A general basis for quarter-power scaling in animals.

It has been known for decades that the metabolic rate of animals scales with body mass with an exponent that is almost always <1, >2/3, and often very close to 3/4. The 3/4 exponent emerges naturally from two models of resource distribution networks, radial explosion and hierarchically branched, which incorporate a minimum of specific details. Both models show that the exponent is 2/3 if velocity of flow remains constant, but can attain a maximum value of 3/4 if velocity scales with its maximum exponent, 1/12. Quarter-power scaling can arise even when there is no underlying fractality. The canonical "fourth dimension" in biological scaling relations can result from matching the velocity of flow through the network to the linear dimension of the terminal "service volume" where resources are consumed. These models have broad applicability for the optimal design of biological and engineered systems where energy, materials, or information are distributed from a single source.

History matters: ecometrics and integrative climate change biology.

Climate change research is increasingly focusing on the dynamics among species, ecosystems and climates. Better data about the historical behaviours of these dynamics are urgently needed. Such data are already available from ecology, archaeology, palaeontology and geology, but their integration into climate change research is hampered by differences in their temporal and geographical scales. One productive way to unite data across scales is the study of functional morphological traits, which can form a common denominator for studying interactions between species and climate across taxa, across ecosystems, across space and through time-an approach we call 'ecometrics'. The sampling methods that have become established in palaeontology to standardize over different scales can be synthesized with tools from community ecology and climate change biology to improve our understanding of the dynamics among species, ecosystems, climates and earth systems over time. Developing these approaches into an integrative climate change biology will help enrich our understanding of the changes our modern world is undergoing.

The May threshold and life-history allometry.

One of Robert May's classic results was finding that population dynamics become chaotic when the average lifetime rate of reproduction exceeds a certain value. Populations whose reproductive rates exceed this May threshold probably become extinct. The May threshold in each case depends upon the shape of the density-dependence curve, which differs among models of population growth. However, species of different sizes and generation times that share a roughly similar density-dependence curve will also share a similar May threshold. Here, we argue that this fact predicts a striking allometric regularity among animal taxa: lifetime reproductive rate should be roughly independent of body size. Such independence has been observed in diverse taxa, but has usually been ascribed to a fortuitous combination of physiologically based life-history allometries. We suggest, instead, that the ecological elimination of unstable populations within groups that share a value of the May threshold is a likely cause of this allometry.

The space-lifetime hypothesis: viewing organisms in four dimensions, literally.

Much of the debate about alternative scaling exponents may result from unawareness of the dimensionality appropriate for different data and questions; in some cases, analysis has to include a fourth temporal dimension, and in others, it does not. Proportional scaling simultaneously applied to an organism and its generation time, treating the latter as a natural fourth dimension, produces a simple explanation for the 3/4 power in large-scale interspecies comparisons. Analysis of data sets of reduced dimensionality (e.g., data sets constructed such that one or more of the four dimensions are fixed), results in predictably lower metabolic exponents of 2/3 and 1/2 under one and two constraints, respectively. Our space-lifetime view offers a predictive framework that may be useful in developing a more complete mechanistic theory of metabolic scaling.

A macroevolutionary explanation for energy equivalence in the scaling of body size and population density.

Across a wide array of animal species, mean population densities decline with species body mass such that the rate of energy use of local populations is approximately independent of body size. This "energetic equivalence" is particularly evident when ecological population densities are plotted across several or more orders of magnitude in body mass and is supported by a considerable body of evidence. Nevertheless, interpretation of the data has remained controversial, largely because of the difficulty of explaining the origin and maintenance of such a size-abundance relationship in terms of purely ecological processes. Here I describe results of a simulation model suggesting that an extremely simple mechanism operating over evolutionary time can explain the major features of the empirical data. The model specifies only the size scaling of metabolism and a process where randomly chosen species evolve to take resource energy from other species. This process of energy exchange among particular species is distinct from a random walk of species abundances and creates a situation in which species populations using relatively low amounts of energy at any body size have an elevated extinction risk. Selective extinction of such species rapidly drives size-abundance allometry in faunas toward approximate energetic equivalence and maintains it there.

Selection on stability across ecological scales.

Much of the focus in evolutionary biology has been on the adaptive differentiation among organisms. It is equally important to understand the processes that result in similarities of structure among systems. Here, we discuss examples of similarities occurring at different ecological scales, from predator-prey relations (attack rates and handling times) through communities (food-web structures) to ecosystem properties. Selection among systemic configurations or patterns that differ in their intrinsic stability should lead generally to increased representation of relatively stable structures. Such nonadaptive, but selective processes that shape ecological communities offer an enticing mechanism for generating widely observed similarities, and have sparked new interest in stability properties. This nonadaptive systemic selection operates not in opposition to, but in parallel with, adaptive evolution.

Climate change and size evolution in an island rodent species: new perspectives on the island rule.

As stated by the island rule, small mammals evolve toward gigantism on islands. In addition they are known to evolve faster than their mainland counterparts. Body size in island mammals may also be influenced by geographical climatic gradients or climatic change through time. We tested the relative effects of climate change and isolation on the size of the Japanese rodent Apodemus speciosus and calculated evolutionary rates of body size change since the last glacial maximum (LGM). Currently A. speciosus populations conform both to Bergmann's rule, with an increase in body size with latitude, and to the island rule, with larger body sizes on small islands. We also found that fossil representatives of A. speciosus are larger than their extant relatives. Our estimated evolutionary rates since the LGM show that body size evolution on the smaller islands has been less than half as rapid as on Honshu, the mainland-type large island of Japan. We conclude that island populations exhibit larger body sizes today not because they have evolved toward gigantism, but because their evolution toward a smaller size, due to climate warming since the LGM, has been decelerated by the island effect. These combined results suggest that evolution in Quaternary island small mammals may not have been as fast as expected by the island effect because of the counteracting effect of climate change during this period.

On the relationship between hypsodonty and feeding ecology in ungulate mammals, and its utility in palaeoecology.

High-crowned (hypsodont) teeth are widely found among both extant and extinct mammalian herbivores. Extant grazing ungulates (hoofed mammals) have hypsodont teeth (a derived condition), and so extinct hypsodont forms have usually been presumed to have been grazers. Thus, hypsodonty among ungulates has, over the past 150 years, formed the basis of widespread palaeoecological interpretations, and has figured prominently in the evolutionary study of the spread of grasslands in the mid Cenozoic. However, perceived inconsistencies between levels of hypsodonty and dental wear patterns in both extant and extinct ungulates have caused some workers to reject hypsodonty as a useful predictive tool in palaeobiology, a view that we consider both misguided and premature. Despite the acknowledged association between grazing and hypsodonty, the quantitative relationship of hypsodonty to the known ecology of living ungulate species, critical in making interpretations of the fossil record, was little studied until the past two decades. Also, much of the literature on ungulate ecology relevant to understanding hypsodonty has yet to be fully incorporated into the perspectives of palaeontologists. Here we review the history and current state of our knowledge of the relationship between hypsodonty and ungulate ecology, and reassert the value of hypsodonty for our understanding of ungulate feeding behaviour. We also show how soil consumption, rather than the consumption of grass plants per se, may be the missing piece of the puzzle in understanding the observed correlation between diets, habitats, and hypsodonty in ungulates. Additionally, we show how hypsodonty may impact life-history strategies, and resolve some controversies regarding the relevance of hypsodonty to the prediction of the diets of extinct species. This in turn strengthens the utility of hypsodonty in the determination of past environmental conditions, and we provide a revised view of a traditional example of evolutionary trends in palaeobiology, that of the evolution of hypsodonty in horses and its correlation with the Miocene spread of grasslands in North America.

Ecometrics: the traits that bind the past and present together.

We outline here an approach for understanding the biology of climate change, one that integrates data at multiple spatial and temporal scales. Taxon-free trait analysis, or "ecometrics," is based on the idea that the distribution in a community of ecomorphological traits such as tooth structure, limb proportions, body mass, leaf shape, incubation temperature, claw shape, any aspect of anatomy or physiology can be measured across some subset of the organisms in a community. Regardless of temporal or spatial scale, traits are the means by which organisms interact with their environment, biotic and abiotic. Ecometrics measures these interactions by focusing on traits which are easily measurable, whose structure is closely related to their function, and whose function interacts directly with local environment. Ecometric trait distributions are thus a comparatively universal metric for exploring systems dynamics at all scales. The main challenge now is to move beyond investigating how future climate change will affect the distribution of organisms and how it will impact ecosystem services and to shift the perspective to ask how biotic systems interact with changing climate in general, and how climate change affects the interactions within and between the components of the whole biotic-physical system. We believe that it is possible to provide believable, quantitative answers to these questions. Because of this we have initiated an IUBS program iCCB (integrative Climate Change Biology).

Scaling in ecosystems and the linkage of macroecological laws.

Scaling provides an elegant framework for understanding power-law behavior and deducing relationships between critical exponents. We demonstrate that scaling theory can be generalized to develop a framework for the analysis of diverse empirical macroecological relationships traditionally treated as independent. Our mathematical arguments predict links between the species-area relationship, the relative species abundance and community size spectra in excellent accord with empirical data.

SELECTION AMONG "SPECIES": A FORMULATION IN TERMS OF NATURAL FUNCTIONAL UNITS.

The unit that directly evolves under the action of higher-level natural selection "among species" must be the higher-level analogue of the population. Contrary to present formulations of "species selection," clades (or other higher taxa) do not fulfill the basic structural and dynamic criteria to be so considered. Clades are not localized, their members do not share an environment, and they cannot be said to respond to local selective regimes. Traditional species selection does not provide a causal mechanism for evolutionary change in terms of the interaction of the units of selection with a shared environment in the way that conventional organismic selection does; as used by some authors, species selection is a purely descriptive term. Communities do fulfill the criteria required by a theory of natural selection. Within communities, selection is among the populations of different species that make up the community, here termed "avatars" of those species. Avatars are the closest analogues of individual organisms in traditional selection theory. Just as populations evolve by organismic selection, communities evolve by avatar selection, and more inclusive units, the higher-level analogues of the species, evolve as their component communities do. This formulation of higher-level selection reveals a congruence with processes at the lower, organism-based level and suggests the most profitable direction to be taken in attempts at formal extension of selection theory.

Cope's rule, hypercarnivory, and extinction in North American canids.

Over the past 50 million years, successive clades of large carnivorous mammals diversified and then declined to extinction. In most instances, the cause of the decline remains a puzzle. Here we argue that energetic constraints and pervasive selection for larger size (Cope's rule) in carnivores lead to dietary specialization (hypercarnivory) and increased vulnerability to extinction. In two major clades of extinct North American canids, the evolution of large size was associated with a dietary shift to hypercarnivory and a decline in species durations. Thus, selection for attributes that promoted individual success resulted in progressive evolutionary failure of their clades.

Supply-demand balance and metabolic scaling.

It is widely accepted that metabolic rates scale across species approximately as the 3/4 power of mass in most if not all groups of organisms. Metabolic demand per unit mass thus decreases as body mass increases. Metabolic rates reflect both the ability of the organism's transport system to deliver metabolites to the tissues and the rate at which the tissues use them. We show that the ubiquitous 3/4 power law for interspecific metabolic scaling arises from simple, general geometric properties of transportation networks constrained to function in biological organisms. The 3/4 exponent and other observed scaling relationships follow when mass-specific metabolic demands match the changing delivery capacities of the network at different body sizes. Deviation from the 3/4 exponent suggests either inefficiency or compensating physiological mechanisms. Our conclusions are based on general arguments incorporating the minimum of biological detail and should therefore apply to the widest range of organisms.