Allometric scaling of biological rhythms in mammals

A wide spectrum of cyclic functions in terrestrial mammals of different size, from the 3-gram shrew to the 3-ton elephant, yields an allometric exponent around 0.25, which is correlated--as a kind of common denominator--with the specific metabolic rate. Furthermore, the applicability of these empirical findings could be extrapolated to chronological events in the sub-cellular realm. On the other hand, the succession of growth periods (T98%) until sexual maturity is reached also follows the 1/4 power rule. By means of Verhulst's logistic equation, it has been possible to simulate three different biological conditions, which means that by modifying the numerical value of only one parameter, revertible physiological and pathological states can be obtained, as for instance isostasis, homeostasis and heterostasis.     

Generalized conjugate priors for Bayesian analysis of risk and survival regressions

Conjugate priors for Bayesian analyses of relative risks can be quite restrictive, because their shape depends on their location. By introducing a separate location parameter, however, these priors generalize to allow modeling of a broad range of prior opinions, while still preserving the computational simplicity of conjugate analyses. The present article illustrates the resulting generalized conjugate analyses using examples from case-control studies of the association of residential wire codes and magnetic fields with childhood leukemia.     

Allometric scaling in animals and plants

In this paper we give a derivation for the allometric scaling relation between the metabolic rate and the mass of animals and plants. We show that the characteristic scaling exponent of 3/4 occurring in this relation is a result of the distribution of sources and sinks within the living organism. We further introduce a principle of least mass and discuss the kind of flows that arise from it.     

Allometric scaling of intraspecific space use

Allometric scaling relationships enable exploration of animal space-use patterns, yet interspecific studies cannot address many of the underlying mechanisms. We present the first intraspecific study of home range (HR) allometry relative to energetic requirements over several orders of magnitude of body mass, using as a model the predatory fish, pike Esox lucius. Analogous with interspecific studies, we show that space use increases more rapidly with mass (exponent = 1.08) than metabolic scaling theories predict. Our results support a theory that suggests increasing HR overlap with body mass explains many of these differences in allometric scaling of HR size. We conclude that, on a population scale, HR size and energetic requirement scale allometrically, but with different exponents.     

Allometric scaling laws for water uptake by plant roots

This paper develops scaling laws for plant roots of any arbitrary volume and branching configuration that maximize water uptake. Water uptake can occur along any part of the root network, and thus there is no branch-to-branch fluid conservation. Maximizing water uptake, therefore, involves balancing two flows that are inversely related: axial and radial conductivity. The scaling laws are tested against the root data of 1759 plants from 77 herbaceous species, and compared with those from the WBE model. I further discuss whether the scaling laws are invariant to soil water distribution. A summary of some of the results follows. (1) The optimal radius for a single root (no branches) scales with volume as . (2) The basic allometric scaling for root radius branches (r_i+1=β*r_i) is of the form , where f(N)=A(N)/(n_b*(1+A(N))), n_b is the number of branches, and A(N) and ε(N) are functions of the number of root diameter classes (not constants as in the WBE model). (3) For large N, β converges to the β from the WBE model. For small N, the β's for the two models diverge, but are highly correlated. (4) The fractal assumption of volume filling of the WBE model are also met in the root model even though they are not explicitly incorporated into it. (5) The WBE model for rigid tubes is an asymptotic solution for large root systems (large N and biomass). (6) The optimal scaling solutions for the root network appears to be independent of soil water distribution or water demand. The data set used for testing is included in the electronic supplementary archive of the journal.     

Effects of metabolic level on the body size scaling of metabolic rate in birds and mammals

Metabolic rate is traditionally assumed to scale with body mass to the 3/4-power, but significant deviations from the '3/4-power law' have been observed for several different taxa of animals and plants, and for different physiological states. The recently proposed 'metabolic-level boundaries hypothesis' represents one of the attempts to explain this variation. It predicts that the power (log-log slope) of metabolic scaling relationships should vary between 2/3 and 1, in a systematic way with metabolic level. Here, this hypothesis is tested using data from birds and mammals. As predicted, in both of these independently evolved endothermic taxa, the scaling slope approaches 1 at the lowest and highest metabolic levels (as observed during torpor and strenuous exercise, respectively), whereas it is near 2/3 at intermediate resting and cold-induced metabolic levels. Remarkably, both taxa show similar, approximately U-shaped relationships between the scaling slope and the metabolic (activity) level. These predictable patterns strongly support the view that variation of the scaling slope is not merely noise obscuring the signal of a universal scaling law, but rather is the result of multiple physical constraints whose relative influence depends on the metabolic state of the organisms being analysed.     

The principle of laplace and scaling of ventricular wall stress and blood pressure in mammals and birds

Maximum left ventricular wall stress is calculated at end-diastolic volume and systemic arterial diastolic blood pressure, according to a thick-walled model for the principle of Laplace. Stress is independent of body mass and averages 13.9 kPa (+/-2.3; 95% confidence interval) in 24 species of mammals weighing 0.025-4,000 kg and 15.5 kPa (+/-4.7) in 12 birds weighing 0.014-110 kg. Birds have higher arterial blood pressures and larger hearts than mammals. Systolic and diastolic arterial blood pressures increase with body mass according to M(0.05) in mammals, and heart mass increases according to M(1.06) in the same species, further supporting the principle. However, blood pressure in birds is independent of body mass, and heart mass scales isometrically. End-diastolic stress values, calculated according to Laplace, are about one-third of peak stresses recorded in isolated mammalian myocardial preparations.     

Allometric scaling of kidney function in green iguanas

Numerous physiological parameters, such as metabolic rate and glomerular filtration rate (GFR), are allometrically related to body mass. Whereas the interspecific relationships between metabolic rate and body mass have been extensively studied in vertebrates, intraspecific studies of renal function have been limited. Therefore, kidney function was studied in 16 green iguanas, (Iguana iguana; 322-4764 g), by using nuclear scintigraphy to measure the renal uptake of 99mTc-diethylenetriamine pentaacetic acid (99mTc-DTPA), following either intravenous or intraosseous administration. Route of 99mTc-DTPA administration did not affect the percentage of the dose that accumulated in the kidney (P > 0.05). Renal uptake of 99mTc-DTPA was related to body mass (W, g) as: %Dose Kidney (min-1) = 11.09W(-0.235). Although not directly measured, the apparent renal clearance of 99mTc-DTPA could be described as: Renal CL 99mTc-DTPA (ml.min-1) = 0.005W(0.759), and the mass exponent did not differ from either the 2/3 or 3/4 values (P > 0.05). The similarity of the mass exponents relating both renal function and metabolic rate to body mass suggests a common mechanism underlying these allometric relationships. As this study also demonstrated that renal scintigraphy can be used to quantify kidney function in iguanas, this technique may be a useful research and diagnostic tool.     

Allometric scaling and locomotor function in the primate pelvis

Identification of positional behavior adaptation in the pelvis of primates is complicated by possible confounding effects of body size and phylogeny. Previous work on primate pelvic allometry has focused primarily on sexual dimorphism and its relationship to obstetric constraints in species with large fetal size relative to maternal size. This study investigates patterns of pelvic scaling with a specific aim to understand how pelvic scaling relates to locomotor function. Patterns of scaling of nine pelvic dimensions were examined in a broad comparative sample of 40 species of primates, covering both haplorhines and strepsirrhines, while accounting for phylogenetic nonindependence. Phylogenetic reduced major axis regressions on pelvic scaling patterns suggest that primate-wide patterns are reflected in haplorhine- and strepsirrhine-specific analyses. Many measures scale isometrically with pelvis size, but notably, features of the ilium tend to scale allometrically. As predicted, ilium width and lower ilium cross-sectional area scale with positive allometry, while lower iliac height scales with negative allometry. Further regression analyses by locomotor group suggest that these ilium measures, as well as pubic symphysis and ischium lengths, differ in their scaling patterns according to locomotor mode. These results suggest that scaling differences within primates, when present, are related to functional differences in locomotor behavior and mechanics. This study supports recent work that identifies adaptations to locomotor loading in the ilium and highlights the need for a better understanding of the relationship between pelvic structural mechanics and the mechanical requirements of primate locomotion. Am J Phys Anthropol 156:511–530, 2015. © 2015 Wiley Periodicals, Inc.     

Behavioral thermoregulation in mammals and birds

Thermoregulation in homoiotherms is achieved by physiological and behavioural adjustments which involve the musculature, skin, sensory capacities, hypothalamus and endocrine glands. Under thermal stress animals exhibit anorexia, body extension, gasping, languor, lethargy, excessive drinking, bathing, decreased locomotor activities, group dispersion, and shade seeking. When exposed to cold, animals show body flexure, huddling, hyperphagia, extra locomotor activities, depressed respiration and nest building. Species and breed differences in the behavioural adjustments to unfavourable climates are related to habitat, morphological characteristics of body covering, degree of physiological adaptability, degree of physiological immaturity at birth or hatching, and the number of young.     

Density-dependent dispersal in birds and mammals

Density‐dependent dispersal can be caused by various mechanisms, from competition inducing individuals to emigrate (positive density‐dependence) to social crowding effects impeding free movement (negative density‐dependence). Various spatial population models have incorporated positively density‐dependent dispersal algorithms, and recent theoretical models have explored the conditions for density‐dependent dispersal (DD) to evolve. However, while the existence of DD is well documented in some taxa such as insects, there is no clear picture on its generality in vertebrates. Here I review the available empirical data on DD in birds and mammals, focusing mainly on variation in dispersal between years and on experimental density manipulations. Surprisingly few studies have explicitly focused on DD, and interpretation of the available data is often hampered by differences in approach, small sample sizes and/or statistical shortcomings. Positive DD was reported in 50 and 33% of the selected mammal and bird studies, respectively, while two studies on mammals (out of eight) reported negative DD. Among bird studies, DD was more often reported for emigration rates or long‐distance recoveries than for average distances within finite study areas. Experimental studies manipulating densities (mainly on mammals) have consistently generated positive DD, typically showing reduced emigration in response to partial population removal. Studies that examined dispersal in relation to seasonal changes in density (small mammals only) have more often reported negative DD. Studies that compared dispersal between sites differing in density, also show a mixture of positive and negative DD. This suggests that dispersal changes in a more complex way with seasonal and spatial density variation than with annual densities, and/or that these results are confounded by other factors differing between seasons and sites, such as habitat quality. I conclude that both correlational and experimental studies support the existence of positive, rather than negative, density‐dependent dispersal in birds and mammals.     

Allometric scaling and seasonality in the epidemics of wildlife diseases

We present a susceptibles-exposed-infectives (SEI) model to analyze the effects of seasonality on epidemics, mainly of rabies, in a wide range of wildlife species. Model parameters are cast as simple allometric functions of host body size. Via nonlinear analysis, we investigate the dynamical behavior of the disease for different levels of seasonality in the transmission rate and for different values of the pathogen basic reproduction number (R(0)) over a broad range of body sizes. While the unforced SEI model exhibits long-term epizootic cycles only for large values of R(0), the seasonal model exhibits multiyear periodicity for small values of R(0). The oscillation period predicted by the seasonal model is consistent with those observed in the field for different host species. These conclusions are not affected by alternative assumptions for the shape of seasonality or for the parameters that exhibit seasonal variations. However, the introduction of host immunity (which occurs for rabies in some species and is typical of many other wildlife diseases) significantly modifies the epidemic dynamics; in this case, multiyear cycling requires a large level of seasonal forcing. Our analysis suggests that the explicit inclusion of periodic forcing in models of wildlife disease may be crucial to correctly describe the epidemics of wildlife that live in strongly seasonal environments.     

Allometric scaling and morphological variation in sinking rate of phytoplankton

Since the first decades of the last century, several hypotheses have been proposed on the role of phytoplankton morphology in maintaining a favorable position in the water column. Here, by an extensive review of literature on sinking rate and cell volume, we firstly attempted to explore the dependency of sinking rate on morphological traits using the allometric scaling approach. We found that sinking rate tends to increase with increasing cell volume showing the allometric scaling exponent of 0.43, which is significantly different than the Stokes’ law exponent of 0.66. The violation of the 2/3 power rule clearly indicates that cell shape changes as size increases. Both size and shape affect how phytoplankton sinking drives nutrient acquisition and losses to sinking. Interestingly, from an evolutionary perspective, simple and complex cylindrical shapes can get much larger than spherical and spheroidal shapes and sink at similar rates, but simple and complex cylindrical shapes cannot get small enough to sink slower than small spherical and spheroidal shapes. Cell shape complexity is a morphological attribute resulting from the combination of two or more simple geometric shapes. While the effect of size on sinking rate is well documented, this study deepens the knowledge on how cell shape or geometry affect sinking rates that still needs further consideration.