Evidence for a Mass Dependent Step-Change in the Scaling of Efficiency in Terrestrial Locomotion

A reanalysis of existing data suggests that the established tenet of increasing efficiency of transport with body size in terrestrial locomotion requires re-evaluation. Here, the statistical model that described the data best indicated a dichotomy between the data for small (<1 kg) and large animals (>1 kg). Within and between these two size groups there was no detectable difference in the scaling exponents (slopes) relating metabolic (E _met) and mechanical costs (E _{mech, CM}) of locomotion to body mass (M _b). Therefore, no scaling of efficiency (E _{mech, CM}/E _met) with M _b was evident within each size group. Small animals, however, appeared to be generally less efficient than larger animals (7% and 26% respectively). Consequently, it is possible that the relationship between efficiency and M _b is not continuous, but, rather, involves a step-change. This step-change in the efficiency of locomotion mirrors previous findings suggesting a postural cause for an apparent size dichotomy in the relationship between E _met and M _b. Currently data for E _{mech, CM} is lacking, but the relationship between efficiency in terrestrial locomotion and M _b is likely to be determined by posture and kinematics rather than body size alone. Hence, scaling of efficiency is likely to be more complex than a simple linear relationship across body sizes. A homogenous study of the mechanical cost of terrestrial locomotion across a broad range of species, body sizes, and importantly locomotor postures is a priority for future research.     

Intraspecific Scaling of the Resting and Maximum Metabolic Rates of the Crucian Carp (Carassius auratus)

The question of how the scaling of metabolic rate with body mass (M) is achieved in animals is unresolved. Here, we tested the cell metabolism hypothesis and the organ size hypothesis by assessing the mass scaling of the resting metabolic rate (RMR), maximum metabolic rate (MMR), erythrocyte size, and the masses of metabolically active organs in the crucian carp (Carassius auratus). The M of the crucian carp ranged from 4.5 to 323.9 g, representing an approximately 72-fold difference. The RMR and MMR increased with M according to the allometric equations RMR = 0.212M ^0.776 and MMR = 0.753M ^0.785. The scaling exponents for RMR (b _r) and MMR (b _m) obtained in crucian carp were close to each other. Thus, the factorial aerobic scope remained almost constant with increasing M. Although erythrocyte size was negatively correlated with both mass-specific RMR and absolute RMR adjusted to M, it and all other hematological parameters showed no significant relationship with M. These data demonstrate that the cell metabolism hypothesis does not describe metabolic scaling in the crucian carp, suggesting that erythrocyte size may not represent the general size of other cell types in this fish and the metabolic activity of cells may decrease as fish grows. The mass scaling exponents of active organs was lower than 1 while that of inactive organs was greater than 1, which suggests that the mass scaling of the RMR can be partly due to variance in the proportion of active/inactive organs in crucian carp. Furthermore, our results provide additional evidence supporting the correlation between locomotor capacity and metabolic scaling.     

Downsizing a giant: re-evaluating Dreadnoughtus body mass

Estimates of body mass often represent the founding assumption on which biomechanical and macroevolutionary hypotheses are based. Recently, a scaling equation was applied to a newly discovered titanosaurian sauropod dinosaur (Dreadnoughtus), yielding a 59 300 kg body mass estimate for this animal. Herein, we use a modelling approach to examine the plausibility of this mass estimate for Dreadnoughtus. We find that 59 300 kg for Dreadnoughtus is highly implausible and demonstrate that masses above 40 000 kg require high body densities and expansions of soft tissue volume outside the skeleton several times greater than found in living quadrupedal mammals. Similar results from a small sample of other archosaurs suggests that lower-end mass estimates derived from scaling equations are most plausible for Dreadnoughtus, based on existing volumetric and density data from extant animals. Although volumetric models appear to more tightly constrain dinosaur body mass, there remains a clear need to further support these models with more exhaustive data from living animals. The relative and absolute discrepancies in mass predictions between volumetric models and scaling equations also indicate a need to systematically compare predictions across a wide size and taxonomic range to better inform studies of dinosaur body size.     

Low scaling of a life history variable: Analysing eutherian gestation periods with and without phylogeny-informed statistics

Traditionally, biological times (gestation period, longevity) are proposed to scale to body mass M as M^0.25. Although phylogeny-informed statistics have become widespread, it is still sometimes assumed that in datasets comprising a very large number of species, analyses that do not and that do account for phylogeny will yield similar results. Here we show, in a large dataset on gestation period length in eutherian mammals (1214 species from 20 orders), that the allometric scaling exponent is about twice as high using conventional statistics (ordinary least squares OLS, M^0.18–0.20) as when using phylogenetic generalised least squares (PGLS, M^0.07–0.10), indicating that among closely related taxa, the scaling of gestation is much lower than generally assumed. This matches the well-known absence of scaling among different-sized breeds of domestic animal species, and indicates that changes in M must be more related to changes in development speed rather than development time among closely related species, which has implications for interpreting life history-consequences of insular dwarfism and gigantism. Only when allowing just one species per order (simulated in 100 randomised datasets of n = 20 species across 20 orders) is 0.25 included in the scaling exponent confidence interval in both OLS and PGLS. Differences in scaling at different taxonomic levels in comparative datasets may indicate evolutionary trends where successive taxonomic groups compete by fundamental variation in organismal design not directly linked to changes in M. Allometries then do not necessarily represent universal scaling rules, but snapshots of evolutionary time that depend on diversification and extinction events before the picture was taken. It is either by analysing subsets separately, or by using PGLS in large datasets, that the underlying relationships with M can then be unveiled.     

Morphometric relationships of the caridean shrimp Nauticaris marionis Bate, 1888 at the Prince Edward Islands (Southern Ocean)

The relationships between three measurements of body size (carapace length, total body length and eye diameter) and three measurements of mass (wet, dry and ash-free dry weights) of the caridean shrimp Nauticaris marionis are presented. It is argued that a precisely defined carapace length is the most accurate indicator of body size. A conversion formula relating carapace length to total body length is also provided, as are conversion equations relating the different measures of mass. Accepted: 17 May 1999     

Circulation,metabolic rate,and body size in mammals

Summary This paper attempts to explain Kleiber's rule, which relates metabolic rate of mammals to their body mass, from the structure and function of the blood circulation system.Abbreviations a scaling factor - fractal dimension - hydrodynamic conductivity - l _n length of an arterial blood vessel at bifurcation level n - M body mass - N maximal number of bifurcation levels - p pressure - Q flow - r size of Bohr effect - r _n radius of an arterial blood vessel at bifurcation level n - V volume - VO ₂ rate of oxygen unloading - Z _n number of arterial blood vessels at bifurcation level n     

Application of leaf size and leafing intensity scaling across subtropical trees

Understanding the scaling between leaf size and leafing intensity (leaf number per stem size) is crucial for comprehending theories about the leaf costs and benefits in the leaf size–twig size spectrum. However, the scaling scope of leaf size versus leafing intensity changes along the twig leaf size variation in different leaf habit species remains elusive. Here, we hypothesize that the numerical value of scaling exponent for leaf mass versus leafing intensity in twig is governed by the minimum leaf mass versus maximum leaf mass (M _min versus M _max) and constrained to be ≤−1.0. We tested this hypothesis by analyzing the twigs of 123 species datasets compiled in the subtropical mountain forest. The standardized major axis regression (SMA) analyses showed the M _min scaled as the 1.19 power of M _max and the ‐α (−1.19) were not statistically different from the exponents of M _min versus leafing intensity in whole data. Across leaf habit groups, the M _max scaled negatively and isometrically with respect to leafing intensity. The pooled data''s scaling exponents ranged from −1.14 to −0.96 for M _min and M _max versus the leafing intensity based on stem volume (LIV). In the case of M _min and M _max versus the leafing intensity based on stem mass (LIM), the scaling exponents ranged from −1.24 to −1.04. Our hypothesis successfully predicts that the scaling relationship between leaf mass and leafing intensity is constrained to be ≤−1.0. More importantly, the lower limit to scaling of leaf mass and leafing intensity may be closely correlated with M _min versus M _max. Besides, constrained by the maximum leaf mass expansion, the broad scope range between leaf size and number may be insensitive to leaf habit groups in subtropical mountain forest.     

Effect of sensitivity to abscisic acid on scaling relationships for biomass production rates and body size in Arabidopsis thaliana

The allometric relationships for plant daily biomass production rates, different measures of body size (dry weight and length) and photosynthetic biomass per plant are reported for two mutants of Arabidopsis thaliana (abi1-1, insensitive to ABA; era1-2, hypersensitive to ABA). Scaling relationships, such as daily rate of growth (G) vs body mass (M), plant body length or plant height (L) vs body mass (M), photosynthetic biomass (M _p ) vs non-photosynthetic biomass (M _n ), and daily rate of growth (G) vs. photosynthetic biomass (M _p ) were significantly different in abi1-1 and era1-2. It is implied that the sensitivity to abscisic acid may change the scaling relationships for plant biomass production rate and body size in Arabidopsis thaliana. Because these scaling relationships are closely related to sensitivity to abscisic acid, they are of importance for phytohormonal ecology.     

Scaling body mass and use of space in three species of marsupials in the Atlantic Forest of Brazil

Abstract Body mass is considered a major determinant of home range size, but usually at a large scale of body mass variation. The exact scale where body size becomes more important than particular adaptations of each species is not clear, and uncertainty in the estimate of home range size is a possible cause of weak intraspecific scaling. We determine the scaling to body mass of two alternative movement measurements, daily home range (DHR) and its intensity of use (IU), in three species of didelphid marsupials, Didelphis aurita, Philander frenatus, and Metachirus nudicaudatus (Didelphimorphia, Didelphidae). The expected scaling exponents DHR ≈ M^0.5 and IU ≈ M^?0.25 were derived from the scaling to body mass of home range and daily movement distance. Animals were tracked in Serra dos Órgãos, Rio de Janeiro, Brazil, using a spool‐and‐line device. Individuals of the three species were compared combining intra and interspecific variation in a single analysis, with species, body mass, and thread tracked as covariates. The model best supported included only body mass as the independent variable, with DHR ≈ M^0.435 and IU ≈ M^?0.218, close to the expected values. The second best supported model included species identity, but with a non‐significant effect. It was surprising that body mass was more important than species identity in a comparison involving only three species, and considering the morphological and locomotory adaptations of the three species. Body mass may become more important than species identity when the scale of variation approaches one order of magnitude.     

Scaling aspects of lymphocyte trafficking

We consider the long lived pool of B and T cells that recirculate through blood, tissues and the lymphatic system of an animal with body mass M. We derive scaling rules (allometric relations) for: (1) the rate of production of mature lymphocytes, (2) the accumulation of lymphocytes in the tissues, (3) the flux of lymphocytes through the lymphatic system, (4) the number of lymph nodes, (5) the number of lymphocytes per clone within a lymph node, and (6) the total number of lymphocytes within a lymph node. Mass-dependent aspects of immune learning and of the immunological self are shown to be not very significant. Our treatment is somewhat heuristic and aims at combining immunological data with recent progress in biological scaling.     

The scaling of ground reaction forces and duty factor in monitor lizards: implications for locomotion in sprawling tetrapods

Geometric scaling predicts a major challenge for legged, terrestrial locomotion. Locomotor support requirements scale identically with body mass (α M¹), while force-generation capacity should scale α M^2/3 as it depends on muscle cross-sectional area. Mammals compensate with more upright limb postures at larger sizes, but it remains unknown how sprawling tetrapods deal with this challenge. Varanid lizards are an ideal group to address this question because they cover an enormous body size range while maintaining a similar bent-limb posture and body proportions. This study reports the scaling of ground reaction forces and duty factor for varanid lizards ranging from 7 g to 37 kg. Impulses (force×time) (α M^0.99−1.34) and peak forces (α M^0.73−1.00) scaled higher than expected. Duty factor scaled α M^0.04 and was higher for the hindlimb than the forelimb. The proportion of vertical impulse to total impulse increased with body size, and impulses decreased while peak forces increased with speed.     

Allometry of the Duration of Flight Feather Molt in Birds

We used allometric scaling to explain why the regular replacement of the primary flight feathers requires disproportionately more time for large birds. Primary growth rate scales to mass (M) as M^0.171, whereas the summed length of the primaries scales almost twice as fast (M^0.316). The ratio of length (mm) to rate (mm/day), which would be the time needed to replace all the primaries one by one, increases as the 0.14 power of mass (M^0.316/M^0.171=M^0.145), illustrating why the time required to replace the primaries is so important to life history evolution in large birds. Smaller birds generally replace all their flight feathers annually, but larger birds that fly while renewing their primaries often extend the primary molt over two or more years. Most flying birds exhibit one of three fundamentally different modes of primary replacement, and the size distributions of birds associated with these replacement modes suggest that birds that replace their primaries in a single wave of molt cannot approach the size of the largest flying birds without first transitioning to a more complex mode of primary replacement. Finally, we propose two models that could account for the 1/6 power allometry between feather growth rate and body mass, both based on a length-to-surface relationship that transforms the linear, cylindrical growing region responsible for producing feather tissue into an essentially two-dimensional structure. These allometric relationships offer a general explanation for flight feather replacement requiring disproportionately more time for large birds.     

A Phenomenological Theory of Muscular Contraction: II. Generalized Length Variations

In part I of this series, the theory of irreversible thermodynamics was applied to the sliding filament model to obtain rate equations for a contracting muscle at the in situ length l_o. In this paper we extend the theory to include length variations derived from the sliding filament model of contracting muscle using the work of Gordon, Huxley, and Julian (1). Accepting the validity of Hill's forcevelocity relation (2) at the in situ length, we show that Hill's equation is valid for any length provided that the values of the parameters, a, b, and V_m vary with length as derived herein. The predicted variation with length of the velocity for a lightly loaded isotonic contraction is shown to agree well with that measured by Gordon, Huxley, and Julian (1). Chemical rates are derived as functions of length using parameters that can be obtained experimentally.     

Shape shifting predicts ontogenetic changes in metabolic scaling in diverse aquatic invertebrates

Metabolism fuels all biological activities, and thus understanding its variation is fundamentally important. Much of this variation is related to body size, which is commonly believed to follow a 3/4-power scaling law. However, during ontogeny, many kinds of animals and plants show marked shifts in metabolic scaling that deviate from 3/4-power scaling predicted by general models. Here, we show that in diverse aquatic invertebrates, ontogenetic shifts in the scaling of routine metabolic rate from near isometry (b_R = scaling exponent approx. 1) to negative allometry (b_R < 1), or the reverse, are associated with significant changes in body shape (indexed by b_L = the scaling exponent of the relationship between body mass and body length). The observed inverse correlations between b_R and b_L are predicted by metabolic scaling theory that emphasizes resource/waste fluxes across external body surfaces, but contradict theory that emphasizes resource transport through internal networks. Geometric estimates of the scaling of surface area (SA) with body mass (b_A) further show that ontogenetic shifts in b_R and b_A are positively correlated. These results support new metabolic scaling theory based on SA influences that may be applied to ontogenetic shifts in b_R shown by many kinds of animals and plants.     

Characterization of uptake and release processes ford- andl-aspartate in primary cultures of astrocytes and cerebellar granule cells

The uptake ofl-andd-aspartate was studied in astrocytes cultured from prefrontal cortex and in granule cells cultured from cerebellum. A high affinity uptake system forl- andd-aspartate was found in both cell types, and the two stereoisomers exhibited essentially the sameK _m - andV _max -values in bouth astrocytes (l-aspartate:K _m 77 μM;V _max 11.8 nmol×min^?1×mg^?1;d-aspartate:K _m 83 μM;V _max 14.0 nmol×min^?1×mg^?1) and granule cells (l-aspartate:K _m 32 μM;V _max 2.8 nmol ×min^?1×mg^?1;d-aspartate:K _m 26 μM;V _max 3.0 nmol×min^?1×mg^?1). To investigate whetherl-glutamate,l-aspartate andd-aspartate use the same uptake system a detailed kenetic analysis was performed. The uptake kinetics of each one of the three amino acids was studied in the presence of the two other amino acids, and no essential differences between the uptake characteristics of the amino acids were found. In addition to the uptake studies the release ofD-aspartate from cerebellar granule cells was investigated and compared withl-glutamate release. A Ca²⁺-dependent, K⁺-induced release was found for both amino acids.     

Characterization of prolidase I and II purified from normal human erythrocytes: comparison with prolidase in erythrocytes from a patient with prolidase deficiency

The effect of various sulfur-containing amino acids on the activities of prolidase isoenzymes I and II isolated from erythrocytes of healthy individuals, and erythrocyte lysates from a patient with prolidase deficiency was investigated. The activity of prolidase I against glycylproline was strongly enhanced by d-methionine. l-Methionine and d,l-methionine slightly enhanced the activity at low concentration, but N-acetyl-l-methionine had no effect. d-Ethionine, l-ethionine, and d,l-ethionine also enhanced the activity of prolidase I. d,l-Homocysteine enhanced the activity at low concentration, but inhibited the activity at 50 mM. The activity of prolidase II against methionylproline was enhanced by d-methionine, d,l-methionine, and l-methionine, but N-acetyl-l-methionine had no effect. d-Ethionine and d,l-ethionine strongly enhanced the activity of prolidase II compared with l-ethionine; d,l-homocysteine weakly enhanced the activity. d,l-Homocysteine-thiolactone inhibited the activities of prolidase I and II in a concentration-dependent manner. The effect of various sulfur-containing amino acids on prolidase activity against methionylproline in erythrocyte lysates from a patient with prolidase deficiency was almost the same as that on prolidase II. The kinetics of the activities of prolidase I, II, and patient prolidase were also studied. Their K _m values were changed by adding sulfur-containing amino acids, but V _max values were unchanged.     

Body size and its consequences: Allometry and the lower limb length of Liang Bua 1 (Homo floresiensis)

Bivariate femoral length allometry in recent humans, Pan, and Gorilla is investigated with special reference to the diminutive Liang Bua (LB) 1 specimen (the holotype of Homo floresiensis) and six early Pleistocene femora referred to the genus Homo. Relative to predicted body mass, Pan and Gorilla femora show strong negative length allometry while recent human femora evince isometry to positive allometry, depending on sample composition and line-fitting technique employed. The allometric trajectories of Pan and Homo show convergence near the small body size range of LB 1, such that LB 1 manifests a low percentage deviation (d_yx of Smith [1980]) from the Pan allometric trajectory and falls well within the 95% confidence limits around the Pan individuals (but also outside the 95% confidence limits for recent Homo). In contrast, the six early Pleistocene Homo femora, belonging to larger individuals, show much greater d_yx values from both Pan and Gorilla and fall well above the 95% confidence limits for these taxa. All but one of these Pleistocene Homo specimens falls within the 95% confidence limits of the recent human sample. Similar results are obtained when femoral length is regressed on femoral head diameter in unlogged bivariate space. Regardless of the ultimate taxonomic status of LB 1, these findings are consistent with a prediction made by us (Franciscus and Holliday, 1992) that hominins in the small body size range of A.L. 288-1 (“Lucy”), including members of the genus Homo, will tend to possess short, ape-like lower limbs as a function of body size scaling.     

Ontogenetic changes in the scaling of cellular respiration with respect to size among sunflower seedlings

The respiration rates R (oxygen uptake per min) and body mass M (mg per individual) of sunflower (Helianthus annuus L.) seedlings were measured for populations raised in the dark (scotomorphogenesis) and for plants subsequently grown in white light (photomorphogenesis) to determine the allometric (scaling) relationship for R vs. M. Based on ordinary least squares and reduced major axis regression protocols, cellular respiration rates were found to increase non-linearly as a ‘broken-stick’ curve of increasing M. During germination, the scaling was ca. 7.5-fold higher than after the emergence of the cotyledons from the seed coat, which can be attributed to the hypoxic conditions of the enclosed embryo. During seedling development, R was found to scale roughly as the 3/7 power of body mass (i.e., R ∼ M^−3/7), regardless of whether plants were grown in the dark or subsequently in white light. The numerical value of 3/7 statistically significantly differs from that reported across small field- or laboratory-grown plants (i.e., R ∼ M^−1.0). It also differs from the expectations of recent allometric theory (i.e., R ∼ M^−0.75 to M^−1.0). This difference is interpreted to be the result of species-specific tissue-compositions that affect the volume fractions of metabolically active and less active cells. These findings, which are supported by cytological and ultrastructural observations (i.e., scanning- and transmission electron micrographs), draw attention to the need to measure R of developing plants in a tissue- or organ-specific context.Key words: dark respiration, metabolic scaling, photomorphogenesis, oxygen uptake, skotomorphogenesis     

Maximum ingested food size in captive strepsirrhine primates: Scaling and the effects of diet

Little is known about ingested food size (V_b) in primates, even though this variable has potentially important effects on food intake and processing. This study provides the first data on V_b in strepsirrhine primates using a captive sample of 17 species. These data can be used for generating and testing models of feeding energetics. Strepsirrhines are of interest because they are hypometabolic and chewing rate and daily feeding time do not show a significant scaling relationship with body size. Using melon, carrot, and sweet potato we found that maximum V_b scales isometrically with body mass and mandible length. Low dietary quality in larger strepsirrhines might explain why V_b increases with body size at a greater rate than does resting metabolic rate. Relative to body size, V_b is large in frugivores but small in folivores; furthermore scaling slopes are higher in frugivores than in folivores. A gross estimate of dietary quality explains much of the variation in V_b that is not explained by body size. Gape adaptations might favor habitually large bites for frugivores and small ones for folivores. More data are required for several feeding variables and for wild populations. Am J Phys Anthropol 142:625–635, 2010. © 2010 Wiley‐Liss, Inc.     

The theoretical possibility of reverse translation of proteins into genes

It is shown on a theoretical basis that the existence of a “power law” relationship between body mass M and total metabolic heat generation rate Q of the form Q = kM^α does not uniquely determine the dependence of metabolic rate on body temperature. However, it is shown that a particular assumption for this temperature dependence, successful in other problems, does predict a “power law” similar to the empirical one. At the same time it also accounts satisfactorily for the linear dependence of metabolic rate on ambient temperature.