Problems of allometric scaling analysis: examples from mammalian reproductive biology.

Biological scaling analyses employing the widely used bivariate allometric model are beset by at least four interacting problems: (1) choice of an appropriate best-fit line with due attention to the influence of outliers; (2) objective recognition of divergent subsets in the data (allometric grades); (3) potential restrictions on statistical independence resulting from phylogenetic inertia; and (4) the need for extreme caution in inferring causation from correlation. A new non-parametric line-fitting technique has been developed that eliminates requirements for normality of distribution, greatly reduces the influence of outliers and permits objective recognition of grade shifts in substantial datasets. This technique is applied in scaling analyses of mammalian gestation periods and of neonatal body mass in primates. These analyses feed into a re-examination, conducted with partial correlation analysis, of the maternal energy hypothesis relating to mammalian brain evolution, which suggests links between body size and brain size in neonates and adults, gestation period and basal metabolic rate. Much has been made of the potential problem of phylogenetic inertia as a confounding factor in scaling analyses. However, this problem may be less severe than suspected earlier because nested analyses of variance conducted on residual variation (rather than on raw values) reveals that there is considerable variance at low taxonomic levels. In fact, limited divergence in body size between closely related species is one of the prime examples of phylogenetic inertia. One common approach to eliminating perceived problems of phylogenetic inertia in allometric analyses has been calculation of 'independent contrast values'. It is demonstrated that the reasoning behind this approach is flawed in several ways. Calculation of contrast values for closely related species of similar body size is, in fact, highly questionable, particularly when there are major deviations from the best-fit line for the scaling relationship under scrutiny.

The top-down mechanism for body-mass-abundance scaling

Scaling relationships between mean body masses and abundances of species in multitrophic communities continue to be a subject of intense research and debate. The top-down mechanism explored in this paper explains the frequently observed inverse linear relationship between body mass and abundance (i.e., constant biomass) in terms of a balancing of resource biomasses by behaviorally and evolutionarily adapting foragers, and the evolutionary response of resources to this foraging pressure. The mechanism is tested using an allometric, multitrophic community model with a complex food web structure. It is a statistical model describing the evolutionary and population dynamics of tens to hundreds of species in a uniform way. Particularities of the model are the detailed representation of the evolution and interaction of trophic traits to reproduce topological food web patterns, prey switching behavior modeled after experimental observations, and the evolutionary adaptation of attack rates. Model structure and design are discussed. For model states comparable to natural communities, we find that (1) the body-mass-abundance scaling does not depend on the allometric scaling exponent of physiological rates in the form expected from the energetic equivalence rule or other bottom-up theories; (2) the scaling exponent of abundance as a function of body mass is approximately -1, independent of the allometric exponent for physiological rates assumed; (3) removal of top-down control destroys this pattern, and energetic equivalence is recovered. We conclude that the top-down mechanism is active in the model, and that it is a viable alternative to bottom-up mechanisms for controlling body-mass-abundance relations in natural communities.

Testing metabolic scaling theory using intraspecific allometries in Antarctic microarthropods

Quantitative scaling relationships among body mass, temperature and metabolic rate of organisms are still controversial, while resolution may be further complicated through the use of different and possibly inappropriate approaches to statistical analysis. We propose the application of a modelling strategy based on the theoretical approach of Akaike's information criteria and non-linear model fitting (nlm). Accordingly, we collated and modelled available data at intraspecific level on the individual standard metabolic rate of Antarctic microarthropods as a function of body mass (M), temperature (T), species identity (S) and high rank taxa to which species belong (G) and tested predictions from metabolic scaling theory (mass-metabolism allometric exponent b = 0.75, activation energy range 0.2-1.2 eV). We also performed allometric analysis based on logarithmic transformations (lm). Conclusions from lm and nlm approaches were different. Best-supported models from lm incorporated T, M and S. The estimates of the allometric scaling exponent linking body mass and metabolic rate resulted in a value of 0.696 +/- 0.105 (mean +/- 95% CI). In contrast, the four best-supported nlm models suggested that both the scaling exponent and activation energy significantly vary across the high rank taxa (Collembola, Cryptostigmata, Mesostigmata and Prostigmata) to which species belong, with mean values of b ranging from about 0.6 to 0.8. We therefore reached two conclusions: 1, published analyses of arthropod metabolism based on logarithmic data may be biased by data transformation; 2, non-linear models applied to Antarctic microarthropod metabolic rate suggest that intraspecific scaling of standard metabolic rate in Antarctic microarthropods is highly variable and can be characterised by scaling exponents that greatly vary within taxa, which may have biased previous interspecific comparisons that neglected intraspecific variability.

One size fits all: stability of metabolic scaling under warming and ocean acidification in echinoderms

Responses by marine species to ocean acidification (OA) have recently been shown to be modulated by external factors including temperature, food supply and salinity. However the role of a fundamental biological parameter relevant to all organisms, that of body size, in governing responses to multiple stressors has been almost entirely overlooked. Recent consensus suggests allometric scaling of metabolism with body size differs between species, the commonly cited 'universal' mass scaling exponent (b) of A3/4 representing an average of exponents that naturally vary. One model, the Metabolic-Level Boundaries hypothesis, provides a testable prediction: that b will decrease within species under increasing temperature. However, no previous studies have examined how metabolic scaling may be directly affected by OA. We acclimated a wide body-mass range of three common NE Atlantic echinoderms (the sea star Asterias rubens, the brittlestars Ophiothrix fragilis and Amphiura filiformis) to two levels of pCO(2) and three temperatures, and metabolic rates were determined using closed-chamber respirometry. The results show that contrary to some models these echinoderm species possess a notable degree of stability in metabolic scaling under different abiotic conditions; the mass scaling exponent (b) varied in value between species, but not within species under different conditions. Additionally, we found no effect of OA on metabolic rates in any species. These data suggest responses to abiotic stressors are not modulated by body size in these species, as reflected in the stability of the metabolic scaling relationship. Such equivalence in response across ontogenetic size ranges has important implications for the stability of ecological food webs.

Of mice, macaques and men: scaling of virus dynamics and immune responses

In this Opinion piece, I argue that the dynamics of viruses and the cellular immune response depend on the body size of the host. I use allometric scaling theory to interpret observed quantitative differences in the infection dynamics of lymphocytic choriomeningitis virus (LCMV) in mice (Mus musculus), simian immunodeficiency virus (SIV) in rhesus macaques (Macaca mulatta) and human immunodeficiency virus (HIV) in humans.

One size fits all: stability of metabolic scaling under warming and ocean acidification in echinoderms

Responses by marine species to ocean acidification (OA) have recently been shown to be modulated by external factors including temperature, food supply and salinity. However the role of a fundamental biological parameter relevant to all organisms, that of body size, in governing responses to multiple stressors has been almost entirely overlooked. Recent consensus suggests allometric scaling of metabolism with body size differs between species, the commonly cited 'universal' mass scaling exponent (b) of ¾ representing an average of exponents that naturally vary. One model, the Metabolic-Level Boundaries hypothesis, provides a testable prediction: that b will decrease within species under increasing temperature. However, no previous studies have examined how metabolic scaling may be directly affected by OA. We acclimated a wide body-mass range of three common NE Atlantic echinoderms (the sea star Asterias rubens, the brittlestars Ophiothrix fragilis and Amphiura filiformis) to two levels of pCO2 and three temperatures, and metabolic rates were determined using closed-chamber respirometry. The results show that contrary to some models these echinoderm species possess a notable degree of stability in metabolic scaling under different abiotic conditions; the mass scaling exponent (b) varied in value between species, but not within species under different conditions. Additionally, we found no effect of OA on metabolic rates in any species. These data suggest responses to abiotic stressors are not modulated by body size in these species, as reflected in the stability of the metabolic scaling relationship. Such equivalence in response across ontogenetic size ranges has important implications for the stability of ecological food webs.

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. (C) 2003 the Fisheries Society of the British Isles.

Defining the allometric relationship between size and individual fatty acid turnover in barramundi Lates calcarifer

An experiment was conducted with barramundi (Asian seabass; Lates calcarifer) to examine the allometric scaling effect of individual fatty acids. Six treatment size classes of fish were deprived of food for 21days (Treatment A, 10.5±0.13g; Treatment B, 19.2±0.11g; Treatment C, 28.3±0.05g; Treatment D, 122.4±0.10g; Treatment E, 217.6±0.36g; Treatment F, 443.7±1.48g; mean±SD) with each treatment comprising of fifteen fish, in triplicate. The assessment of somatic losses of whole-body energy and lipid were consistent with previous studies, validating the methodology to be extended to individual fatty acids. Live-weight (LW) exponent values were determined to be 0.817±0.010 for energy and 0.895±0.007 for lipid. There were significant differences among the fatty acids ranging from 0.687±0.005 for 20:5n-3 (eicosapentaenoic acid) and 0.954±0.008 for 18:1n-9 (oleic acid). The LW exponent values were applied to existing fatty acid intake and deposition data of barramundi fed with either 100% fish oil or 100% poultry oil. From this the maintenance requirement for each fatty acid was determined. The metabolic demands for maintenance and growth were then iteratively determined for fish over a range of size classes. Application of these exponent values to varying levels of fatty acid intake demonstrated that the biggest driver in the utilisation of fatty acids in this species is deposition demand and despite their reputed importance, the long-chain polyunsaturated fatty acids had nominal to no maintenance requirement.

Exploring metrics to express energy expenditure of physical activity in youth

Background Several approaches have been used to express energy expenditure in youth, but no consensus exists as to which best normalizes data for the wide range of ages and body sizes across a range of physical activities. This study examined several common metrics for expressing energy expenditure to determine whether one metric can be used for all healthy children. Such a metric could improve our ability to further advance the Compendium of Physical Activities for Youth. Methods A secondary analysis of oxygen uptake (VO2) data obtained from five sites was completed, that included 947 children ages 5 to 18 years, who engaged in 14 different activities. Resting metabolic rate (RMR) was computed based on Schofield Equations [Hum Nutr Clin Nut. 39(Suppl 1), 1985]. Absolute oxygen uptake (ml.min-1), oxygen uptake per kilogram body mass (VO2 in ml.kg-1.min-1), net oxygen uptake (VO2 – resting metabolic rate), allometric scaled oxygen uptake (VO2 in ml.kg-0.75.min-1) and YOUTH-MET (VO2.[resting VO2] -1) were calculated. These metrics were regressed with age, sex, height, and body mass. Results Net and allometric-scaled VO2, and YOUTH-MET were least associated with age, sex and physical characteristics. For moderate-to-vigorous intensity activities, allometric scaling was least related to age and sex. For sedentary and low-intensity activities, YOUTH-MET was least related to age and sex. Conclusions No energy expenditure metric completely eliminated the influence of age, physical characteristics, and sex. The Adult MET consistently overestimated EE. YOUTH-MET was better for expressing energy expenditure for sedentary and light activities, whereas allometric scaling was better for moderate and vigorous intensity activities. From a practical perspective, The YOUTH-MET may be the more feasible metric for improving of the Compendium of Physical Activities for Youth.

The Mechanical Genome in Regulation and Infection

Biological information storage and retrieval is a dynamic process that requires the genome to undergo dramatic structural rearrangements. Recent advances in single-molecule techniques have allowed precise quantification of the nano-mechanical properties of DNA [1, 2], and direct in vivo observation of molecules in action [3]. In this work, we will examine elasticity in protein-mediated DNA looping, whose structural rearrangement is essential for transcriptional regulation in both prokaryotes and eukaryotes. We will look at hydrodynamics in the process of viral DNA ejection, which mediates information transfer and exchange and has prominent implications in evolution. As in the case of Kepler's laws of planetary motion leading to Newton's gravitational theory, and the allometric scaling laws in biology revealing the organizing principles of complex networks [4], experimental data collapse in these biological phenomena has guided much of our studies and urged us to find the underlying physical principles.

杜鹃花属(Rhododendron)种间亲缘关系及小枝异速生长分析

杜鹃花属(Rhododendron)植物种间有着丰富的遗传变异，表型变异并不能完全或真实地反映遗传变异，需要利用信息大分子(DNA)的变化来评价其亲缘关系及系统发育。当年生小枝作为一个独立的构件单元，是植物体上最有活力的部分之一，具有重要的生态学意义。本文以杜鹃为材料，首先全面分析了杜鹃花属种间亲缘关系和小枝功能性状间的关系(异速生长)，然后对小枝水平功能属性间的关系进行系统独立比较分析研究，同时验证小枝异速生长关系。 选取23种杜鹃花属植物为材料，利用ISSR分子标记手段对其种间的亲缘关系进行研究和评价，结果发现：1) ISSR位点变异丰富。通过10条ISSR随机引物对供试的混合DNA样品进行分析，共检测到207个标记，其中多态性标记为197个，多态百分率为95.17%，种间表现出丰富的遗传多样性;2) 对ISSR产物进行统计分析的聚类分析结果同传统分类的结果基本一致。说明，ISSR分子标记技术在构建系统发育树方面具有较高的成熟性和可靠性。 本研究还对42种杜鹃花属植物小枝的功能属性进行了异速生长分析，结果发现：1)小枝大小对叶片生物量分配比率的影响不显著，SMA斜率为1.040 (95%的置信区间(CI)=0.998～1.085);但是，小枝越大，叶柄生物量分配比例越高(SMA斜率为1.245，显著大于1.0，呈显著的异速生长关系);2)小枝越小，单叶面积越小(支持Corner法则)，单位质量小枝所支持的叶面积越大，即具有较小枝条和较小叶片的物种可能具有较高的叶面积支持效率。结果有助于更好地理解亲缘关系十分接近的杜鹃花属植物，在不同生境条件下叶片大小的差异，以及在胁迫生境条件下小叶物种更为常见的原因。 此外，本文利用系统独立比较方法结合传统种间比较方法对23种杜鹃植物小枝进行异速生长分析，其中这23种杜鹃是前两方面研究的共有材料。系统独立比较分析分别依据ISSR得出的系统关系和中国植物志提供的系统关系构建两种系统树。结果表明：1)系统独立比较与种间比较分析得出的相关性结果一致;2)两种系统树所得的独立比较分析结果基本一致，相关性均达到极显著水平，即这两种方法作为构建系统树的依据是一致的。

Interaction strengths and net effects in food web models

Understanding how dynamic ecological communities respond to anthropogenic drivers of change such as habitat loss and fragmentation, climate change and the introduction of alien species requires that there is a theoretical framework able to predict community dynamics. At present there is a lack of empirical data that can be used to inform and test predictive models, which means that much of our knowledge regarding the response of ecological communities to perturbations is obtained from theoretical analyses and simulations. This thesis is composed of two strands of research: an empirical experiment conducted to inform the scaling of intraspecific and interspecific interaction strengths in a three species food chain and a series of theoretical analyses on the changes to equilibrium biomass abundances following press perturbations. The empirical experiment is a consequence of the difficulties faced when parameterising the intraspecific interaction strengths in a Lotka-Volterra model. A modification of the dynamic index is used alongside the original dynamic index to estimate intraspecific interactions and interspecific interaction strengths in a three species food. The theoretical analyses focused on the effect of press perturbations to focal species on the equilibrium biomass densities of all species in the community; these perturbations allow for the quantification of a species total net effect. It was found that there is a strong and consistent positive relationship between a species body size and its total net effect for a set of 97 synthetic food webs and also for the Ythan Estuary and Tuesday Lake food webs (empirically described food webs). It is shown that ecological constraints (due to allometric scaling) on the magnitude of entries in the community matrix cause the patterns observed in the inverse community matrix and thus explain the relationship between a species body mass and its total net effect in a community.