The origin of allometric scaling laws in biology from genomes to ecosystems: towards a quantitative unifying theory of biological structure and organization

Life is the most complex physical phenomenon in the Universe, manifesting an extraordinary diversity of form and function over an enormous scale from the largest animals and plants to the smallest microbes and subcellular units. Despite this many of its most fundamental and complex phenomena scale with size in a surprisingly simple fashion. For example, metabolic rate scales as the 3/4-power of mass over 27 orders of magnitude, from molecular and intracellular levels up to the largest organisms. Similarly, time-scales (such as lifespans and growth rates) and sizes (such as bacterial genome lengths, tree heights and mitochondrial densities) scale with exponents that are typically simple powers of 1/4. The universality and simplicity of these relationships suggest that fundamental universal principles underly much of the coarse-grained generic structure and organisation of living systems. We have proposed a set of principles based on the observation that almost all life is sustained by hierarchical branching networks, which we assume have invariant terminal units, are space-filling and are optimised by the process of natural selection. We show how these general constraints explain quarter power scaling and lead to a quantitative, predictive theory that captures many of the essential features of diverse biological systems. Examples considered include animal circulatory systems, plant vascular systems, growth, mitochondrial densities, and the concept of a universal molecular clock. Temperature considerations, dimensionality and the role of invariants are discussed. Criticisms and controversies associated with this approach are also addressed.

The rate of DNA evolution: effects of body size and temperature on the molecular clock

Observations that rates of molecular evolution vary widely within and among lineages have cast doubts on the existence of a single "molecular clock." Differences in the timing of evolutionary events estimated from genetic and fossil evidence have raised further questions about the accuracy of molecular clocks. Here, we present a model of nucleotide substitution that combines theory on metabolic rate with the now-classic neutral theory of molecular evolution. The model quantitatively predicts rate heterogeneity and may reconcile differences in molecular- and fossil-estimated dates of evolutionary events. Model predictions are supported by extensive data from mitochondrial and nuclear genomes. By accounting for the effects of body size and temperature on metabolic rate, this model explains heterogeneity in rates of nucleotide substitution in different genes, taxa, and thermal environments. This model also suggests that there is indeed a single molecular clock, as originally proposed by Zuckerkandl and Pauling [Zuckerkandl, E. & Pauling, L. (1965) in Evolving Genes and Proteins, eds. Bryson, V. & Vogel, H. J. (Academic, New York), pp. 97-166], but that it "ticks" at a constant substitution rate per unit of mass-specific metabolic energy rather than per unit of time. This model therefore links energy flux and genetic change. More generally, the model suggests that body size and temperature combine to control the overall rate of evolution through their effects on metabolism.

The scaling of animal space use

Space used by animals increases with increasing body size. Energy requirements alone can explain how population density decreases, but not the steep rate at which home range area increases. We present a general mechanistic model that predicts the frequency of interaction, spatial overlap, and loss of resources to neighbors. Extensive empirical evidence supports the model, demonstrating that spatial constraints on defense cause exclusivity of home range use to decrease with increasing body size. In large mammals, over 90% of available resources may be lost to neighbors. Our model offers a general framework to understand animal space use and sociality.

The contribution of small individuals to density-body size relationships: examination of energetic equivalence in reef fishes

A key relationship in ecology is that between density and body size, with the emphasis placed on energetic rules constraining the abundance of larger organisms below that of smaller organisms. Most studies have focused upon the density-body size relationship at the species level. However, energy is gathered at an individual level. We therefore examined this relationship in a coral reef fish assemblage, focusing on individuals. Using a comprehensive data set, with over 14,000 observations we found that the relationship between local density and adult body size differs from the linear relationship predicted by the 'energetic equivalence rule'. However, excluding the smallest size classes, the relationship between body size and individual abundance for intermediate to larger fish did not depart from the predicted -0.75. Unlike plants and intermediate to large reef fishes, the smallest fishes appear to have constraints that may reflect different patterns of resource acquisition.

Similarity of Mammalian Body Size across the Taxonomic Hierarchy and across Space and Time

Although it is commonly assumed that closely related animals are similar in body size, the degree of similarity has not been examined across the taxonomic hierarchy. Moreover, little is known about the variation or consistency of body size patterns across geographic space or evolutionary time. Here, we draw from a data set of terrestrial, nonvolant mammals to quantify and compare patterns across the body size spectrum, the taxonomic hierarchy, continental space, and evolutionary time. We employ a variety of statistical techniques including "sib-sib" regression, phylogenetic autocorrelation, and nested ANOVA. We find an extremely high resemblance (heritability) of size among congeneric species for mammals over approximately 18 g; the result is consistent across the size spectrum. However, there is no significant relationship among the body sizes of congeneric species for mammals under approximately 18 g. We suspect that life-history and ecological parameters are so tightly constrained by allometry at diminutive size that animals can only adapt to novel ecological conditions by modifying body size. The overall distributions of size for each continental fauna and for the most diverse orders are quantitatively similar for North America, South America, and Africa, despite virtually no overlap in species composition. Differences in ordinal composition appear to account for quantitative differences between continents. For most mammalian orders, body size is highly conserved, although there is extensive overlap at all levels of the taxonomic hierarchy. The body size distribution for terrestrial mammals apparently was established early in the Tertiary, and it has remained remarkably constant over the past 50 Ma and across the major continents. Lineages have diversified in size to exploit environmental opportunities but only within limits set by allometric, ecological, and evolutionary constraints.

Effects of Body Size and Temperature on Population Growth

For at least 200 years, since the time of Malthus, population growth has been recognized as providing a critical link between the performance of individual organisms and the ecology and evolution of species. We present a theory that shows how the intrinsic rate of exponential population growth, rmax, and the carrying capacity, K, depend on individual metabolic rate and resource supply rate. To do this, we construct equations for the metabolic rates of entire populations by summing over individuals, and then we combine these population-level equations with Malthusian growth. Thus, the theory makes explicit the relationship between rates of resource supply in the environment and rates of production of new biomass and individuals. These individual-level and population-level processes are inextricably linked because metabolism sets both the demand for environmental resources and the resource allocation to survival, growth, and reproduction. We use the theory to make explicit how and why rmax exhibits its characteristic dependence on body size and temperature. Data for aerobic eukaryotes, including algae, protists, insects, zooplankton, fishes, and mammals, support these predicted scalings for rmax. The metabolic flux of energy and materials also dictates that the carrying capacity or equilibrium density of populations should decrease with increasing body size and increasing temperature. Finally, we argue that body mass and body temperature, through their effects on metabolic rate, can explain most of the variation in fecundity and mortality rates. Data for marine fishes in the field support these predictions for instantaneous rates of mortality. This theory links the rates of metabolism and resource use of individuals to life-history attributes and population dynamics for a broad assortment of organisms, from unicellular organisms to mammals.

Pediatric cervical spine: normal anatomy, variants, and trauma

Emergency radiologic evaluation of the pediatric cervical spine can be challenging because of the confusing appearance of synchondroses, normal anatomic variants, and injuries that are unique to children. Cervical spine injuries in children are usually seen in the upper cervical region owing to the unique biomechanics and anatomy of the pediatric cervical spine. Knowledge of the normal embryologic development and anatomy of the cervical spine is important to avoid mistaking synchondroses for fractures in the setting of trauma. Familiarity with anatomic variants is also important for correct image interpretation. These variants include pseudosubluxation, absence of cervical lordosis, wedging of the C3 vertebra, widening of the predental space, prevertebral soft-tissue widening, intervertebral widening, and "pseudo-Jefferson fracture." In addition, familiarity with mechanisms of injury and appropriate imaging modalities will aid in the correct interpretation of radiologic images of the pediatric cervical spine.

Localization, cDNA sequence and genomic organization of the rat seipin gene (Bscl2) and sequence analysis in inbred rat models of Type 2 diabetes mellitus

Mutations in the gene encoding seipin cause Berardinelli-Seip congenital lipodystrophy 2, with symptoms including near-absence of adipose tissue and altered glucose tolerance. Radiation hybrid analysis localized the seipin gene (Bscl2) in rat to a major quantitative trait locus in rat chromosome 1 linked to glucose intolerance in the Goto-Kakizaki (GK) rat model of Type 2 diabetes. We determined the genomic organization of Bscl2 and screened coding exons and flanking intron sequences for mutations in GK, Wistar and Brown Norway rats, as well as in the Otsuka Long-Evans Tokushima Fatty (OLETF) diabetic rat. Two silent single nucleotide polymorphisms that were identified also were found in non-diabetic rat strains. We conclude that mutations in the gene for seipin are unlikely to contribute to diabetes in GK and OLETF rats.