McNab, 2008) are the intrinsic factors that account for the greatest portion of the interspecific variation in BMR (Kleiber, 1932;Lovegrove, 2000;McNab, 2012;White and Kearney, 2013), although the principles that explain the relationship between body size and metabolism are still under study (Brown et al., 2004;Kozłowski et al., 2003Kozłowski et al., , 2020Nisbet et al., 2023;Speakman and Król, 2010;White and Marshall, 2023). A number of traits at the level of the organism have been proposed as additional intrinsic modulators of metabolic rate (e.g. ...
Basal metabolic rate (BMR) is the most commonly measured energetic variable in endothermic animals. Identifying the underlying factors driving interspecific variation in BMR remains a major question in the field of energetics. While body size (M) and taxonomic affiliation are the intrinsic factors that account for most of the interspecific variation in BMR, haploid genome size (C-value) is hypothesized to directly influence cell size and indirectly, the specific metabolic rate. Climatic variables, mostly ambient temperature, have also been proposed as predictors of mass-independent BMR for endotherms. Therefore, in this study, we aimed to investigate the relative importance of intrinsic (C-value: CV) and extrinsic (climatic variables) factors as predictors of BMR in 67 rodent species in a phylogenetic context. The best ordinary least square (OLS) and phylogenetic generalized linear (PGLS) models explaining interspecific variation in BMR included the variables log M, log CV, maximum temperature of the warmest month (Tmax), minimum temperature of the coldest month (Tmin) and net primary productivity (NPP). Log M is the main determinant of log BMR variation in the rodents analyzed. Part of the remaining variation is attributed to a negative effect of genome size explaining 14% of the BMR variance, when Tmin is included in the model. As expected, one or two climatic variables were involved in explaining the remaining BMR variation (Tmin, Tmax and NPP). Our study highlights the importance of a denser sampling within vertebrate clades and the use of a phylogenetic context to elucidate the factors that contribute to explain BMR variation.
... The commonly used rodent models, unlike humans, have a substantial amount of brown adipose tissue (BAT) that can be highly metabolically active, affect EE, and influence the treatment effect of a drug on EE [9,10]. The resemblances in anatomy, size, and metabolic rate between humans and pigs emphasize the potential for the greater translational relevance of the pig compared to rodents [11,12]. Furthermore, pigs lack functional BAT with uncoupling protein 1, which eliminates this variable when measuring EE [13]. ...
Background
Obesity affects nearly a billion people globally and is associated with various health consequences. Current anti-obesity medications primarily target appetite, but drug candidates that modulate energy expenditure (EE) and substrate utilization based on respiratory exchange ratio (RER) are also essential to continuously improve the treatment modalities for people living with obesity. Selecting appropriate animal models and methods is crucial to improving translational value in preclinical research. While pig obesity models provide a relevant alternative to rodent models due to their similarities to humans, little is known about the assessment and translatability of EE in pigs. The aim of this study was to evaluate the translatability of minipigs for assessing the effect of EE-modulating drugs using indirect calorimetry and three positive control compounds that have known effects on EE and/or RER in humans. The study consisted of five sub-studies: Sub-study 1 assessed EE and RER based on sex (male/female) and diet (chow/high-fat diet) with and without correction for body composition; Sub-studies 2–4 evaluated changes in EE and RER after treatment with three positive control compounds: 2,4-dinitrophenol, DNP; a glucagon receptor agonist, GCG-RA; and a melanocortin receptor 4 agonist, MC4-RA; and sub-study 5 established three predictive equations for resting metabolic rate.
Results
Sub-study 1 resulted in detectable differences in EE and RER based on diet/body sizes (P-value < 0.0001), while EE adjusted for body composition resulted in differences based on sex (P-value < 0.0001). Sub-studies 2–4 revealed that the three pharmacological interventions known to affect EE in humans, DNP, GCG-RA, and MC4-RA, showed similar effects in the Göttingen Minipigs by significantly increasing EE by 26.1% (P-value: 0.0014), 21.3% (P-value: 0.0491), and 25.4% (P-value: 0.0013), respectively, emphasizing the translational value of the model. In sub-study 5, three predictive equations were established for RMR based on body composition, demographic and anthropometric measurements, and the most accurate equation based on all variables. All three equations demonstrated acceptable accuracy (adjusted R²: 0.73–0.85).
Conclusions
The present study qualifies the use of Göttingen Minipigs for investigating EE in preclinical research and provides a framework for conducting such research.
Supplementary Information
The online version contains supplementary material available at 10.1186/s42826-024-00233-3.
... There was a significant phylogenetic signal for seed mass (λ = 0.949) and SMR (λ = 0.906) (figure 2; table 1), and the optimal PGLS regression (with λ = 0.612), but the phylogenetically corrected allometric slope was similar at 0.75. These allometric slopes for SMR of seeds using OLS and PGLS regression are similar to the expected value of about 0.75 for both plants (including seeds) and animals [14][15][16]18,94] although near isometric scaling (i.e. b is about 1) has been reported for some plants [9,10,95] and seeds [19]. ...
Energetics is considered a fundamental ‘currency’ of ecology and the way that metabolic rate (MR)—the rate of energy expenditure on biological processes—scales relative to the size of the organism can be both an adaptive benefit and a constraint in mediating the energetic demands of ecological processes. Since few investigations have examined this relationship for angiosperm seeds, we measured standard metabolic rate (SMR) of 108 species’ seeds, spanning a broad suite of species. We used fluorescence-based closed-system respirometry at temperatures between 18°C and 30°C, based on optimal germination conditions, and Q10 corrected to 20°C. The allometric relationship for SMR as a function of seed mass was 0.081 × M0.780 with ordinary least squares regression and 0.057 × M0.746 with phylogenetic generalized least squares regression. This relationship is consistent with the pervasive metabolic allometry documented for both vegetative plants and domesticated cultivars (n = 14) which had higher SMR residuals than wild species (seven weeds and 87 Australian native species). For native species, seed SMR was strongly related to measures of increasing environmental aridity (annual mean temperature and precipitation, and precipitation in the wettest quarter), consistent with seeds from arid environments having a high MR to supply energy needed to germinate rapidly. By comparing SMR of seeds for diverse angiosperm species, we provide insights into inter-relationships of physiology, distribution, climate and domestication on seed ecology and suggest that energetics represents a valuable addition to established functional trait libraries for seed biology.
... Heat loss estimations in cetaceans have been mainly based on Fourier's law of heat conduction and Kleiber's concept of a homeothermic animal (Kleiber, 1932), wherein a heat-producing body core has a constant temperature and is surrounded by an insulating layer with a specified thermal conductivity, thickness, surface area and surface temperature. Only a few studies have discussed the interspecific scaling of these parameters in cetaceans (Hokkanen, 1990;Ryg et al., 1993). ...
Maintaining a stable core body temperature is essential for endotherms. Cetaceans live in a highly thermally conductive medium, requiring special adaptations to reduce heat loss and maintain homeothermy. We employed a combination of aerial photogrammetry and existing data sources to estimate heat loss rates in five sympatric cetaceans of varying sizes, inhabiting the sub-arctic waters (∼3.7 °C) of NE-Iceland: harbour porpoises (Phocoena phocoena, 1.0 - 1.6 m, n=50), white-beaked dolphins (Lagenorhynchus albirostris, 1.1 - 2.9 m, n=294), minke whales (Balaenoptera acutorostrata, 4.4 - 8.6 m, n=30), humpback whales (Megaptera novaeangliae, 6.0 - 14.2 m, n=282) and blue whales (Balaenoptera musculus, 13.2 - 24.2 m, n=29). Further, we investigated the effect of body size (length), body shape (surface-area-to-volume ratio, SVR), body temperature, and blubber thermal conductivity and thickness on heat loss for all species. Smaller species had higher volume-specific heat loss compared to larger species due to their higher SVRs, a fundamental consequence of scaling. Apart from body size, blubber thickness had the largest effect on heat loss, followed by thermal conductivity. Smaller cetaceans seem to rely primarily on physiological and morphological adaptations to reduce heat loss, such as increased blubber thickness and lower thermal conductivity, whereas larger species offset heat loss by having larger bodies and lower SVRs. Our findings provide valuable insights into the thermal biology of these species and its implications for habitat use and prey requirements.
... For example, an isometric or linear scaling relationship is present in organisms whose individual body parts grow in proportion to their total body size (Huxley, 1932). In contrast, there is an allometric or power law scaling relationship between most mammals' basal metabolic rates and body mass, where the former scales to the latter to the power of ¾ (Kleiber, 1932). Thus, allometric analysis is particularly appropriate for examining the GPG because it allows us to compare the growth rates of two variables that display either exponential or linear growth (i.e. ...
Purpose
The purpose of this study is to examine the narrowing of the gender publication gap (GPG) and predict when gender publication parity will be achieved. It investigates if women’s publication rates are catching up with men’s when the proportion of published articles by women will match their representation in the field, and how the gender gap and parity are changing concerning lead authorships. The study analyzes data from 11,097 researchers across 8 management journals from 2002 to 2020, revealing a higher growth rate in women’s publications and varying degrees of parity achievement between micro and macro domains.
Design/methodology/approach
We created a database of all researchers who published at least one article in eight management journals from January 2002 through December 2020. It included 11,097 unique researchers who produced 7,357 unique articles, resulting in 21,361 authorships. We used data from the Web of Science to identify articles and their authors, filtering for “articles” and “reviews” only. We used allometric modeling and time series analysis to examine the GPG and forecast gender publication parity.
Findings
We found that the GPG is narrowing, with women’s publication rates growing faster than men’s. Parity in lead authorships has already been achieved or is within reach for many journals, especially in micro domains. However, macro-oriented journals show slower progress, with some not expected to reach parity until 2045 or later. These improvements are linked to increased representation of women in leadership positions and targeted mentoring programs in micro domains.
Research limitations/implications
While our study focused on publications, it did not account for citations, which could provide a more comprehensive view of research impact. Future research should explore other journals and different time windows and include citation analysis to understand the GPG and parity further.
Practical implications
The narrowing GPG is a positive development for organization studies, particularly in micro domains. This progress can mitigate stereotypes about women’s abilities, promote equity in hiring and promotion by considering authorship order and highlight the importance of targeted mentoring programs to reduce barriers for women. Additionally, business schools should identify and address performance situational constraints that disproportionately affect women, using techniques like the critical incidents approach to design effective interventions.
Social implications
The study’s societal implications include fostering greater gender equity in academic publishing, which can influence broader social norms and reduce gender stereotypes in academia. Achieving gender parity in publications can lead to more equitable hiring, promotion and recognition practices. Additionally, it highlights the importance of removing performance situational constraints and biases that hinder women’s academic progress, thus promoting a more inclusive and fair academic environment. These changes can inspire other fields to implement similar measures, contributing to societal progress toward gender equality.
Originality/value
The study’s originality/value lies in its longitudinal approach to analyzing the GPG in organization studies, contrasting with prior cross-sectional studies. It provides new insights by predicting when gender parity will be achieved in various journals, showing faster progress in micro domains compared to macro domains. Additionally, the study introduces methodological innovations such as allometric modeling and scenario-based analyses, highlighting the importance of reducing situational constraints for women in academia. These findings offer a nuanced understanding of the ongoing efforts and challenges in achieving gender equity in academic publishing.
... However, the central role of the gut as exchange surface for nutrients and the previous body of theoretical work on the putative relation between the structure of branching transport networks and metabolic scaling [42,43] provides an intriguing direction for future exploration. Across animal phylogeny, metabolic rate scales as P ∝ M 3/4 with animal mass M , which is known as Kleiber's law [50]. Although the mechanistic origins of the 3/4 exponent remain unknown, we have recently shown that planarian growth and degrowth follows Kleiber's law [35]. ...
The growth and scaling of organs is a fundamental aspect of animal development. However, how organs grow to the right size and shape required by physiological demands, remains largely unknown. Here, we provide a framework combining theory and experiment to study the scaling of branched organs. As a biological model, we focus on the branching morphogenesis of the planarian gut, which is a highly branched organ responsible for the delivery of nutrients. Planarians undergo massive body size changes requiring gut morphology to adapt to these size variations. Our experimental analysis shows that various gut properties scale with organism size according to power laws. We introduce a theoretical framework to understand the growth and scaling of branched organs. Our theory considers the dynamics of the interface between organ and surrounding tissue to be controlled by a morphogen and illustrates how a shape instability of this interface can give rise to the self-organized formation and growth of complex branched patterns. Considering the reaction-diffusion dynamics in a growing domain representative of organismal growth, we show that a wide range of scaling behaviors of the branching pattern emerges from the interplay between interface dynamics and organism growth. Our model can recapitulate the scaling laws of planarian gut morphology that we quantified and also opens new directions for understanding allometric scaling laws in various other branching systems in organisms.
... Depth and body size are important structuring mechanisms of marine food webs influencing spatial variability in predatorprey interactions through depth-driven variation of benthicpelagic coupling (Duffill Telsnig et al. 2019;Ying et al. 2020;Kiljunen et al. 2020) and biologically mediated access to trophic resources (Potapov et al. 2019;Keppeler et al. 2021). Body size, in the context of within-and between-species characteristics, is of paramount importance for several life history and ecological processes within and across many levels of biological organization (Peters 1983;Calder 1984), influencing metabolic rates (Kleiber 1932), population density (Reuman et al. 2008), community trophic structure, and matter fluxes (Ings et al. 2009;Potapov et al. 2019). Thus, previous theoretical considerations highlight the importance of considering sizestructured food webs that reflect size-based feeding by individuals to model marine ecosystems (Cohen et al. 1993;Trebilco et al. 2013;Blanchard et al. 2017). ...
Understanding how energy is transferred within and across ecosystems is essential to better understand drivers and future consequences of shifts in energy pathways. We used stable isotope ratios of 1932 fish individuals belonging to the 11 most abundant fish species collected across 300,000 km² along the English Channel–Celtic Sea continuum. To examine cross‐ecosystem differences in trophic functioning, we assessed the effects of both extrinsic (depth) and intrinsic factors (body size and feeding guild) on resource use and trophic position of fish consumers. Positive relationships between trophic position and body size were observed for zoobenthivore and piscivore fishes, whereas the relationship was negative for benthivore fishes. Body size is thus an important structuring mechanism in the systems. Trophic position decreased with increasing depth for all levels of biological organization. The amplitude of the change between shallow and deep stations was equivalent to more than one trophic level for generalist planktivores and piscivores. In the shallow English Channel, the food web is marked by stronger coupling of benthic and pelagic habitats via diverse pathways, due to the proximity of benthic and pelagic species, whereas in the Celtic Sea, increasing depth leads to a decoupling of benthic and pelagic pathways. For piscivores, a consistent pattern of increasing dependence on benthic subsidies with increasing size and depth highlights the importance of large consumers coupling energy across food web compartments. This study describes the relationship between production and trophic functioning and provides an empirical ecological explanation for cross‐ecosystem differences in observed trophic structures.
... Already in 1614, Santorio Santorio conducted the first documented investigation into human metabolism, demonstrating a quantifiable and predictable relationship between ingested food mass and excreted fecal matter (Céspedes Restrepo & Morales-Pinzón, 2018). Later on, Kleiber established that the metabolic rate in mammals scales as a power law of the animal's body mass with an ¾ exponent (Kleiber, 1932). This discovery has sparked strong scientific inquiries regarding the underlying mechanisms responsible for such a predictable behavior (Bettencourt et al., 2007;West et al., 1997). ...
Understanding the quantitative patterns behind scientific disciplines is fundamental for informed research policy. While many fields have been studied from this perspective, Urban Science (USc) and its subfields remain underexplored. As organisms, urban systems rely on materials and energy inputs and transformation (i.e. metabolism) to sustain essential dynamics. This concept has been adopted by various disciplines, including architecture and sociology, and by those focused on metabolic processes, such as ecology and industrial ecology. This study addresses the structure and evolution of Urban Metabolism (UM) and Sustainability research, analyzing articles by disciplines, study subjects (e.g., cities, regions), methodologies, and author diversity (nationality and gender). Our review suggests that UM is an emerging field that grew until 2019, primarily addressed by environmental science and ecology. Common methods include Ecological Network Analysis, and Life Cycle Assessment, and Material Flow Analysis, focusing flows over stocks, ecosystem dynamics and evolutionary perspectives of the urban system. Authors are predominantly from China and the USA, and there are less gender gaps compared to general science research. Our analysis identifies relevant challenges that have become evident in the statistical properties of this scientific field and which might be helpful for the design of improved research policies.
... Since the pioneering of Huxley and Teissier [17,18], Kleiber [91], and Kleiber [92] the debate on the underlying mathematics of allometry scaling of heat transfer processes has been on going, and is now used in other fields of research [16,90], Gillooly [93], Downs [94], Rue [95], Agutter and Tuszynski [96], Niklas and Kutschera [97], and Lamont et al. [98]. Law and Dowling [7,8] successfully used allometry scaling for the probing the dynamics and structure of microwave-assisted synthesis Database B. In particular the use of novel non-linear dual allometry test that bracket recommend Green Chemistry within the dataset. ...
The study brings together in a single publication the phase-space projection analysis of microwave-assisted synthesis of transition monometallic (palladium, silver, platinum, and gold), binary zinc oxide, and metals supported on carbon framework nanostructures. It is shown for a database of fifty microwave-assisted syntheses, a two-variable power-law signature (y = cxn) over four orders of magnitude. The purpose of this study is therefore to identify the underlying dynamics of the power-law signature. A dual allometry test is used to discriminate between transition metal period and row, and between recommended Green Chemistry, problematic Green Chemistry, and non-Green Chemistry hazardous solvents. Typically, recommended Green Chemistry exhibits a broad y-axis distribution within an upper exponent = 1 and lower exponent = 0.5. Problematic Green Chemistry exhibits a y-axes narrower distribution with an upper exponent = 0.94 and a lower exponent = 0.64. Non-Green Chemistry hazardous data shows a further narrowing of the y-axis distribution within upper exponent = 0.87 and lower exponent = 0.66. Mass-based environmental factor is used to calculate the ‘Greenness’ of single-step (facile) transition metal synthesis. The power-law signature also exhibits phase transitions associated with microwave applicator type.
... Decades of research quantified how physiological traits vary with body size and temperature including Rubner (1883), Kleiber (1932), Brody (1945) and Hemmingsen (1960). A seminal finding that respiration rates of mammals and birds increase non-linearly as the ¾ power of body mass known as "Kleiber's rule" led to a flurry of empirical studies synthesized in several books (Peters (1986), McMahon and Bonner (1983), Calder (1984) and Schmidt-Nielsen (1984)). ...
Natural selection has produced an extraordinary diversity of life histories spanning many orders of magnitude in body size, vital rates, and biological times. In general, big and cold organisms grow and reproduce slowly and live long lives; small and warm organisms grow and reproduce quickly and live short lives. The Metabolic Theory of Ecology (MTE) predicts equal and opposite scaling exponents of mass-specific biological rates (e.g., respiration, growth, and reproduction) and times (e.g., development, lifespan, and generation) as a function of size. However, empirical support for these predictions varies depending on trait and taxon. Here I: 1) provide background and mixed support for the quarter-power scaling exponents for life history rates and times predicted by MTE, 2) discuss possible explanations, including effects of natural selection on taxonomic and functional groups, and inadequate data for life history traits, 3) briefly summarize the Equal Fitness Paradigm (EFP) as a unifying theory of bioenergetics, life history and demography that does not depend on any particular allometric scalings, and 4) discuss ramifications of the EFP for other biological phenomena, including physiological performance metrics and trophic energetics of ecosystems. I draw mostly from my knowledge of mammals, yet in many cases the mammalian examples can be generalized to other organisms. I end with prospects for further evaluating and extending the EFP.
... Снижение удельной скорости энергетического обмена с размером тела животных (аллометрия метаболизма) отмечено более века назад (Kleiber 1932;Schmidt-Nielsen 1984). При этом, удовлетворительного объяснения эта фундаментальная биологическая закономерность до сих пор не получила, и активная дискуссия на эту тему продолжается (см. ...
Mitochondria play a crucial role in energy metabolism, and the relationship between metabolic rate and body size (metabolic allometry) may be linked to membrane properties and their lipid composition. We studied the influence of body size on the lipid and fatty acid composition of mitochondria in bivalve mollusks, specifically in mussels Mytilus edulis L. from the White Sea. This study analyzed mussels of varying sizes, ranging from 0.3 to 12.7 g of soft tissue wet mass. Mitochondria were isolated from gill tissues, and their lipid and fatty acid composition was determined. It was shown that, unlike phospholipids and triacylglycerols, the sterol proportion in mitochondrial membranes varied depending on mussel size. Larger mussels had lower cholesterol proportion but higher levels of monounsaturated fatty acids. In the composition of mitochondrial phospholipids, saturated fatty acids (SFAs), especially palmitic (16:0) and stearic (18:0) acids, predominated. The proportion of SFAs decreased with increasing mussel size. Conversely, monounsaturated fatty acids (MUFAs) showed a positive correlation with body size, significantly increasing in larger individuals. The proportion of polyunsaturated fatty acids (PUFAs) in White Sea mussel mitochondria was relatively low (less than 25% of the total fatty acids) and did not depend on body mass. The reduced proportion of PUFAs is characteristic of bivalve mitochondria from Arctic seas and long-lived bivalve species. Our data indicate the relative stability of the lipid and fatty acid composition of White Sea mussel mitochondria. Such fatty acid profile of mitochondrial phospholipids is likely a biochemical adaptation, enabling mussels to maintain effective activity of membrane-associated proteins regardless of their body size.
... Our findings could therefore reflect size-mediated shifts in maternal investment over the feeding season, carrying implications for female resilience and offspring survival (Boltnev et al., 1998;Bowen et al., 2015;Burton et al., 2020;Pirotta et al., 2019). For example, maternal investment trade-offs are more likely to affect smaller females, due to their greater energetic demands, such as mass-specific metabolism and transport costs (Brody, 1968;Kleiber, 1932;Williams, 1999). As a result, smaller females and their offspring could be less resilient to environmental stressors due to their reduced size, limited energy stores and increased metabolic demands (Bowen et al., 2015;Burton et al., 2020;McMahon et al., 2017). ...
Given recent declines in North Pacific humpback whale (Megaptera novaeangliae) reproductive output and calf survival, there is additional urgency to better understand how mother–calf pairs allocate energy resources across their migratory cycle. Here, unoccupied aerial system (UAS; or drone) photogrammetry was used to quantify the body size and condition (BC) of humpback whales on their Hawaiʻi (HI) breeding and Southeast Alaska (SEAK) feeding grounds. Between 2018 and 2022, we collected 2410 measurements of 1659 individuals. Rates of change in body volume (BV) and length (BL) were quantified using 803 repeat measurements of 275 individuals. On average, HI mothers lost 0.106 m³ or 96.84 kg day⁻¹ while fasting, equivalent to 2641 MJ day⁻¹ or 830 kg of krill and 424 kg of Pacific herring daily. HI calf BV and BL increased by 0.035 m³ and 2.6 cm day⁻¹, respectively. In SEAK, maternal BV increased by 0.015 m³ or 14.54 kg day⁻¹ (367 MJ day⁻¹), while calf BV and BL increased by 0.039 m³ and 0.93 cm day⁻¹, respectively. Maternal investment in calf growth correlated with both female BL and BC, with larger females producing larger, faster‐growing calves. Finally, using 330 measurements from 156 females, we quantified differences in BC increase over four feeding seasons. Lactating females exhibited an average BC increase of 6.10%, half that of unclassified females (13.51%) and six times lower than pregnant females (37%). These findings represent novel insights into the life history of humpback whales across their migratory cycle, providing key baseline data for bioenergetic models elucidating the effects of anthropogenic disturbance and rapidly changing ocean ecosystems. image
Key points
On average, Hawaiʻi (HI) mothers lost 0.106 m³ or 96.84 kg day⁻¹, equivalent to 2641 MJ day⁻¹. Over a 60 day period, this corresponded to an estimated mean energetic cost of 158 GJ, or ≈50 tons of krill or ≈25 tons of Pacific herring, surpassing the total energetic cost of gestation estimated for humpback whales of similar length.
In Southeast Alaska (SEAK), maternal body volume (BV) increased by just 0.015 m³ or 14.54 kg day⁻¹ (367 MJ day⁻¹). Further, SEAK lactating females showed the slowest rates of growth in body width and condition over a 150 day period compared to non‐lactating females.
Maternal investment in calf growth correlated with both maternal length and body condition, with larger females producing larger, faster‐growing calves. In HI, however, the ratio between maternal BV lost and calf BV gained (conversion efficiency) was relatively low compared to other mammals.
Energy rate density (ERD) corresponds to the energy flow through a dissipative system to maintain its energy gradient and is defined as the energy rate (ER), normalised to mass. ERD has been proposed by Chaisson (2001) as a single, simple metric for complexity of a wide variety of systems over big time. The main objective of this study is to assess the usefulness of this metric over the lifetimes of dissipative systems. For this purpose, mass and ER(D) data have been collected over the lifetimes of a low-mass star, like our Sun, a human, and the Roman Empire, as representative examples of dissipative systems from the cosmological, biological, and cultural realms, respectively. Time profiles of proxies are very useful for further interpretation of the ER(D) time profiles. ER(D) of a low-mass star as a contracting proto-star (< 0.05 Gyr) as well as during its red giant stage and helium flashes (11 to 12.5 Gyr) is much larger than during its stable appearance as a yellow dwarf star in its main sequence (0.05 to 11 Gyr). ERD of a human peaks at 1.5 yr, reflecting the large relative growth of a baby. ER of a human represents the biochemical activities of the human body, especially as a result of physical activities, and reaches a maximum when a human is in the prime of its life between 20 and 30 yr. Cognitive and emotional functions do not impose any additional energy requirements. For the Roman Empire ERD has decreased over time, because the growth rate of the total mass including that of man-made constructs (note that Chaisson only uses mass of humans) was larger than that of ER. ER per capita has hardly varied, because human (slave) labour was the main energy source powering the empire. The Roman Empire was at the height of its power between 100 and 200 CE, which is best reflected by maxima in ER or simply population. Thus, it is concluded that ERD runs in to several issues, when it is applied as a metric of complexity of systems over their lifetimes. ERD does not capture information processing and, as a result, underestimates the complexity of biological and cultural systems. This hampers its application in a BH context, including its use for BH periodisation. Alternative complexity metrics related to information processing need to be developed: information rate density may be a suitable candidate.
Allometry explores the relationship between an organism’s body size and its various components, offering insights into ecology, physiology, metabolism, and disease. The cell is the basic unit of biological systems, and yet the study of cell-type allometry remains relatively unexplored. Single-cell RNA sequencing (scRNA-seq) provides a promising tool for investigating cell-type allometry. Planarians, capable of growing and degrowing following allometric scaling rules, serve as an excellent model for these studies. We used scRNA-seq to examine cell-type allometry in asexual planarians of different sizes, revealing that they consist of the same basic cell types but in varying proportions. Notably, the gut basal cells are the most responsive to changes in size, suggesting a role in energy storage. We capture the regulated gene modules of distinct cell types in response to body size. This research sheds light on the molecular and cellular aspects of cell-type allometry in planarians and underscores the utility of scRNA-seq in these investigations.
Although it is intuitive that large mammals need more food than smaller ones, it is not so obvious that, relative to their body mass, larger mammals consume less than smaller ones. In fact, on a per kg basis, the resting metabolic rate of a mouse is some 50 times higher than that of an elephant. The fact that metabolism could not be proportional to the mass of the animal was suggested by Sarrus and Rameaux in 1838. The first indication that oxygen consumption (or other indices of metabolic rate, Y ) related to the animal body mass ( M ) according to an exponential of the type Y = a · M b , where b was about 0.75, was presented by Max Kleiber in 1932. Two years later Samuel Brody had collected sufficient data to construct the first “mouse‐to‐elephant” metabolic curve. The physiological basis of the relationship has been the object of many hypotheses, often accompanied by a great deal of controversy. This historical essay traces the origin of the mouse‐to‐elephant metabolic function, recalling the earliest concepts of metabolism and its measurements to understand the body size dependency, which is still one of the most elusive phenomena in comparative physiology. A brief look at the metabolic scaling of nonmammalian organisms will be included to frame the mouse‐to‐elephant curve into a broader context and to introduce some interesting interpretations of the mammalian function. © 2023 American Physiological Society. Compr Physiol 13:4513‐4558, 2023.
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. © 2014 American Physiological Society. Compr Physiol 4:231‐256, 2014.
Comparative physiology often provides unique insights in animal structure and function. It is specifically through this lens that we discuss the fundamental properties of skeletal muscle and animal locomotion, incorporating variation in body size and evolved difference among species. For example, muscle frequencies in vivo are highly constrained by body size, which apparently tunes muscle use to maximize recovery of elastic recoil potential energy. Secondary to this constraint, there is an expected linking of skeletal muscle structural and functional properties. Muscle is relatively simple structurally, but by changing proportions of the few muscle components, a diverse range of functional outputs is possible. Thus, there is a consistent and predictable relation between muscle function and myocyte composition that illuminates animal locomotion. When animals move, the mechanical properties of muscle diverge from the static textbook force‐velocity relations described by A. V. Hill, as recovery of elastic potential energy together with force and power enhancement with activation during stretch combine to modulate performance. These relations are best understood through the tool of work loops. Also, when animals move, locomotion is often conveniently categorized energetically. Burst locomotion is typified by high‐power outputs and short durations while sustained, cyclic, locomotion engages a smaller fraction of the muscle tissue, yielding lower force and power. However, closer examination reveals that rather than a dichotomy, energetics of locomotion is a continuum. There is a remarkably predictable relationship between duration of activity and peak sustainable performance. © 2013 American Physiological Society. Compr Physiol 3:289‐314, 2013.
Symmorphosis is a concept of economy of biological design, whereby structural properties are matched to functional demands. According to symmorphosis, biological structures are never over designed to exceed functional demands. Based on this concept, the evolution of the diaphragm muscle (DIAm) in mammals is a tale of two structures, a membrane that separates and partitions the primitive coelomic cavity into separate abdominal and thoracic cavities and a muscle that serves as a pump to generate intra‐abdominal (P ab ) and intrathoracic (P th ) pressures. The DIAm partition evolved in reptiles from folds of the pleural and peritoneal membranes that was driven by the biological advantage of separating organs in the larger coelomic cavity into separate thoracic and abdominal cavities, especially with the evolution of aspiration breathing. The DIAm pump evolved from the advantage afforded by more effective generation of both a negative P th for ventilation of the lungs and a positive P ab for venous return of blood to the heart and expulsive behaviors such as airway clearance, defecation, micturition, and child birth. © 2019 American Physiological Society. Compr Physiol 9:715‐766, 2019.
Although firmly grounded in metabolic biochemistry, the study of energy metabolism has gone well beyond this discipline and become integrative and comparative as well as ecological and evolutionary in scope. At the cellular level, ATP is hydrolyzed by energy‐expending processes and resynthesized by pathways in bioenergetics. A significant development in the study of bioenergetics is the realization that fluxes through pathways as well as metabolic rates in cells, tissues, organs, and whole organisms are “system properties.” Therefore, studies of energy metabolism have become, increasingly, experiments in systems biology. A significant challenge continues to be the integration of phenomena over multiple levels of organization. Body mass and temperature are said to account for most of the variation in metabolic rates found in nature. A mechanistic foundation for the understanding of these patterns is outlined. It is emphasized that evolution, leading to adaptation to diverse lifestyles and environments, has resulted in a tremendous amount of deviation from popularly accepted scaling “rules.” This is especially so in the deep sea which constitutes most of the biosphere. © 2012 American Physiological Society. Compr Physiol 2:2527‐2540, 2012.
All life history traits, external behavior and internal elements such as morphology and physiology, affect survival, reproduction, and fitness. The long-term study of elephant seals is unusual in that it incorporates numerous physiological studies along with the behavioral studies of individuals. The physiological studies have emphasized studies where the seals are exceptional: natural fasting, the vital role of blubber, milk composition dynamics, water conservation, movement of pollutants in blubber, and sleep apnea. Newly weaned pups are frequently used subjects, both in the field and in the laboratory, because they fast for 2.5 months before going to sea to forage for the first time. Blubber is an especially important “organ” that provides energy and water for females while they fast and nurse their pups for a month and for males that fast for 100 days while fighting and mating during the breeding season. The seals are capital breeders that lay down the blubber during months of feeding at sea prior to reproducing on land. The milk composition changes over the course of nursing, with water decreasing and lipids increasing, resulting in milk that is 55% fat near weaning. Water is conserved in numerous ways, one of which is to stop breathing for up to 25 min while sleeping, which reduces water loss by reducing exhalations. Physiological studies have revealed much important information about mechanisms that enhance survival and reproduction. Nevertheless, investigators of new studies must consider the pros and cons of combining physiological and behavior studies in the same long-term study because the two disciplines have conflicts of research interests.
Complex biological systems operate under non‐equilibrium conditions and exhibit emergent properties associated with correlated spatial and temporal structures. These properties may be individually unpredictable, but tend to be governed by power‐law probability distributions and/or correlation. This article reviews the concepts that are invoked in the treatment of complex systems through a wide range of respiratory‐related examples. Following a brief historical overview, some of the tools to characterize structural variabilities and temporal fluctuations associated with complex systems are introduced. By invoking the concept of percolation, the notion of multiscale behavior and related modeling issues are discussed. Spatial complexity is then examined in the airway and parenchymal structures with implications for gas exchange followed by a short glimpse of complexity at the cellular and subcellular network levels. Variability and complexity in the time domain are then reviewed in relation to temporal fluctuations in airway function. Next, an attempt is given to link spatial and temporal complexities through examples of airway opening and lung tissue viscoelasticity. Specific examples of possible and more direct clinical implications are also offered through examples of optimal future treatment of fibrosis, exacerbation risk prediction in asthma, and a novel method in mechanical ventilation. Finally, the potential role of the science of complexity in the future of physiology, biology, and medicine is discussed. © 2011 American Physiological Society. Compr Physiol 1:995‐1029, 2011.
Describing Scaling Relationships
Scaling relationships are a central feature of global ecology, quantifying general biological patterns across broad spatial and temporal scales. Traditionally characterised as scale‐invariant power laws, the scope of biological scaling has expanded in recent decades to include log–log curvilinearity and exponential functions. In macroecology and biogeography, a major focus is on quantifying these general relationships using empirical data, comparing observations across datasets and testing their consistency with theoretical predictions. This is typically accomplished by fitting linear models to log‐transformed data, estimating slopes (representing scaling exponents or exponential rate constants) and 95% confidence intervals (CIs), and evaluating whether these CIs align with empirical observations or theoretical predictions.
Challenges of Existing Methods
The accuracy of general slope estimates depends critically on the distribution of data across the range of the abscissa. When observations are unevenly distributed, with clustering in some portions of the range, slope and CI estimates become biased toward regions of higher data density. This imbalance increases the risk of type I or II errors, potentially leading to erroneous conclusions in comparisons of data with observations or predictions.
Bootstrapping Enables Accurate Estimates of Scaling Relationships
We introduce a novel bootstrapping approach to address data imbalance in biological scaling analyses that improves the accuracy of general slope and CI estimates. This method enables more precise comparisons with empirical observations and theoretical predictions. We validate the approach by accurately reproducing a known slope from plant height‐diameter data. Additionally, we demonstrate that fitting linear models to imbalanced and balanced metabolic rate‐body mass data yields different slope estimates, leading to different conclusions regarding agreement between data and theory. Finally, we evaluate three common data processing methods and show that model fits to balanced data are superior for reliable quantification of general scaling relationships.
Larger, longer-lived species are expected to have a higher cancer prevalence compared to smaller, shorter-lived species owing to the greater number of cell divisions that occur during their lifespan. Yet, to date, no evidence has been found to support this expectation, and no association has been found between cancer prevalence and body size across species—a phenomenon known as Peto’s paradox. Specifically, while anticancer mechanisms have been identified for individual species, wider phylogenetic evidence has remained elusive. Here, we show that there is no evidence for Peto’s paradox across amphibians, birds, mammals, and squamate reptiles: Larger species do in fact have a higher cancer prevalence compared to smaller species. Moreover, we demonstrate that the accumulation of repeated instances of accelerated body size evolution in mammals and birds is associated with a reduction in the prevalence of neoplasia and malignancy, suggesting that increased rates of body size evolution are associated with the evolution of improved cellular growth control. These results represent empirical evidence showing that larger body size is related to higher cancer prevalence, thus rejecting Peto’s paradox, and demonstrating the importance of heterogenous routes of body size evolution in shaping anticancer defenses.
Glucose transporters (GLUTs) play vital roles in cellular metabolism. Understanding their evolutionary dynamics in birds is essential for elucidating avian physiology and adaptation. However, the choice of gene detection method in gene family analysis may affect the conclusion. Here, we present a comprehensive investigation of methodologies and GLUT gene loss events in avian lineages, focusing on the loss of GLUT4 and GLUT8. To illustrate the effects of these methods, we first employed BUSCO-based homolog identification, calculated pairwise evolutionary distances between different species, and performed separate blastn and blastp searches to identify homologs in two groups of animals. Our analyses revealed a significant decline in blastn accuracy with increasing evolutionary distance, represented by relative divergence times. Through a more robust blastp-based gene detection pipeline, we provide evidence for the loss of GLUT genes in birds based on 58 vertebrate genomes, including 47 bird species. Our results support the reported early loss of GLUT4 in Aves. We also newly emphasize the absence of GLUT8 in passerines, potentially due to adaptation to high-sugar diets in their ancestors. These findings enhance our knowledge of avian metabolism and the evolution of GLUT genes.
Small mammals have a higher heart rate and, relative to body mass (Mb), a higher metabolic rate than large mammals. In contrast, heart weight and stroke volume scale linearly with Mb. With mitochondria filling approximately 50% of a shrew cardiomyocyte – space unavailable for myofibrils – it is unclear how small mammals generate enough contractile force to pump blood into circulation. Here, we investigated whether the total number or volume of cardiomyocytes in the left ventricle compensates for allometry-related volume shifts of cardiac mitochondria and myofibrils. Through statistical analysis of data from 25 studies with 19 different mammalian species with Mb spanning seven orders of magnitude (2.2 g to 920 kg), we determined how number, volume density and total volume of cardiomyocytes, mitochondria and myofibrils in the left ventricle depend on Mb. We found that these biological variables follow scaling relationships and are proportional to a power b of Mb. The number [b=1.02 (95% CI: 0.89, 1.14); t-test for b=1: P=0.72] and volume [b=0.95 (95% CI: 0.89, 1.03); t-test for b=1: P=0.18] of cardiomyocytes in the left ventricle increases linearly with increasing Mb. In cardiomyocytes, volume density of mitochondria decreases [b=–0.056 (95% CI: −0.08, −0.04); t-test for b=0: P<0.0001] and that of myofibrils increases [b=0.024 (95%CI: 0.01, 0.04); t-test for b=0: P<0.01] with increasing Mb. Thus, the number or volume of left ventricular cardiomyocytes does not compensate for the higher heart rate and specific metabolic rate of small mammals although a higher mitochondrial and lower myofibrillar volume per cardiomyocyte are present.
In the previous chapters we described how statistical laws have been used in complex-systems research: Chap. 1 provided a brief historical overview and a working definition of statistical laws; Chap. 2 listed examples from different disciplines, focusing on the similar role played by statistical laws in connecting data and models; and Chap. 3 introduced increasingly sophisticated quantitative methods that have been employed to test, fit, and explore statistical laws. In this last chapter, we will move away from the description of how statistical laws have been used and, instead, focus on the role they can and should play in the study of complex systems. We will propose different ways in which methods and interpretations can be coherently employed, highlight possible pitfalls, suggest good practices, and speculate about the future of statistical laws in data-driven research.
This chapter contains a case by case description of paradigmatic statistical laws. While acknowledging their distinctiveness, our focus is on the common aspects across different statistical laws, in particular the similar role they have played in different research areas. The aim is to facilitate a comparative analysis that highlights the significance of this concept in complex-systems studies, supporting the unified treatment proposed in this monograph. In each case, we briefly describe how these laws were proposed, the most prominent explanations for their origin, and some of their uses. While we attempt to refer to original work, and to give credit to the original proponents of the laws, the description should be interpreted as a historical narrative that justified (and still justifies) the use of statistical laws and not as an attempt to reproduce the historical steps involved in this process. For readers interested in specific statistical laws, we hope the content of this chapter will provide a contextual introduction and point to relevant work where more specific aspects are discussed.
This chapter introduces and critically discusses the quantitative (statistical) methods used to study statistical laws.
A common feature of mycorrhizal observation is the growth of the infection on the plant root as a percent of the infected root or root tip length. Often, this is measured as a logistic curve with an eventual, though usually transient, plateau. It is shown in this paper that the periods of stable percent infection in the mycorrhizal growth cycle correspond to periods where both the plant and mycorrhiza growth rates and likely metabolism are tightly coupled.
The metabolism of a Berkshire and a Middle White pig has been investigated by means of the calorimeters at the School of Agriculture, Cambridge. The general routine and technique of the observations have been as heretofore.
Measurements of the fasting katabolism of each of the two pigs have been obtained in a series extending from an early age to maturity, and the phenomena in general follow the lines of those originally discovered in the Large White; but the fasting katabolism of the Middle White was below that of the Large White earlier studied.
The fall in body temperature and in metabolism during the fasts were found to be correlated, and the possible effect of skin colour in this matter is noted.
The effect of environmental temperature is investigated and reasons are given for supposing that the critical temperature of the Middle White pig is very low.
It is concluded that the existence of a maximum somewhere in the curve showing fasting katabolism per unit area at different ages is necessitated by the two physiological facts ( a ) that warm blooded animals have to be maintained at a temperature which varies only within very narrow limits, and ( b ) that the processes of growth are accompanied by waste of energy as heat.
Das Absinken des Energieumsatzes pro Masseneinheit im Laufe der Entwicklung hat man hauptschlich auf zweierlei Weise zu erklren versucht: einerseits durch die Annahme, es handle sich beim Energieumsatz nicht um eine Massen-, sondern um eine Flchenfunktion, anderseits durch die Annahme, es werde die lebende ttige Masse im engeren Sinne des Wortes, das Protoplasma, in fortschreitendem Ma\e durch eine im Stoffwechsel minder aktive Masse, das Paraplasma, ersetzt.Zur Flchenfunktionslehre wird im Vorstehenden ausgefhrt, da\ unter gewissen Voraussetzungen das Bestimmende weder die u\ere Haut- noch die eine oder andere innere Schleimhautoberflche sein knne, sondern eher die gesamte Assimilationsflche, das ist die Summe der Oberflchen aller am Stoffwechsel teilnehmenden Elemente und zwar nach Ma\gabe dieser Teilnahme — weiter, da\ die Struktur des Protoplasmas in diesem, mithin im Organismus berhaupt ein Flchensystem erblicken l\t.Zur Paraplasmalehre wird gezeigt, da\ — wieder unter gewissen und zwar biologisch begrndbaren Voraussetzungen — die fortschreitende Paraplasmierung den Umsatz der Gewichtseinheit in solchem Grade reduzieren mu\, da\ er als eine (allerdings unreine) Krperflchenfunktion erscheinen kann.
- Benedict
- Benedict
- Carman
- DuBois
- Krogh
- Kunde
- Lindhard
- Lusk
- Benedict
- Boothby
- Cowgill
- Grafe
Die Verteilung von Querschnitt, Widerstand, Druckgefälle und Strömungsgeschwindigkeit im Blutkreislauf
- Hess
- Horst
Die Gase des Körpers und der Gaswechsel
- Loewy
The science of nutrition
- G Lusk
- Mitchell
- Mitchell
- Mitchell