Mammalian Metabolic Allometry: Do Intraspecific Variation, Phylogeny, and Regression Models Matter?

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.

Phylogenetic analyses: comparing species to infer adaptations and physiological mechanisms

Comparisons among species have been a standard tool in animal physiology to understand how organisms function and adapt to their surrounding environment. During the last two decades, conceptual and methodological advances from different fields, including evolutionary biology and systematics, have revolutionized the way comparative analyses are performed, resulting in the advent of modern phylogenetic statistical methods. This development stems from the realization that conventional analytical methods assume that observations are statistically independent, which is not the case for comparative data because species often resemble each other due to shared ancestry. By taking evolutionary history explicitly into consideration, phylogenetic statistical methods can account for the confounding effects of shared ancestry in interspecific comparisons, improving the reliability of standard approaches such as regressions or correlations in comparative analyses. Importantly, these methods have also enabled researchers to address entirely new evolutionary questions, such as the historical sequence of events that resulted in current patterns of form and function, which can only be studied with a phylogenetic perspective. Here, we provide an overview of phylogenetic approaches and their importance for studying the evolution of physiological processes and mechanisms. We discuss the conceptual framework underlying these methods, and explain when and how phylogenetic information should be employed. We then outline the difficulties and limitations inherent to comparative approaches and discuss potential problems researchers may encounter when designing a comparative study. These issues are illustrated with examples from the literature in which the incorporation of phylogenetic information has been useful, or even crucial, for inferences on how species evolve and adapt to their surrounding environment.

A macrophysiological analysis of energetic constraints on geographic range size in mammals

Physiological processes are essential for understanding the distribution and abundance of organisms, and recently, with widespread attention to climate change, physiology has been ushered back to the forefront of ecological thinking. We present a macrophysiological analysis of the energetics of geographic range size using combined data on body size, basal metabolic rate (BMR), phylogeny and range properties for 574 species of mammals. We propose three mechanisms by which interspecific variation in BMR should relate positively to geographic range size: (i) Thermal Plasticity Hypothesis, (ii) Activity Levels/Dispersal Hypothesis, and (iii) Energy Constraint Hypothesis. Although each mechanism predicts a positive correlation between BMR and range size, they can be further distinguished based on the shape of the relationship they predict. We found evidence for the predicted positive relationship in two dimensions of energetics: (i) the absolute, mass-dependent dimension (BMR) and (ii) the relative, mass-independent dimension (MIBMR). The shapes of both relationships were similar and most consistent with that expected from the Energy Constraint Hypothesis, which was proposed previously to explain the classic macroecological relationship between range size and body size in mammals and birds. The fact that this pattern holds in the MIBMR dimension indicates that species with supra-allometric metabolic rates require among the largest ranges, above and beyond the increasing energy demands that accrue as an allometric consequence of large body size. The relationship is most evident at high latitudes north of the Tropics, where large ranges and elevated MIBMR are most common. Our results suggest that species that are most vulnerable to extinction from range size reductions are both large-bodied and have elevated MIBMR, but also, that smaller species with elevated MIBMR are at heightened risk. We also provide insights into the global latitudinal trends in range size and MIBMR and more general issues of phylogenetic and geographic scale.

New macroecological insights into functional constraints on mammalian geographical range size

Understanding the determinants of variation in the extent of species distributions is a fundamental goal of ecology. The diversity of geographical range sizes (GRSs) in mammals spans 12 orders of magnitude. A long-standing macroecological model of this diversity holds that as body size increases, species are increasingly restricted to occupying larger GRS. Here, we show that the body size-GRS relationship is more complex than previously recognized. Our study reveals that the positive relationship between body size and GRS does not hold across the entire size range of mammals. Instead, there is a break point in the relationship around the modal mammal body size. For species smaller than the mode, GRS actually decreases with body size. We discuss mechanisms to account for these observations in the context of the energetics of body size. We also examine the possibility that the patterns are the result of a statistical artefact from combining two random, uni-modal, skewed distributions, but conclude that the patterns we describe are not artefactual. Our results redefine our view of the functional relationship between body size, energetics and GRS in mammals with implications for assessing vulnerability to extinction resulting from range size reductions driven by large-scale environmental change.

Assessing the Jarman-Bell Principle: Scaling of intake, digestibility, retention time and gut fill with body mass in mammalian herbivores

Differences in allometric scaling of physiological characters have the appeal to explain species diversification and niche differentiation along a body mass (BM) gradient - because they lead to different combinations of physiological properties, and thus may facilitate different adaptive strategies. An important argument in physiological ecology is built on the allometries of gut fill (assumed to scale to BM(1.0)) and energy requirements/intake (assumed to scale to BM(0.75)) in mammalian herbivores. From the difference in exponents, it has been postulated that the mean retention time (MRT) of digesta should scale to BM(1.0-0.75)=BM(0.25). This has been used to argue that larger animals have an advantage in digestive efficiency and hence can tolerate lower-quality diets. However, empirical data does not support the BM(0.25) scaling of MRT, and the deduction of MRT scaling implies, according to physical principles, no scaling of digestibility; basing assumptions on digestive efficiency on the thus-derived MRT scaling amounts to circular reasoning. An alternative explanation considers a higher scaling exponent for food intake than for metabolism, allowing larger animals to eat more of a lower quality food without having to increase digestive efficiency; to date, this concept has only been explored in ruminants. Here, using data for 77 species in which intake, digestibility and MRT were measured (allowing the calculation of the dry matter gut contents (DMC)), we show that the unexpected shallow scaling of MRT is common in herbivores and may result from deviations of other scaling exponents from expectations. Notably, DMC have a lower scaling exponent than 1.0, and the 95% confidence intervals of the scaling exponents for intake and DMC generally overlap. Differences in the scaling of wet gut contents and dry matter gut contents confirm a previous finding that the dry matter concentration of gut contents decreases with body mass, possibly compensating for the less favorable volume-surface ratio in the guts of larger organisms. These findings suggest that traditional explanations for herbivore niche differentiation along a BM gradient should not be based on allometries of digestive physiology. In contrast, they support the recent interpretation that larger species can tolerate lower-quality diets because their intake has a higher allometric scaling than their basal metabolism, allowing them to eat relatively more of a lower quality food without having to increase digestive efficiency.

An information-theoretic approach to evaluating the size and temperature dependence of metabolic rate

The effects of body mass and temperature on metabolic rate (MR) are among the most widely examined physiological relationships. Recently, these relationships have been incorporated into the metabolic theory of ecology (MTE) that links the ecology of populations, communities and ecosystems to the MR of individual organisms. The fundamental equation of MTE derives the relation between mass and MR using first principles and predicts the temperature dependence of MR based on biochemical kinetics. It is a deliberately simple, zeroth-order approximation that represents a baseline against which variation in real biological systems can be examined. In the present study, we evaluate the fundamental equation of MTE against other more parameter-rich models for MR using an information-theoretic approach to penalize the inclusion of additional parameters. Using a comparative database of MR measurements for 1359 species, from 11 groups ranging from prokaryotes to mammals, and spanning 16 orders of magnitude in mass and a 59°C range in body temperature, we show that differences between taxa in the mass and temperature dependence of MR are sufficiently large as to be retained in the best model for MR despite the requirement for estimation of 22 more parameters than the fundamental equation of MTE.

Gravity and the evolution of cardiopulmonary morphology in snakes

Physiological investigations of snakes have established the importance of heart position and pulmonary structure in contexts of gravity effects on blood circulation. Here we investigate morphological correlates of cardiopulmonary physiology in contexts related to ecology, behavior and evolution. We analyze data for heart position and length of vascular lung in 154 species of snakes that exhibit a broad range of characteristic behaviors and habitat associations. We construct a composite phylogeny for these species, and we codify gravitational stress according to species habitat and behavior. We use conventional regression and phylogenetically independent contrasts to evaluate whether trait diversity is correlated with gravitational habitat related to evolutionary transitions within the composite tree topology. We demonstrate that snake species living in arboreal habitats, or which express strongly climbing behaviors, possess relatively short blood columns between the heart and the head, as well as relatively short vascular lungs, compared to terrestrial species. Aquatic species, which experience little or no gravity stress in water, show the reverse - significantly longer heart-head distance and longer vascular lungs. These phylogenetic differences complement the results of physiological studies and are reflected in multiple habitat transitions during the evolutionary histories of these snake lineages, providing strong evidence that heart-to-head distance and length of vascular lung are co-adaptive cardiopulmonary features of snakes.

Phylogenetic differences of mammalian basal metabolic rate are not explained by mitochondrial basal proton leak

Metabolic rates of mammals presumably increased during the evolution of endothermy, but molecular and cellular mechanisms underlying basal metabolic rate (BMR) are still not understood. It has been established that mitochondrial basal proton leak contributes significantly to BMR. Comparative studies among a diversity of eutherian mammals showed that BMR correlates with body mass and proton leak. Here, we studied BMR and mitochondrial basal proton leak in liver of various marsupial species. Surprisingly, we found that the mitochondrial proton leak was greater in marsupials than in eutherians, although marsupials have lower BMRs. To verify our finding, we kept similar-sized individuals of a marsupial opossum (Monodelphis domestica) and a eutherian rodent (Mesocricetus auratus) species under identical conditions, and directly compared BMR and basal proton leak. We confirmed an approximately 40 per cent lower mass specific BMR in the opossum although its proton leak was significantly higher (approx. 60%). We demonstrate that the increase in BMR during eutherian evolution is not based on a general increase in the mitochondrial proton leak, although there is a similar allometric relationship of proton leak and BMR within mammalian groups. The difference in proton leak between endothermic groups may assist in elucidating distinct metabolic and habitat requirements that have evolved during mammalian divergence.

Industrial energy use and the human life history

The demographic rates of most organisms are supported by the consumption of food energy, which is used to produce new biomass and fuel physiological processes. Unlike other species, modern humans use ‘extra-metabolic' energy sources acquired independent of physiology, which also influence demographics. We ask whether the amount of extra-metabolic energy added to the energy budget affects demographic and life history traits in a predictable way. Currently it is not known how human demographics respond to energy use, and we characterize this response using an allometric approach. All of the human life history traits we examine are significant functions of per capita energy use across industrialized populations. We find a continuum of traits from those that respond strongly to the amount of extra-metabolic energy used, to those that respond with shallow slopes. We also show that the differences in plasticity across traits can drive the net reproductive rate to below-replacement levels.

Modeling hippocampal neurogenesis across the lifespan in seven species

The aim of this study was to estimate the number of new cells and neurons added to the dentate gyrus across the lifespan, and to compare the rate of age-associated decline in neurogenesis across species. Data from mice (Mus musculus), rats (Rattus norvegicus), lesser hedgehog tenrecs (Echinops telfairi), macaques (Macaca mulatta), marmosets (Callithrix jacchus), tree shrews (Tupaia belangeri), and humans (Homo sapiens) were extracted from 21 data sets published in 14 different reports. Analysis of variance (ANOVA), exponential, Weibull, and power models were fit to the data to determine which best described the relationship between age and neurogenesis. Exponential models provided a suitable fit and were used to estimate the relevant parameters. The rate of decrease of neurogenesis correlated with species longevity (r = 0.769, p = 0.043), but not body mass or basal metabolic rate. Of all the cells added postnatally to the mouse dentate gyrus, only 8.5% (95% confidence interval [CI], 1.0% to 14.7%) of these will be added after middle age. In addition, only 5.7% (95% CI 0.7% to 9.9%) of the existing cell population turns over from middle age and onward. Thus, relatively few new cells are added for much of an animal's life, and only a proportion of these will mature into functional neurons.

Scaling dynamic response and destructive metabolism in an immunosurveillant anti-tumor system modulated by different external periodic interventions

On the basis of two universal power-law scaling laws, i.e. the scaling dynamic hysteresis in physics and the allometric scaling metabolism in biosystem, we studied the dynamic response and the evolution of an immunosurveillant anti-tumor system subjected to a periodic external intervention, which is equivalent to the scheme of a radiotherapy or chemotherapy, within the framework of the growth dynamics of tumor. Under the modulation of either an abrupt or a gradual change external intervention, the population density of tumors exhibits a dynamic hysteresis to the intervention. The area of dynamic hysteresis loop characterizes a sort of dissipative-therapeutic relationship of the dynamic responding of treated tumors with the dose consumption of accumulated external intervention per cycle of therapy. Scaling the area of dynamic hysteresis loops against the intensity of an external intervention, we deduced a characteristic quantity which was defined as the theoretical therapeutic effectiveness of treated tumor and related with the destructive metabolism of tumor under treatment. The calculated dose-effectiveness profiles, namely the dose cumulant per cycle of intervention versus the therapeutic effectiveness, could be well scaled into a universal quadratic formula regardless of either an abrupt or a gradual change intervention involved. We present a new concept, i.e., the therapy-effect matrix and the dose cumulant matrix, to expound the new finding observed in the growth and regression dynamics of a modulated anti-tumor system.

A general basis for quarter-power scaling in animals

It has been known for decades that the metabolic rate of animals scales with body mass with an exponent that is almost always <1, >2/3, and often very close to 3/4. The 3/4 exponent emerges naturally from two models of resource distribution networks, radial explosion and hierarchically branched, which incorporate a minimum of specific details. Both models show that the exponent is 2/3 if velocity of flow remains constant, but can attain a maximum value of 3/4 if velocity scales with its maximum exponent, 1/12. Quarter-power scaling can arise even when there is no underlying fractality. The canonical "fourth dimension" in biological scaling relations can result from matching the velocity of flow through the network to the linear dimension of the terminal "service volume" where resources are consumed. These models have broad applicability for the optimal design of biological and engineered systems where energy, materials, or information are distributed from a single source.

Curvature in metabolic scaling

For more than three-quarters of a century it has been assumed that basal metabolic rate increases as body mass raised to some power p. However, there is no broad consensus regarding the value of p: whereas many studies have asserted that p is 3/4 (refs 1-4; 'Kleiber's law'), some have argued that it is 2/3 (refs 5-7), and others have found that it varies depending on factors like environment and taxonomy. Here we show that the relationship between mass and metabolic rate has convex curvature on a logarithmic scale, and is therefore not a pure power law, even after accounting for body temperature. This finding has several consequences. First, it provides an explanation for the puzzling variability in estimates of p, settling a long-standing debate. Second, it constitutes a stringent test for theories of metabolic scaling. A widely debated model based on vascular system architecture fails this test, and we suggest modifications that could bring it into compliance with the observed curvature. Third, it raises the intriguing question of whether the scaling relation limits body size.

Maximal heat dissipation capacity and hyperthermia risk: neglected key factors in the ecology of endotherms

1. The role of energy in ecological processes has hitherto been considered primarily from the standpoint that energy supply is limited. That is, traditional resource-based ecological and evolutionary theories and the recent 'metabolic theory of ecology' (MTE) all assume that energetic constraints operate on the supply side of the energy balance equation. 2. For endothermic animals, we provide evidence suggesting that an upper boundary on total energy expenditure is imposed by the maximal capacity to dissipate body heat and therefore avoid the detrimental consequences of hyperthermia--the heat dissipation limit (HDL) theory. We contend that the HDL is a major constraint operating on the expenditure side of the energy balance equation, and that processes that generate heat compete and trade-off within a total boundary defined by heat dissipation capacity, rather than competing for limited energy supply. 3. The HDL theory predicts that daily energy expenditure should scale in relation to body mass (M(b)) with an exponent of about 0.63. This contrasts the prediction of the MTE of an exponent of 0.75. 4. We compiled empirical data on field metabolic rate (FMR) measured by the doubly-labelled water method, and found that they scale to M(b) with exponents of 0.647 in mammals and 0.658 in birds, not significantly different from the HDL prediction (P > 0.05) but lower than predicted by the MTE (P < 0.001). The same statistical result was obtained using phylogenetically independent contrasts analysis. Quantitative predictions of the model matched the empirical data for both mammals and birds. There was no indication of curvature in the relationship between Log(e) FMR and Log(e)M(b). 5. Together, these data provide strong support for the HDL theory and allow us to reject the MTE, at least when applied to endothermic animals. 6. The HDL theory provides a novel conceptual framework that demands a reframing of our views of the interplay between energy and the environment in endothermic animals, and provides many new interpretations of ecological and evolutionary phenomena.

Scaling of basal metabolic rate with body mass and temperature in mammals

1. We present a statistical analysis of the scaling of resting (basal) metabolic rate, BMR, with body mass, B(m) and body temperature, T(b), in mammals. 2. Whilst the majority of the variance in ln BMR is explained by ln B(m), the T(b) term is statistically significant. The best fit model was quadratic, indicating that the scaling of ln BMR with ln B(m) varies with body size; the value of any scaling exponent estimated for a sample of mammals will therefore depend on the size distribution of species in the study. This effect can account for much of the variation in scaling exponents reported in the literature for mammals. 3. In all models, inclusion of T(b) reduced the strength of scaling with ln B(m). The model including T(b) suggests that birds and mammals have a similar underlying thermal dependence of BMR, equivalent to a Q(10) of 2.9 across the range of T(b) values 32-42 degrees C. 4. There was significant heterogeneity in both the mass scaling exponent and mean BMR across mammalian orders, with a tendency for orders dominated by larger taxa to have steeper scaling exponents. This heterogeneity was particularly marked across orders with smaller mean B(m) and the taxonomic composition of the sample will thus also affect the observed scaling exponent. After correcting for the effects of ln B(m) and T(b), Soricomorpha, Didelphimorphia and Artiodactyla had the highest BMR of those orders represented by more than 10 species in the data set. 5. Inclusion of T(b) in the model removed the effect of diet category evident from a model in ln B(m) alone and widely reported in the literature; this was caused by a strong interaction between diet category and T(b) in mammals. 6. Inclusion of mean ambient temperature, T(a), in the model indicated a significant inverse relationship between ln BMR and T(a), complicated by an interaction between T(a) and T(b). All other things being equal, a polar mammal living at -10 degrees C has a body temperature approximately 2.7 degrees C warmer and a BMR higher by approximately 40% than a tropical mammal of similar size living at 25 degrees C.