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.     

Simultaneous confidence bands for log‐logistic regression with applications in risk assessment

In risk assessment, it is often desired to make inferences on the low dose levels at which a specific benchmark risk is attained. Applications of simultaneous hyperbolic confidence bands for low‐dose risk estimation with quantal data under different dose‐response models (multistage, Abbott‐adjusted Weibull, and Abbott‐adjusted log‐logistic models) have appeared in the literature. The use of simultaneous three‐segment bands under the multistage model has also been proposed recently. In this article, we present explicit formulas for constructing asymptotic one‐sided simultaneous hyperbolic and three‐segment bands for the simple log‐logistic regression model. We use the simultaneous construction to estimate upper hyperbolic and three‐segment confidence bands on extra risk and to obtain lower limits on the benchmark dose by inverting the upper bands on risk under the Abbott‐adjusted log‐logistic model. Monte Carlo simulations evaluate the characteristics of the simultaneous limits. An example is given to illustrate the use of the proposed methods and to compare the two types of simultaneous limits at very low dose levels.     

Allometric equations for predicting body mass of dinosaurs

We use data from the literature to compare two statistical procedures for estimating mass (or size) of quadrupedal dinosaurs and other extraordinarily large animals in extinct lineages. Both methods entail extrapolation from allometric equations fitted to data for a reference group of contemporary animals having a body form similar to that of the dinosaurs. The first method is the familiar one of fitting a straight line to logarithmic transformations, followed by back-transformation of the resulting equation to a two-parameter power function in the arithmetic scale. The second procedure entails fitting a two-parameter power function directly to arithmetic data for the extant forms by nonlinear regression. In the example presented here, the summed circumferences for humerus plus femur for 33 species of quadrupedal mammals was the predictor variable in the reference sample and body mass was the response variable. The allometric equation obtained by back-transformation from logarithms was not a good fit to the largest species in the reference sample and presumably led to grossly inaccurate estimates for body mass of several large dinosaurs. In contrast, the allometric equation obtained by nonlinear regression described data in the reference sample quite well, and it presumably resulted in better estimates for body mass of the dinosaurs. The problem with the traditional analysis can be traced to change in the relationship between predictor and response variables attending transformation, thereby causing measurements for large animals not to be weighted appropriately in fitting models by least squares regression. Extrapolations from statistical models obtained by back-transformation from lines fitted to logarithms are unlikely to yield reliable predictions for body size in extinct animals. Numerous reports on the biology of dinosaurs, including recent studies of growth, may need to be reconsidered in light of our findings.     

On the analysis of non‐linear allometries

Abstract 1. Non‐linear allometries are those where a log–log scatterplot of trait size against body size deviates from simple linearity. These are found in many insects, including the horns of beetles, the forceps of earwigs, and the heads of certain castes of ant. 2. Non‐linear allometries are often associated with polyphenism that is itself related to behaviour: for example, the alternative mating tactics displayed by many species of beetle are widely associated with dimorphisms in horn size. 3. This paper critically reviews the current techniques used to analyse these datasets. 4. Recommendations include the use of scatterplots and assessment of the goodness of fit of simple linear models as an initial screen for non‐linear allometry. The use of recently developed algorithms for ‘segmented' regression to analyse continuous allometric relationships, and a pragmatic approach to the analysis of discontinuous relationships that recognises that there is no simple way to distinguish between morphs in some cases, and that all of the proposed methods for doing so have some drawbacks. 5. Worked examples of the analysis of two sets of data from animals that have been the subject of controversy regarding the nature of their allometric relationships are given: further worked examples are provided as online Supporting Information.     

Estimating the effects of non‐native species on nutrient recycling using species‐specific and general allometric models

相似文献   

Scaling of rectal gland mass in the European lesser-spotted dogfish

In the European lesser-spotted dogfish Scyliorhinus canicula , rectal gland mass in mg ( M _Rg) followed the allometric relationship: M _Rg = 1·15 M ^0·68, where M is body mass (g). The concept of allometric scaling is an important consideration in studies investigating the function of osmoregulatory organs.     

Scaling of metabolic rate in the lesser wax moth Achroia grisella does not fit the 3/4‐power law and shows significant sex differences

Allometric scaling of metabolic rates is commonly described as a power function and 0.75 is a widely accepted exponent. The universality of this exponent is in doubt and, particularly for insects, contradictory results have been obtained. Furthermore, sexual differences in scaling exponents are observed for several species that could lead to artefacts when they are not considered in intra‐ and interspecific scaling. Whether the metabolic scaling exponent in the lesser wax moth Achroia grisella differs significantly from 0.75 is tested, as well as whether it differs between the sexes. Adults of this moth neither feed nor drink, rendering them as suitable subjects for a study of metabolic rates. Neglecting sex differences, a metabolic scaling exponent of 0.8 is recorded. However, there are significant differences in metabolic scaling between the sexes. When considered separately, males scale with 0.96 and females with 0.67. Thus, in this species, a scaling exponent of 0.75 does not appear to exist either for males or females. The body size optimization model offers a potential explanation for the sex differences in metabolic scaling, although it remains to be tested in wax moths. With insects in particular, there is the need for more detailed studies on the scaling of metabolic rates that also take sexual differences into account.     

Coevolution of body size and metabolic rate in vertebrates: a life‐history perspective

Despite many decades of research, the allometric scaling of metabolic rates (MRs) remains poorly understood. Here, we argue that scaling exponents of these allometries do not themselves mirror one universal law of nature but instead statistically approximate the non‐linearity of the relationship between MR and body mass. This ‘statistical’ view must be replaced with the life‐history perspective that ‘allows’ organisms to evolve myriad different life strategies with distinct physiological features. We posit that the hypoallometric allometry of MRs (mass scaling with an exponent smaller than 1) is an indirect outcome of the selective pressure of ecological mortality on allocation ‘decisions’ that divide resources among growth, reproduction, and the basic metabolic costs of repair and maintenance reflected in the standard or basal metabolic rate (SMR or BMR), which are customarily subjected to allometric analyses. Those ‘decisions’ form a wealth of life‐history variation that can be defined based on the axis dictated by ecological mortality and the axis governed by the efficiency of energy use. We link this variation as well as hypoallometric scaling to the mechanistic determinants of MR, such as metabolically inert component proportions, internal organ relative size and activity, cell size and cell membrane composition, and muscle contributions to dramatic metabolic shifts between the resting and active states. The multitude of mechanisms determining MR leads us to conclude that the quest for a single‐cause explanation of the mass scaling of MRs is futile. We argue that an explanation based on the theory of life‐history evolution is the best way forward.     

Effect of body size, temperature, and salinity on the routine metabolism of larval and juvenile spotted seatrout

Routine oxygen consumption rates of young spotted seatrout Cynoscion nebulosus (Sciaenidae) were measured over a range of temperatures (24, 28, 30 and 32° C) and salinities (5, 10, 20, 35 and 45). Larvae and juveniles, 4·1–39·5 mm standard length ( L _S), ranging several orders of magnitude in dry body mass were used to estimate the mass–metabolism relationship. Oxygen consumption (μl O₂ larva⁻¹ h⁻¹) scaled isometrically with body mass for larvae <5·8 mm L _S(phase I, slope = 1·04) and allometrically thereafter (phase II, slope = 0·78). The inflection in the mass–metabolism relationship coincided with the formation of the hypural plate and an increase in the relative tail size of larvae. Salinity did not have a significant effect on routine metabolism during phase I. Temperature and salinity significantly affected routine metabolism during phase II of the mass–metabolism relationship. The effect of salinity was temperature dependent, and was significant only at 30° C. Response surfaces describing the environmental influences on routine metabolism were developed to provide a bioenergetic basis for modelling environmental constraints on growth.     

Allometric and non‐allometric consequences of inbreeding on Drosophila melanogaster wings

Inbreeding is expected to increase the variability in size and shape within populations. The distinct effects of inbreeding on size and shape suggest that they are governed by different developmental pathways. One unresolved question is whether the non‐allometric shape component is partially unconstrained developmentally and therefore whether shape is evolvable. In the present study, we utilized a mass outbred population of Drosophila melanogaster maintained at standard laboratory conditions. Eight lines with equivalent expected levels of inbreeding (F ≈ 0.67) were obtained by restricting the size of each population to two pairs for nine generations. Nine landmarks were measured on Drosophila wings of the inbreed lines and compared with those of the mass population. Wing landmarks comprise an excellent model system for studying evolution of size and shape. Landmark measurements were analyzed with a Procrustes generalized least squares procedure. To visualize global shape changes among samples, we reconstructed the mean shape and the shape changes related to both the allometric and non‐allometric components. An increased variability in the non‐allometric shape component was found with inbreeding. This indicated that shape was not entirely developmentally constrained, and therefore that shape appears to be evolvable. © 2011 The Linnean Society of London, Biological Journal of the Linnean Society, 2011, 102 , 626–634.     

Variation in scorpion metabolic rate and rate-temperature relationships: implications for the fundamental equation of the metabolic theory of ecology

The fundamental equation of the metabolic theory of ecology (MTE) indicates that most of the variation in metabolic rate are a consequence of variation in organismal size and environmental temperature. Although evolution is thought to minimize energy costs of nutrient transport, its effects on metabolic rate via adaptation, acclimatization or acclimation are considered small, and restricted mostly to variation in the scaling constant, b(0). This contrasts strongly with many conclusions of evolutionary physiology and life-history theory, making closer examination of the fundamental equation an important task for evolutionary biologists. Here we do so using scorpions as model organisms. First, we investigate the implications for the fundamental equation of metabolic rate variation and its temperature dependence in the scorpion Uroplectes carinatus following laboratory acclimation. During 22 days of acclimation at 25 degrees C metabolic rates declined significantly (from 127.4 to 78.2 microW; P = 0.0001) whereas mean body mass remained constant (367.9-369.1 mg; P = 0.999). In field-fresh scorpions, metabolic rate-temperature (MRT) relationships varied substantially within and among individuals, and therefore had low repeatability values (tau = 0.02) and no significant among-individual variation (P = 0.181). However, acclimation resulted in a decline in within-individual variation of MRT slopes which subsequently revealed significant differences among individuals (P = 0.0031) and resulted in a fourfold increase in repeatability values (tau = 0.08). These results highlight the fact that MRT relationships can show substantial, directional variation within individuals over time. Using a randomization model we demonstrate that the reduction in metabolic rate with acclimation while body mass remains constant causes a decline both in the value of the mass-scaling exponent and the coefficient of determination. Furthermore, interspecific comparisons of activation energy, E, demonstrated significant variation in scorpions (0.09-1.14 eV), with a mean value of 0.77 eV, significantly higher than the 0.6-0.7 eV predicted by the fundamental equation. Our results add to a growing body of work questioning both the theoretical basis and empirical support for the MTE, and suggest that alternative models of metabolic rate variation incorporating explicit consideration of life history evolution deserve further scrutiny.     

On the use of EEG autointervalograms for analyzing the responses to periodic light stimulation

Autointervalograms of the extremums of human electroencephalograms (EEGs) recorded under periodic stimulation were analyzed. The method was compared with visual EEG analysis and EEG sinusoid testing. It was shown that, in most cases, the construction of intervalograms is as good as, or even better than, the other two methods, because it allows us to detect the responses and obtain additional information.     

New perspectives on the evolution of exaggerated traits

The scaling of body parts is central to the evolution of morphology and shape. Most traits scale proportionally with each other and body size such that larger adults are essentially magnified versions of smaller ones. This pattern is so ubiquitous that departures from it – disproportionate scaling between trait and body size – pique interest because it can generate dramatically exaggerated traits. These extreme morphologies are frequently hypothesized to result from sexual selection and their study has a long history, with several hypotheses seeking to explain their evolution. Despite this effort, surprisingly little progress has been made in demonstrating the forms of selection that produce different scaling patterns or in identifying the mechanisms that underlie the expression and evolution of scaling relationships. Here we review recent insights regarding the proximate mechanisms that regulate and integrate trait growth and that offer a new framework for studying the evolution of morphological scaling.     

On the use of structural templates for high‐resolution docking

Reliable high‐resolution prediction of protein complex structures starting from the free monomers is a considerable challenge toward large‐scale mapping of the structural details of protein‐protein interactions. The current major bottleneck is to model the conformational changes of the monomer backbone upon binding. We evaluate the use of homolog structures as source for conformational diversity, within the framework of RosettaDock—a leading high‐resolution docking protocol. We find that the use of homolog templates can improve significantly the modeling of a complex structure, including known difficult cases. Several conformational changes however are not sampled by any of the templates, indicating the need for additional sources of conformational variability. Interestingly, the successful homolog templates are not restricted to a confined range of sequence identity, highlighting the importance of the backbone conformation rather than the sequence. Proteins 2010. © 2010 Wiley‐Liss, Inc.