Geoffrey B. West

TOWARD A METABOLIC THEORY OF ECOLOGY

Metabolism provides a basis for using first principles of physics, chemistry, and biology to link the biology of individual organisms to the ecology of populations, communities, and ecosystems. Metabolic rate, the rate at which organisms take up, transform, and expend energy and materials, is the most fundamental biological rate. We have developed a quantitative theory for how metabolic rate varies with body size and temperature. Metabolic theory predicts how metabolic rate, by setting the rates of resource uptake from the environment and resource allocation to survival, growth, and reproduction, controls ecological processes at all levels of organization from individuals to the biosphere. Examples include: (1) life history attributes, including devel- opment rate, mortality rate, age at maturity, life span, and population growth rate; (2) population interactions, including carrying capacity, rates of competition and predation, and patterns of species diversity; and (3) ecosystem processes, including rates of biomass production and respiration and patterns of trophic dynamics. Data compiled from the ecological literature strongly support the theoretical predictions. Even- tually, metabolic theory may provide a conceptual foundation for much of ecology, just as genetic theory provides a foundation for much of evolutionary biology.

Growth, innovation, scaling, and the pace of life in cities

Humanity has just crossed a major landmark in its history with the majority of people now living in cities. Cities have long been known to be societys predominant engine of innovation and wealth creation, yet they are also its main source of crime, pollution, and disease. The inexorable trend toward urbanization worldwide presents an urgent challenge for developing a predictive, quantitative theory of urban organization and sustainable development. Here we present empirical evidence indicating that the processes relating urbanization to economic development and knowledge creation are very general, being shared by all cities belonging to the same urban system and sustained across different nations and times. Many diverse properties of cities from patent production and personal income to electrical cable length are shown to be power law functions of population size with scaling exponents, β, that fall into distinct universality classes. Quantities reflecting wealth creation and innovation have β ≈1.2 >1 (increasing returns), whereas those accounting for infrastructure display β ≈0.8 <1 (economies of scale). We predict that the pace of social life in the city increases with population size, in quantitative agreement with data, and we discuss how cities are similar to, and differ from, biological organisms, for which β<1. Finally, we explore possible consequences of these scaling relations by deriving growth equations, which quantify the dramatic difference between growth fueled by innovation versus that driven by economies of scale. This difference suggests that, as population grows, major innovation cycles must be generated at a continually accelerating rate to sustain growth and avoid stagnation or collapse.

A general model for the structure and allometry of plant vascular systems

Vascular plants vary in size by about twelve orders of magnitude, and a single individual sequoia spans nearly this entire range as it grows from a seedling to a mature tree. Size influences nearly all of the structural, functional and ecological characteristics of organisms,. Here we present an integrated model for the hydrodynamics, biomechanics and branching geometry of plants, based on the application of a general theory of resource distribution through hierarchical branching networks to the case of vascular plants. The model successfully predicts a fractal-like architecture and many known scaling laws, both between and within individual plants, including allometric exponents which are simple multiples of 1/4. We show that conducting tubes must taper and, consequently, that the resistance and fluid flow per tube are independent of the total path length and plant size. This resolves the problem of resistance increasing with length, thereby allowing plants to evolve vertical architectures and explaining why the maximum height of trees is about 100 m. It also explains why the energy use of plants in ecosystems is size independent.

A general model for ontogenetic growth.

Several equations have been proposed to describe ontogenetic growth trajectories for organisms justified primarily on the goodness of fit rather than on any biological mechanism. Here, we derive a general quantitative model based on fundamental principles for the allocation of metabolic energy between maintenance of existing tissue and the production of new biomass. We thus predict the parameters governing growth curves from basic cellular properties and derive a single parameterless universal curve that describes the growth of many diverse species. The model provides the basis for deriving allometric relationships for growth rates and the timing of life history events.

Allometric Scaling of Plant Energetics and Population Density

Scaling relationships that describe variation in population density with body size in ecological communities, such as the thinning law in plant ecology, can be explained in terms of how individuals use resources as a function of their size. Data for rates of xylem transport as a function of stem diameter show that rates of resource use in individual plants scale as approximately the 3/4 power of body mass, which is the same as metabolic rates of animals. Here we use this relationship to develop a mechanistic model for relationships between density and mass in resource-limited plants. It predicts that average plant size should scale as the −4/3 power of maximum population density, in agreement with empirical evidence and comparable relationships in animals,,, but significantly less than the −3/2 power predicted by geometric models. Our model implies that fundamental constraints on metabolic rate are reflected in the scaling of population density and other ecological and evolutionary phenomena, including the finding that resource allocation among species in ecosystems is independent of body size,,.

Effects of size and temperature on developmental time

Body size and temperature are the two most important variables affecting nearly all biological rates and times. The relationship of size and temperature to development is of particular interest, because during ontogeny size changes and temperature often varies. Here we derive a general model, based on first principles of allometry and biochemical kinetics, that predicts the time of ontogenetic development as a function of body mass and temperature. The model fits embryonic development times spanning a wide range of egg sizes and incubation temperatures for birds and aquatic ectotherms (fish, amphibians, aquatic insects and zooplankton). The model also describes nearly 75% of the variation in post-embryonic development among a diverse sample of zooplankton. The remaining variation is partially explained by stoichiometry, specifically the whole-body carbon to phosphorus ratio. Development in other animals at other life stages is also described by this model. These results suggest a general definition of biological time that is approximately invariant and common to all organisms.

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, \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape

Allometric scaling of production and life-history variation in vascular plants

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