Scaling relationships (where body size features as the independent variable) and power-law distributions are commonly reported in ecological systems. In this review we analyze scaling relationships related to energy acquisition and transformation and power-laws related to fluctuations in numbers. Our aim is to show how individual level attributes can help to explain and predict patterns at the level of populations that can propagate at upper levels of organization. We review similar relationships also appearing in the analysis of aquatic ecosystems (i.e. the biomass spectra) in the context of ecological invariant relationships (i.e. independent of size) such as the 'energetic equivalence rule' and the 'linear biomass hypothesis'. We also discuss some power-law distributions emerging in the analysis of numbers and fluctuations in ecological attributes as they point to regularities that are yet to be integrated with traditional scaling relationships and which we foresee as an exciting area of future research.

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Climate change could profoundly affect the status of agricultural insect pests. Several approaches have been used to predict how the temperature and precipitation changes could modify the abundances, distributions or status of insect pests. In this article it is demonstrated how the use of simple models, such as Ricker’s classic equation, including a mechanistic representation of the influence of exogenous forces may improve our predictive capacity of the dynamic behaviour of insect populations. Using data from classical experiments in population ecology, we evaluate how temperature and humidity influence the density of two stored grain insect pest, Tribolium confusum and Callosobruchus chinensis, and then, using the A2 and B2 scenarios proposed by the Intergovernmental Panel on Climate Change and the previous modelling, we develop predictions over the future pest status of T. confusum along South America austral region, and specifically for eight cities in the continental Chilean territory. Tribolium confusum and C. chinensis show qualitatively different responses to the exogenous forcing of temperature and humidity, respectively. Our simulations predict a change in the equilibrium density of T. confusum from 10 to 14% under the moderate B2 scenario and 12 to 22% under the extreme A2 scenario to the period, 2071–2100. Both results imply a severe change in the pest status of this species in the southern region. This study illustrates how the use of theoretically based models may improve our predictive capacity. This approach provides an opportunity to examine the link between invasive species and climate change and how new suitable habitat may become available for species whose niche space is limited in some degree by climatic conditions. The use of different scenarios allows us to examine the sensitivity of the predictions, and to improve the communication with the general public and decision‐makers; a key aspect in integrated pest management.

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Complex ecological and economic systems show fluctuations in macroscopic quantities such as exchange rates, size of companies or populations that follow non-Gaussian tent-shaped probability distributions of growth rates with power-law decay, which suggests that fluctuations in complex systems may be governed by universal mechanisms, independent of particular details and idiosyncrasies. We propose here that metabolic rate within individual organisms may be considered as an example of an emergent property of a complex system and test the hypothesis that the probability distribution of fluctuations in the metabolic rate of individuals has a ''universal'' form regardless of body size or taxonomic affiliation. We examined data from 71 individuals belonging to 25 vertebrate species (birds, mammals, and lizards). We report three main results. First, for all these individuals and species, the distribution of metabolic rate fluctuations follows a tent-shaped distribution with power-law decay. Second, the standard deviation of metabolic rate fluctuations decays as a powerlaw function of both average metabolic rate and body mass, with exponents ؊0.352 and ؊1/4 respectively. Finally, we find that the distributions of metabolic rate fluctuations for different organisms can all be rescaled to a single parent distribution, supporting the existence of general principles underlying the structure and functioning of individual organisms.allometry ͉ body mass ͉ Laplace distribution L iving organisms have been described as the most complex system in the universe, emerging from the activity of an adaptive network of interacting components that allows energy, materials, and information to be acquired, stored, distributed, and transformed (1, 2), and whose end result is the maintenance and reproduction of the network itself (3). A striking feature of complex systems is that they show regularities in the behavior of macroscopic variables, which emerge as the result of nonlinear interactions among multiple components and because of the competition of opposing control forces (4-6). These regularities commonly take the form of simple scaling relationships or power-laws (7,8). A macroscopic variable that shows scaling relationships is metabolic rate (VO 2 ) (the rate at which an animal consumes oxygen), which scales with body mass (M) such that VO 2 ϰ M a with ␣Ͻ1.For over a century, biologists have documented and tried to explain both the value of ␣, and the effects ecological factors have on it (1, 9-17). Most of these studies focus on average values of VO 2 and M, and do not consider the temporal variability in individual energy use. However, physiological variables, such as cardiac and breathing dynamics, display complex rhythms, which often show changes both with disease and aging (17)(18)(19)(20). In this context, the study of fluctuations in VO 2 can shed light on the determinants of metabolic scaling and provide a way to test competing models and explanations. Indeed, work on complex systems has shown that study of the scaling prope...

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