Testing the allometric scaling laws

Allometric scaling laws have received increasing attention due to the recent theoretical advancements. However, existing evidence suggests that the scaling relationships may vary a lot without much consistency, which poses a challenge to the applicability of general theories. In this report, I demonstrate that much of the discrepancy may be an artefact caused by the limited use of methods for estimating the parameters in the allometric scaling equations. I suggest alternative procedures that can be utilized to avoid biased interpretations. The comments are largely applicable to any research that involves parameterization of equations.     

Pharmacokinetic allometric scaling of oligonucleotides

The objective of this study was to evaluate the predictive performance of interspecies scaling of oligonucleotides to predict clearance and volume of distribution at steady state in humans from animal data. The human pharmacokinetic parameters were predicted using 1, 2, or at least 3 animal species. The results of the study indicated that the pharmacokinetic parameters of oligonucleotides can be predicted with reasonable accuracy in humans when at least 3 animal species are employed. On the other hand, allometric scaling based on 1 or 2 species or fixed coefficient or fixed exponent can be erratic and unreliable. Further work should be conducted in this direction.     

Genetic mapping of allometric scaling laws

Many biological processes, from cellular metabolism to population dynamics, are characterized by particular allometric scaling relationships between rate and size (power laws). A statistical model for mapping specific quantitative trait loci (QTLs) that are responsible for allometric scaling laws has been developed. We present an improved model for allometric mapping of QTLs based on a more general allometry equation. This improved model includes two steps: (1) use model II regression analysis to estimate the parameters underlying universal allometric scaling laws, and (2) substitute the estimated allometric parameters in the mixture-based mapping model to obtain the estimation of QTL position and effects. This model has been validated by a real example for a mouse F2 progeny, in which two QTLs were detected on different chromosomes that determine the allometric relationship between growth rate and body weight.     

How allometric scaling relates to soil abiotics

For most species, the logarithm of their average body mass is negatively related to the logarithm of their relative population density, i.e. the numerical abundance. In this way, the allometric scaling (both mass–abundance regressions and body–size spectra) becomes useful in ecological theory to build and explain food webs. Using empirical evidence derived from 145 Dutch sites, a hypothesis is formulated to explain how soil microbivores, detritivores and predators react to increasing resource availability. Shifts in size distribution, and subsequently changes in soil food‐web structure, are further discussed in the perspective of Holling's sequential interactions between basic system functions. We show that the allometric scaling and the averages of the (log‐transformed) prey:predator body‐mass ratios are reliable predictors for assessing faunal responses to nutrient availability. We view this work as a first attempt toward an extensive comparison of ecological processes in different soil systems.     

The origin of allometric scaling laws in biology

The empirical rules relating metabolic rate and body size are described in terms of (i) a scaling exponent, which refers to the ratio of the fractional change in metabolic rate to a change in body size, (ii) a proportionality constant, which describes the rate of energy expenditure in an organism of unit mass. This article integrates the chemiosmotic theory of energy transduction with the methods of quantum statistics to propose a molecular mechanism which, in sharp contrast to competing models, explains both the variation in scaling exponents and the taxon-specific differences in proportionality constants. The new model is universal in the sense that it applies to unicellular organisms, plants and animals.     

Evidence of variant intra- and interspecific scaling of tree crown structure and relevance for allometric theory

General scaling rules or constants for metabolic and structural plant allometry as assumed by the theory of Euclidian geometric scaling (2/3-scaling) or metabolic scaling (3/4-scaling) may meet human's innate propensity for simplicity and generality of pattern and processes in nature. However, numerous empirical works show that variability of crown structure rather than constancy is essential for a tree's success in coping with crowding. In order to link theory and empiricism, we analyzed the intra- and inter-specific scaling of crown structure for 52 tree species. The basis is data from 84 long-term plots of temperate monospecific forests under survey since 1870 and a set of 126 yield tables of angiosperm and gymnosperm forest tree species across the world. The study draws attention to (1) the intra-specific variation and correlation of the three scaling relationships: tree height versus trunk diameter, crown cross-sectional area versus trunk diameter, and tree volume versus trunk diameter, and their dependence on competition, (2) the inter-specific variation and correlation of the same scaling exponents ([Formula: see text] and [Formula: see text]) across 52 tree species, and (3) the relevance of the revealed variable scaling of crown structure for leaf organs and metabolic scaling. Our results arrive at suggesting a more extended metabolic theory of ecology which includes variability and covariation between allometric relationships as prerequisite for the individual plant's competitiveness.     

Sizing up size ratios

The investigation of the causes of observed size differences between coexisting related animal species requires a knowledge of the statistical distributions of size ratios in randomly constructed guilds. Null models can be useful, but are often subject to constraints that severely limit their applicability. New work on the statistics of size distributions may lead to a better understanding of why animals are the sizes they are.     

Biomechanics and allometric scaling in primate locomotion and morphology

Body size has a dominant influence on locomotor performance and the morphology of the locomotor apparatus. In locomotion under the influence of gravity, body mass acts as weight force and is a mechanical variable. Accordingly, the application of biomechanical principles and methods allows a functional understanding of scaling effects in locomotion. This is demonstrated here using leaping primates as an example. With increasing body size, the decreasing ratio of muscle force available for acceleration during takeoff to the body mass that has to be accelerated dictates both the movement pattern and the proportions of the hindlimbs. In an arm-swinging movement, the long, heavy arms of the large-bodied leapers are effectively used to gain additional momentum. A new perspective on decreasing size identifies the absolutely small acceleration distance and time available for propulsion as factors limiting leaping distance and extensively determining locomotor behavior and body proportions. As the mechanical constraints differ according to body size for a given mode of locomotion, a typological approach to morphology in relation to locomotor category is ruled out. Across locomotor categories, dynamic similarity (sensu Alexander) can be expected if the propulsive mechanisms as well as the selective pressures acting upon locomotion are the same.     

The allometric approach for interspecies scaling of pharmacokinetic parameters

A long standing problem in pharmacokinetics and toxicology is the extrapolation and correlation between results obtained in different animal species and man. Animal data may be scaled-up to predict PPs in man using the allometric approach. The allometric approach is empirical, but easy, and is based on the fact that the underlying physiological processes such as blood flow, heartbeat duration, breath duration etc. are essentially physical and related to B. This approach is generally applicable to compounds that are essentially renally excreted. For substances that are highly extracted by the liver, Cl_tot is a function of the LBF among various species. Based on the concept of neoteny, use of brain weight affords a more correct approach to the scaling of Cl_int of low extraction ratio drugs.By using the invariant pharmacokinetic time, the superficial differences in concentration-time profiles due to chronological time among different species are removed. Finally, as Boxenbaum (1984) has said “parameters to be scaled, independent variables, and the mathematical relationships used in the scaling process are all at the discretion of the investigator. There are no proper or improper approaches; the only limitations are those imposed by the investigator.”     

Testing metabolic ecology theory for allometric scaling of tree size, growth and mortality in tropical forests

The theory of metabolic ecology predicts specific relationships among tree stem diameter, biomass, height, growth and mortality. As demographic rates are important to estimates of carbon fluxes in forests, this theory might offer important insights into the global carbon budget, and deserves careful assessment. We assembled data from 10 old-growth tropical forests encompassing censuses of 367 ha and > 1.7 million trees to test the theory's predictions. We also developed a set of alternative predictions that retained some assumptions of metabolic ecology while also considering how availability of a key limiting resource, light, changes with tree size. Our results show that there are no universal scaling relationships of growth or mortality with size among trees in tropical forests. Observed patterns were consistent with our alternative model in the one site where we had the data necessary to evaluate it, and were inconsistent with the predictions of metabolic ecology in all forests.     

Why allometric scaling enhances stability in food web models

It has recently been shown that the incorporation of allometric scaling into the dynamic equations of food web models enhances network stability if predators are assigned a higher body mass than their prey. We investigate the underlying mechanisms leading to this stability increase. The dynamic equations can be written such that allometric scaling influences these equations at three places: the time scales of predator and prey dynamics become separated, the energy outflow to the predators is decreased, and intraspecific competition is increased relative to metabolic rates. For five food web topologies and various network sizes (i.e., species richness), we study the effect of each of these modifications on the percentage of surviving species separately and find that the decreased interaction strengths and the increased intraspecific competition are responsible for the enhanced stability. We also investigate the range of parameter values for which an enhanced stability is observed.     

The natural selection of metabolism explains curvature in allometric scaling

I simulate the natural selection of metabolism and mass to explain the curvature in the metabolic allometry for placental and marsupial mammals. The simulation model starts with a single ancestor in each clade at the Cretaceous–Palaeogene boundary 65 million years ago. The release of inter‐specific competition by the extinction of dinosaurs make it possible for each clade to diversify into a multitude of species across a wide range of empty niches. The selection of mass in these species depends on the net assimilated energy that depends on 1) the handling of the resources in the different niches, and on 2) mass‐specific metabolism that defines the pace of the handling process. The model is fitted to explain the maximum observed body masses over time and the current inter‐specific allometry for metabolism. The selection of mass‐specific metabolism is found to bend the metabolic allometry over time, even when all species have the same selection on the per‐generation time‐scale of natural selection. This is because the smaller species evolve over a larger number of generations than the larger species. The strongest curvature is in the placental clade, where the estimated rate of exponential increase in mass‐specific metabolism is 9.3 × 10^?9 (95% CI: 7.3 × 10^?9 – 1.1 × 10^?8) on the per‐generation time‐scale. This is an order of magnitude larger than the estimate for marsupials, in agreement with an average metabolism that is 30% larger in placentals relative to marsupials of similar size.     

Phylogenetic analysis of the allometric scaling of therapeutic regimes for birds

The use of allometric scaling to estimate drug doses, regimes, and clearance rates (metabolic dosing) is based on the principle that the amount of drug to be administered is more closely related to daily energy use than to body mass (kg). Thus, by using the allometric estimations of minimal energy consumption (MEC) in kcal day⁻¹ based on the formula MEC= kM _b ^b , where b =3, it is thought to be possible to extrapolate appropriate drug dosage regimens to species for which direct MEC data are unavailable. However, the allometric equations for respiratory variables in birds were developed 30 years ago, and were based on a very small sample size, while the appropriate scaling exponent for the allometry of energy use is a matter of considerable debate. Hence, we revisit the issue of the scaling of therapeutic regimes in birds using the most current expanded database available (resting metabolic rate data for 296 species across 17 bird orders), taking account of the non-independence of species in this process using a phylogenetically independent approach. We show that the use of caloric values to estimate daily energy consumption introduces significant error into the formula, as there are a number of assumptions that are made when converting rate of oxygen consumption to a caloric value. We also show that there are significant differences in the proportionality or Hainsworth coefficients k across taxa when the data are examined in a phylogenetic context, although the allometric scaling exponent does not vary. We therefore recommend the use of only data based on oxygen consumption values, and not caloric values, and a multi-order phylogenetic model when calculating the appropriate drug dosage regime.