Allometric Scaling Relationships Research Articles

Young dove trees tend to invest more biomass in vegetative and reproductive organs than old trees at the twig level

Research on the functional traits of twigs is of great significance to clarify the plant life-history strategies, especially for endangered plants. However, little attention has been given to the environmental adaptation strategy of different age twigs. The dove tree (Davidia involucrata Baill.), a relict and critically endangered Chinese species, was employed as a model species. Total lamina mass and area, stem mass and length, total bract mass and area, and total petiole mass were measured for 100 current-year terminal twigs (50 per age group) from old and young dove trees in Pingwu County, Sichuan, southwest China. Then, the scaling relationships within the twig were determined using the standardized major axis (SMA) regression method. Our results showed that the significantly positive correlations among traits of D. involucrata twigs, and scaling relationships between these traits are different between the two age groups. At the twig level, isometric scaling relationships exist between stem mass and lamina size (or bract size) and between total lamina mass and total lamina area (or total petiole mass). In contrast, allometric scaling relationships exist between lamina size (total mass and area) and stem length (with a common slope > 1), and between total lamina mass and total petiole mass (with a common slope < 1). For a given stem mass, stem length and bract, young trees have larger total lamina mass and total bract mass, larger total lamina mass and area, and larger total bract mass than old trees, respectively. The results suggest that young trees tend to have more vegetative and reproductive organ mass per unit of supporting organ mass than old trees to meet their rapid growth needs.

Beyond the kill: The allometry of predation behaviours among large carnivores.

The costs of foraging can be high while also carrying significant risks, especially for consumers feeding at the top of the food chain. To mitigate these risks, many predators supplement active hunting with scavenging and kleptoparasitic behaviours, in some cases specializing in these alternative modes of predation. The factors that drive differential utilization of these tactics from species to species are not well understood. Here, we use an energetics approach to investigate the survival advantages of hunting, scavenging and kleptoparasitism as a function of predator, prey and potential competitor body sizes for terrestrial mammalian carnivores. The results of our framework reveal that predator tactics become more diverse closer to starvation, while the deployment of scavenging and kleptoparasitism is strongly constrained by the ratio of predator to prey body size. Our model accurately predicts a behavioural transition away from hunting towards alternative modes of predation with increasing prey size for predators spanning an order of magnitude in body size, closely matching observational data across a range of species. We then show that this behavioural boundary follows an allometric power-law scaling relationship where the predator size scales with an exponent nearing 3/4 with prey size, meaning that this behavioural switch occurs at relatively larger threshold prey body size for larger carnivores. We suggest that our approach may provide a holistic framework for guiding future observational efforts exploring the diverse array of predator foraging behaviours.

Eco-evolutionary emergence of macroecological scaling in plankton communities.

Macroecological scaling patterns, such as between prey and predator biomass, are fundamental to our understanding of the rules of biological organization and ecosystem functioning. Although these scaling patterns are ubiquitous, how they arise is poorly understood. To explain these patterns, we used an eco-evolutionary predator-prey model parameterized using data for phytoplankton and zooplankton. We show that allometric scaling relationships at lower levels of biological organization, such as body-size scaling of nutrient uptake and predation, give rise to scaling relationships at the food web and ecosystem levels. Our predicted macroecological scaling exponents agree well with observed values across ecosystems. Our findings explicitly connect scaling relationships at different levels of biological organization to ecological and evolutionary mechanisms, yielding testable hypotheses for how observed macroecological patterns emerge.

Metabolic scaling as an emergent outcome of variation in metabolic rate.

The allometric scaling of metabolic rate and what drives it are major questions in biology with a long history. Since the metabolic rate at any level of biological organization is an emergent property of its lower-level constituents, it is an outcome of the intrinsic heterogeneity among these units and the interactions among them. However, the influence of lower-level heterogeneity on system-level metabolic rate is difficult to investigate, given the tightly integrated body plan of unitary organisms. In this context, social insects such as honeybees can serve as important model systems because unlike unitary organisms, these superorganisms can be taken apart and reassembled in different configurations to study metabolic rate and its various drivers at different levels of organization. This commentary discusses the background of such an approach and how combining it with artificial selection to generate heterogeneity in metabolic rate with an analytical framework to parse out the different mechanisms that contribute to the effects of heterogeneity can contribute to the various models of metabolic scaling. Finally, the absence of the typical allometric scaling relationship among different species of honeybees is discussed as an important prospect for deciphering the role of top-down ecological factors on metabolic scaling. This article is part of the theme issue 'The evolutionary significance of variation in metabolic rates'.

Allometric scaling of retrogressive thaw slumps

Abstract. In the warming Arctic, retrogressive thaw slumping (RTS) has emerged as the primary thermokarst modifier of ice-rich permafrost slopes, raising urgency to investigate the distribution and intensification of disturbances and the cascade of effects. Tracking RTS is challenging due to the constraints of remote sensing products and a narrow understanding of complex, thaw-driven landforms; however, high-resolution elevation models provide new insights into geomorphic change. Structural traits, such as RTS depth of thaw or volume, can be obtained through allometric scaling. To address fundamental knowledge gaps related to area–volume scaling of RTS, a suitable surface interpolation technique was first needed to model pre-disturbance topography upon which volume estimates could be based. Among eight methods with 32 parameterizations, natural neighbour surface interpolation achieved the best precision in reconstructing pre-disturbed slope topography (90th percentile root mean square difference ±1.0 m). An inverse association between RTS volume and relative volumetric error was observed, with uncertainties &lt; 10 % for large slumps and &lt; 20 % for small to medium slumps. Second, a multisource slump inventory (MSI) for two study areas in the Beaufort Delta (Canada) region was developed to characterize the diverse range of disturbance morphologies and activity levels, which provided consistent characterization of thaw-slump-affected slopes between regions and through time. The MSI delineation of high-resolution hillshade digital elevation models (DEMs) for three time periods (airborne stereo-imagery, lidar, ArcticDEM) revealed temporal and spatial trends in these chronic mass-wasting features. For example, in the Tuktoyaktuk Coastlands, a +38 % increase in active RTS counts and +69 % increase in total active surface area were observed between 2004 and 2016. However, the total disturbance area of RTS-affected terrain did not change considerably (+3.5 %) because the vast majority of active thaw slumping processes occurred in association with past disturbances. Interpretation of thaw-driven change is thus dependent on how active RTS is defined to support disturbance inventories. Our results highlight that active RTS is tightly linked to past disturbances, underscoring the importance of inventorying inactive scar areas. Third, the pre-disturbance topographies, MSI digitizations, and DEMs were integrated to explore allometric scaling relationships between RTS area and eroded volume. The power-law model indicated non-linearity in the rates of RTS expansion and intensification across scales (adj-R2 of 0.85, n= 1522) but also revealed that elongated, shoreline RTS reflects outliers poorly represented by the modelling. These results indicate that variation in the allometric scaling of RTS populations is based on morphometry, terrain position, and complexity of the disturbance area, as well as the method and ontology by which slumps are inventoried. This study highlights the importance of linking field-based knowledge to feature identification and the utility of high-resolution DEMs in quantifying rates of RTS erosion beyond tracking changes in the planimetric area.

Universal ontogenetic growth without fitted parameters: implications for life history invariants and population growth

Since the work of von Bertalanffy (Q Rev Boil 32:217–231, 1957), several models have been proposed that relate the ontogenetic scaling of energy assimilation and metabolism to growth, which are able to describe ontogenetic growth trajectories for living organisms and collapse them onto a single universal curve (West et al. in Nature 413:628–631, 2001; Barnavar et al. in Nature 420:626, 2002). Nevertheless, all these ontogenetic growth models critically depend on fitting parameters and on the allometric scaling of the metabolic rate. Using a new metabolic rate relation (Escala in Theor Ecol 12(4):415–425, 2019) applied to a Bertalanffy-type ontogenetic growth equation, we find that ontogenetic growth can also be described by a universal growth curve for all studied species, but without the aid of any fitting parameters (i.e., no fitting procedure is performed on individual growth curves). We find that the inverse of the heart frequency mathrm f_H, rescaled by the ratio of the specific energies for biomass creation and metabolism, defines the characteristic timescale for ontogenetic growth. Moreover, our model also predicts a generation time and lifespan that explain the origin of several “Life History Invariants’ (Charnov in Oxford University Press, Oxford, 1993) and predict that the Malthusian parameter should be inversely proportional to both the generation time and lifespan, in agreement with the data in the literature (Duncan et al. in Ecology 88:324–333 2007; Dillingham et al. in Paper 535, 2016; Hatton et al. in PNAS 116(43):21616–21622 2019). In our formalism, several critical timescales and rates (lifespan, generation time, and intrinsic population growth rate) are all proportional to the heart frequency mathrm f_H, and thus, their allometric scaling relations come directly from the allometry of the heart frequency, which is typically mathrm f_H propto M^{-0.25} under basal conditions.

Signal size allometry in Anolis lizard dewlaps.

Positive allometry of signalling traits has often been taken as evidence for sexual selection. However, few studies have explored interspecific differences in allometric scaling relationships among closely related species that vary in their degree of ecological similarity. Anolis lizards possess an elaborate retractable throat fan called a dewlap that is used for visual communication and differs greatly in size and colour among species. We observed that Anolis dewlaps demonstrate positive allometry: relative dewlap size increases with body size. We also observed that coexisting species are divergent in signal size allometries, while convergent species-similar in other aspects of ecology, morphology and behaviour-typically share similar dewlap allometric scaling relationships. These patterns suggest that dewlap scaling relationships may follow the same pattern as other traits in the anole radiation, where ecologically different sympatric species have evolved a suite of divergent traits.

Empirical analysis and modeling of the allometric scaling of urban freight systems

Heavy trucks which undertake the majority of freight volume play an important role in urban freight systems. By analyzing heavy truck trip data, we find a superlinear scaling relationship for heavy truck trips and a sublinear scaling relationship for heavy truck numbers relative to urban population size. Although these allometric scaling relationships that widely appear in nature and social systems have been explained by many models, a simple model that can cover a wide range of scaling exponents in these systems is still lacking. Here, we develop a partially mixing city operation model by quantifying the mixability of the urban population to explain why the superlinear and sublinear scaling exponents are in the range of 1 and . This simple model not only helps us understand the mechanism of allometric scaling of urban freight systems, but also provides a new framework for other superlinear and sublinear scaling relationships in cities.

Enhancing fetal alcohol spectrum disorders diagnosis with a classifier based on the intracerebellar gradient of volumetric undersizing.

In fetal alcohol spectrum disorders (FASD), brain growth deficiency is a hallmark of subjects both with fetal alcohol syndrome (FAS) and with non-syndromic FASD (NS-FASD, i.e., those without specific diagnostic features). However, although the cerebellum was suggested to be more severely undersized than the rest of the brain, it has not yet been given a specific place in the FASD diagnostic criteria where neuroanatomical features still count for little if anything in diagnostic specificity. We applied a combination of cerebellar segmentation tools on a 1.5 T 3DT1 brain MRI dataset from a monocentric population of 89 FASD (52 FAS, 37 NS-FASD) and 126 typically developing controls (6-20 years old), providing 8 volumes: cerebellum, vermis and 3 lobes (anterior, posterior, inferior), plus total brain volume. After adjustment of confounders, the allometric scaling relationship between these cerebellar volumes (Vi ) and the total brain or cerebellum volume (Vt ) was fitted (Vi = bVt a ), and the effect of group (FAS, control) on allometric scaling was evaluated. We then estimated for each cerebellar volume in the FAS population the deviation from the typical scaling (v DTS) learned in the controls. Lastly, we trained and tested two classifiers to discriminate FAS from controls, one based on the total cerebellum v DTS only, the other based on all the cerebellar v DTS, comparing their performance both in the FAS and the NS-FASD group. Allometric scaling was significantly different between FAS and control group for all the cerebellar volumes (p < .001). We confirmed the excess of total cerebellum volume deficit (v DTS = -10.6%) and revealed an antero-inferior-posterior gradient of volumetric undersizing in the hemispheres (-12.4%, 1.1%, 2.0%, respectively) and the vermis (-16.7%, -9.2%, -8.6%, repectively). The classifier based on the intracerebellar gradient of v DTS performed more efficiently than the one based on total cerebellum v DTS only (AUC = 92% vs. 82%, p = .001). Setting a high probability threshold for >95% specificity of the classifiers, the gradient-based classifier identified 35% of the NS-FASD to have a FAS cerebellar phenotype, compared to 11% with the cerebellum-only classifier (pFISHER = 0.027). In a large series of FASD, this study details the volumetric undersizing within the cerebellum at the lobar and vermian level using allometric scaling, revealing an anterior-inferior-posterior gradient of vulnerability to prenatal alcohol exposure. It also strongly suggests that this intracerebellar gradient of volumetric undersizing may be a reliable neuroanatomical signature of FAS that could be used to improve the specificity of the diagnosis of NS-FASD.

Tail feather strength in tail-assisted climbing birds is achieved through geometric, not material change.

Birds encompass vast ecomorphological diversity and practise numerous distinct locomotor modes. One oft-cited feature seen in climbing birds is an increase in tail 'stiffness', yet it remains unclear to what extent these feathers are altered, and the specific mechanism by which differences in functional performance are attained. We collected a broad taxonomic sample of tail feathers (6525 total, from 774 species representing 21 avian orders and ranging in size from approximately 3 g to greater than 11 kg) and present data on their material properties, cross-sectional geometry and morphometrics. Ordinary and phylogenetic least-squares regressions of each variable versus body mass were conducted to assess scaling relationships and demonstrate that tail-supported climbers exhibit longer tail feathers with a wider rachis base and tip, and a greater second moment of area and maximum bending moment. However, no differences were observed in the material properties of the keratin itself. This suggests that tail-supported arboreal climbing birds of multiple orders have independently adopted similar morphologies. Moreover, these geometric relationships follow the same allometric scaling relationships as seen in the long bones of mammalian limbs, suggesting that the morphology of these developmentally and evolutionarily distinct structures are governed by similar functional constraints of weight support.

Scaling of Activity Space in Marine Organisms across Latitudinal Gradients.

AbstractUnifying models have shown that the amount of space used by animals (e.g., activity space, home range) scales allometrically with body mass for terrestrial taxa; however, such relationships are far less clear for marine species. We compiled movement data from 1,596 individuals across 79 taxa collected using a continental passive acoustic telemetry network of acoustic receivers to assess allometric scaling of activity space. We found that ectothermic marine taxa do exhibit allometric scaling for activity space, with an overall scaling exponent of 0.64. However, body mass alone explained only 35% of the variation, with the remaining variation best explained by trophic position for teleosts and latitude for sharks, rays, and marine reptiles. Taxon-specific allometric relationships highlighted weaker scaling exponents among teleost fish species (0.07) than sharks (0.96), rays (0.55), and marine reptiles (0.57). The allometric scaling relationship and scaling exponents for the marine taxonomic groups examined were lower than those reported from studies that had collated both marine and terrestrial species data derived using various tracking methods. We propose that these disparities arise because previous work integrated summarized data across many studies that used differing methods for collecting and quantifying activity space, introducing considerable uncertainty into slope estimates. Our findings highlight the benefit of using large-scale, coordinated animal biotelemetry networks to address cross-taxa evolutionary and ecological questions.

Allometric relationships between leaf and petiole traits across 31 floating-leaved plants reveal a different adaptation pattern from terrestrial plants.

Allometric scaling between stomata and xylem for terrestrial woody plants is a widely observed pattern that may be constrained by water transport. Floating-leaved plants, a particular life form of aquatic plants, have leaves in direct contact with both air and water and a poorly developed xylem that may not be limited by water supply as for terrestrial plants. However, whether such an allometric scaling relationship still exists in floating-leaved plants has not been explored. We analysed 31 floating-leaved species/varieties with a range in leaf area covering six orders of magnitude. For all 31 floating-leaved plants, we studied the allometric relationships between leaf area and petiole transverse area, and between total stomatal area and petiole vascular area. The slopes of both relationships were similar to the slope of the allometric relationship (1.23) between total stomatal area and xylem area of 53 terrestrial plants. However, for ten of them with xylem that can be clearly defined, the strong positive relationship between total stomatal area and petiole xylem area had a significantly smaller slope than that of terrestrial plants (0.64 vs. 1.23). Furthermore, after considering phylogeny, the scaling relationships between total stomatal area and petiole traits in floating-leaved plants remained significant. We speculated that for floating-leaved plants, the hyperallometric relationship (slope >1) between the construction of leaf/stoma and petiole was promoted by the high demand for photosynthesis and thus more leaves/stomata. While the hypoallometric relationship (slope <1) between stomatal and xylem area was related more to hydraulic processes, the selection pressure on stomata was lower than xylem of floating-leaved plants. Allometric relationships among the hydraulic traits on water transport of aquatic plants are the result of natural selection to achieve maximum carbon gain, which is similar to terrestrial plants.

Differences and allometric relationships among assimilative branch traits of four shrubs in Central Asia.

Shrubs play a major role in maintaining ecosystem stability in the arid deserts of Central Asia. During the long-term adaptation to extreme arid environments, shrubs have developed special assimilative branches that replace leaves for photosynthesis. In this study, four dominant shrubs with assimilative branches, namely Haloxylon ammodendron, Haloxylon persicum, Calligonum mongolicum, and Ephedra przewalskii, were selected as the research objects, and the dry mass, total length, node number, and basal diameter of their assimilative branches and the average length of the first three nodes were carefully measured, and the allometric relationships among five traits of four species were systematically compared. The results indicated that: (1) Four desert shrubs have different assimilative branches traits. Compared with H. persicum and H. ammodendron, C. mongolicum and E. przewalskii have longer internodes and fewer nodes. The dry mass of H. ammodendron and the basal diameter of H. persicum were the smallest; (2) Significant allometric scaling relationships were found between dry mass, total length, basal diameter, and each trait of assimilative branches, all of which were significantly less than 1; (3) The scaling exponents of the allometric relationship between four traits and the dry mass of assimilative branches of H. persicum were greater or significantly greater than those of H. ammodendron. The scaling exponents of the relationships between the basal diameter, dry mass, and total length of E. przewalskii were higher than those of the other three shrubs. Therefore, although different species have adapted to drought and high temperatures by convergence, there was great variability in morphological characteristics of assimilative branches, as well as in the scaling exponents of relationships among traits. The results of this study will provide valuable insights into the ecological functions of assimilative branches and survival strategies of these shrubs to cope with aridity and drought in desert environments.

Allometric scaling relationships in mouse placenta.

Fetal growth and maturation are highly intertwined with placental development during pregnancy. Here we used placental vascular morphology measurements (depth and span) as well as the umbilical artery (UA) diameter of previously published studies on three different mouse strains (C57BL6/J, CD-1 and BALB/c), which were exposed to different conditions (combination antiretroviral therapy, chronic maternal hypoxia and malaria infection) at different embryonic days, to test the hypothesis that placental vascularization and specifically the UA size affect conceptus weight. Interaction of each study parameter with embryonic day, strain and exposure to treatments are studied to investigate the stability of the scaling relationships across and/or within strains and conditions. In addition, the effect of UA diameter on the placental growth measurements (depth and span) is studied. These results show that the power-law scaling relationship of conceptus weight and placental depth with the UA diameter is conserved across strains and conditions with the scaling exponent of approximately 3/8 and 5/8, respectively. By contrast, the relationship between conceptus weight and either the placental span or depth is different between strains and conditions, suggesting multiple mechanisms of vascular adaptation.

From permafrost soil to thermokarst lake sediment: A view from C:N:P stoichiometry

Thermokarst lakes are formed as a result of thawing ice-rich permafrost, transforming vast permafrost soil into lake sediment and changing the biogeochemistry of carbon (C), nitrogen (N), and phosphorus (P). Degraded permafrost soil and thermokarst lake sediment are two distinct fates of pristine permafrost in the thermokarst processes. However, we do not clearly understand the differences and relationships between degraded permafrost soil and thermokarst lake sediment from a stoichiometric perspective. In this study, 44 thermokarst lakes across the Qinghai-Tibet Plateau were investigated to collect lake sediment and surrounding degraded permafrost soil. In general, C, N, and P concentrations as well as C:N, C:P, and N:P ratios in soil and sediment decreased with increasing latitude, while increased with increasing mean annual precipitation. The degraded permafrost soil had much higher C, N, and P concentrations and C:N:P stoichiometric ratios than the lake sediment, particularly for C. Moreover, the concentrations of C, N, and P, as well as the ratios of C:P and N:P in sediment showed significant positive relationships with their corresponding components in soil but with different slopes. Standard major axis regression showed allometric scaling relationships between C, N, and P. The C:N:P ratio was 269:18:1 in degraded permafrost soil and 178:15:1 in lake sediment. The results suggest that the process from pristine permafrost to lake sediment releases more C, N, and P than the process from pristine permafrost to degraded permafrost soil, and that C changes more profoundly than N and P. Moreover, thermokarst processes substantially change the elemental balance and decouple the C:N:P relationship between degraded permafrost soil and lake sediment, suggesting that the further transformation from degraded permafrost soil to lake sediment will lose more C, which can be intensified by increasing precipitation. The results enriched our understanding of the variations in C, N, and P biogeochemistry during thermokarst processes.

Plankton energy flows using a global size-structured and trait-based model

Plankton community models are critical tools for understanding the processes that shape marine plankton communities, how plankton communities impact biogeochemical cycles, and the feedbacks between community structure and function. Here, using the flexible Marine Biogeochemistry Library (MARBL), we present the Size-based Plankton ECological TRAits (MARBL-SPECTRA) model, which is designed to represent a diverse plankton community while remaining computationally tractable. MARBL-SPECTRA is composed of nine phytoplankton and six zooplankton size classes represented using allometric scaling relationships for physiological traits and interactions within multiple functional types. MARBL-SPECTRA is embedded within the global ocean component of the Community Earth System Model (CESM) and simulates large-scale, emergent patterns in phytoplankton growth limitation, plankton phenology, plankton generation time, and trophic transfer efficiency. The model qualitatively reproduces observed global patterns of surface nutrients, chlorophyll biomass, net primary production, and the biogeographies of a range of plankton size classes. In addition, the model simulates how predator:prey dynamics and trophic efficiency vary across gradients in total ecosystem productivity. Shorter food chains that export proportionally more carbon from the surface to the ocean interior occur in productive, eutrophic regions, whereas in oligotrophic regions, the food chains are relatively long and export less organic matter from the surface. The union of functional type modeling with size-resolved, trait-based modeling approaches allows MARBL-SPECTRA to capture both large-scale elemental cycles and the structure of planktonic food webs affecting trophic transfer efficiency.

Nutrient-dependent allometric plasticity in a male-diphenic mite.

Male secondary sexual traits often scale allometrically with body size. These allometries can be variable within species and may shift depending on environmental conditions, such as food quality. Such allometric plasticity has been hypothesized to initiate local adaptation and evolutionary diversification of scaling relationships, but is under‐recorded, and its eco‐evolutionary effects are not well understood. Here, we tested for allometric plasticity in the bulb mite (Rhizoglyphus robini), in which large males tend to develop as armed adult fighters with thickened third legs, while small males become adult scramblers without thickened legs. We first examined the ontogenetic timing for size‐ and growth‐dependent male morph determination, using experimentally amplified fluctuations in growth rate throughout juvenile development. Having established that somatic growth and body size determine male morph expression immediately before metamorphosis, we examined whether the relationship between adult male morph and size at metamorphosis shifts with food quality. We found that the threshold body size for male morph expression shifts toward lower values with deteriorating food quality, confirming food‐dependent allometric plasticity. Such allometric plasticity may allow populations to track prevailing nutritional conditions, potentially facilitating rapid evolution of allometric scaling relationships.

Physiologically Based Pharmacokinetic Modeling of Cefadroxil in Mouse, Rat, and Human to Predict Concentration-Time Profile at Infected Tissue.

The aim of this study was to develop physiologically based pharmacokinetic (PBPK) models capable of simulating cefadroxil concentrations in plasma and tissues in mouse, rat, and human. PBPK models in this study consisted of 14 tissues and 2 blood compartments. They were established using measured tissue to plasma partition coefficient (K p) in mouse and rat, absolute expression levels of hPEPT1 along the entire length of the human intestine, and the transporter kinetic parameters. The PBPK models also assumed that all the tissues were well-stirred compartments with perfusion rate limitations, and the ratio of the concentration in tissue to the unbound concentration in plasma is identical across species. These PBPK models were validated strictly by a series of observed plasma concentration–time profile data. The average fold error (AFE) and absolute average fold error (AAFE) values were all less than 2. The models’ rationality and accuracy were further demonstrated by the almost consistent V ss calculated by the PBPK model and noncompartmental method, as well as the good allometric scaling relationship of V ss and CL. The model suggests that hPEPT1 is the major transporter responsible for the oral absorption of cefadroxil in human, and the plasma concentration–time profiles of cefadroxil were not sensitive to dissolution rate faster than T85% = 2 h. The cefadroxil PBPK model in human is reliable and can be used to predict concentration–time profile at infected tissue. It may be useful for dose selection and informative decision-making during clinical trials and dosage form design of cefadroxil and provide a reference for the PBPK model establishment of hPEPT1 substrate.

Information-theoretic approach in allometric scaling relations of DNA and proteins.

Allometric scaling relations can be observed in between molecular parameters. Hence, we looked for presence of such relation among sizes (i.e., lengths) of proteins and genes. Protein lengths exist in the literature as the number of amino acids. They can also be derived from the mRNA lengths. Here, we looked for allometric scaling relation by using such data and simultaneously, the data was compared with the sizes of genes and proteins that were obtained from our modified information-theoretic approach. Results implied presence of scaling relation in the calculated results. This was expected due to the implemented modification in the information-theoretic calculation. Relation in the literature-based data was lacking high goodness of fit value. It could be due to physical factors and selective pressures, which ended up in deviations of the literature-sourced values from those in the model. Genome size is correlated with cell size. Intracellular volume, which is related to the DNA size, would require certain number of proteins, the sizes of which can therefore be correlated with the protein sizes. Cell sizes, genome sizes, and average protein and gene sizes, along with the number of proteins, namely the expression levels of the genes, are the physical factors, and the molecular factors influence those physical factors. The selective pressures on those can act through the connection between those physical factors and limit the dynamic ranges. Biological measures could be prone to such forces and are likely to deviate from expected models, regardless of the validity of assumptions, unless those are also implemented in the models. Yet, present discrepancies could be pointing at the need for model improvement, data imperfection, invalid assumptions, etc. Still, current work highlights possible use of information-theoretic approach in allometric scaling relations' studies.

Exploring Allometric Scaling Relations between Fractal Dimensions of Metro Networks and Economic, Environmental and Social Indicators: A Case Study of 26 Cities in China

Allometric scaling originates in biology, where it refers to scaling relations between the size of a body part and the size of the whole body when an organism grows. In cities, various allometric relations have also been discovered, such as those between the complexity of traffic networks and urban quantities. Metro networks are typical traffic networks in cities. However, whether allometric relations with metro networks exist is still uncertain. In this study, “fractal dimension” was employed as the complexity measure of metro networks, and potential allometric relations between fractal dimensions and urban indicators in 26 main cities in China were explored. It was found that fractal dimensions of metro networks had positive allometric relations with gross domestic product (GDP), population, particulate matter with a diameter less than 2.5 microns (PM2.5), the road congestion index and the average price of second-hand housing (with Spearman’s R of 0.789, 0.806, 0.273, 0.625 and 0.335, respectively) but inverse allometric relations with sulfur dioxide (SO2) and residential satisfaction (with Spearman’s R of −0.270 and −0.419, respectively). Such discoveries imply that allometric relations do exist with metro networks, which is helpful in deepening our understanding of how metro systems interact with urban quantities in the self-organized evolution of cities.