The role of stochasticity and its interplay with nonlinearity are central current issues in studies of the complex population patterns observed in nature, including the pronounced oscillations of wildlife and infectious diseases. The dynamics of childhood diseases have provided influential case studies to develop and test mathematical models with practical application to epidemiology, but are also of general relevance to the central question of whether simple nonlinear systems can explain and predict the complex temporal and spatial patterns observed in nature outside laboratory conditions. Here, we present a stochastic theory for the major dynamical transitions in epidemics from regular to irregular cycles, which relies on the discrete nature of disease transmission and low spatial coupling. The full spectrum of stochastic fluctuations is derived analytically to show how the amplification of noise varies across these transitions. The changes in noise amplification and coherence appear robust to seasonal forcing, questioning the role of seasonality and its interplay with deterministic components of epidemiological models. Childhood diseases are shown to fall into regions of parameter space of high noise amplification. This type of ‘endogenous’ stochastic resonance may be relevant to population oscillations in nonlinear ecological systems in general.

A central problem in ecology is determining the processes that shape the complex networks known as food webs formed by species and their feeding relationships. The topology of these networks is a major determinant of ecosystems' dynamics and is ultimately responsible for their responses to human impacts. Several simple models have been proposed for the intricate food webs observed in nature. We show that the three main models proposed so far fail to fully replicate the empirical data, and we develop a likelihood-based approach for the direct comparison of alternative models based on the full structure of the network. Results drive a new model that is able to generate all the empirical data sets and to do so with the highest likelihood.

In ecosystems, species interact with other species directly and through abiotic factors in multiple ways, often forming complex networks of various types of ecological interaction. Out of this suite of interactions, predator–prey interactions have received most attention. The resulting food webs, however, will always operate simultaneously with networks based on other types of ecological interaction, such as through the activities of ecosystem engineers or mutualistic interactions. Little is known about how to classify, organize and quantify these other ecological networks and their mutual interplay. The aim of this paper is to provide new and testable ideas on how to understand and model ecosystems in which many different types of ecological interaction operate simultaneously. We approach this problem by first identifying six main types of interaction that operate within ecosystems, of which food web interactions are one. Then, we propose that food webs are structured among two main axes of organization: a vertical (classic) axis representing trophic position and a new horizontal ‘ecological stoichiometry’ axis representing decreasing palatability of plant parts and detritus for herbivores and detrivores and slower turnover times. The usefulness of these new ideas is then explored with three very different ecosystems as test cases: temperate intertidal mudflats; temperate short grass prairie; and tropical savannah.

Climate change impacts on malaria are typically assessed with scenarios for the long-term future. Here we focus instead on the recent past (1970–2003) to address whether warmer temperatures have already increased the incidence of malaria in a highland region of East Africa. Our analyses rely on a new coupled mosquito–human model of malaria, which we use to compare projected disease levels with and without the observed temperature trend. Predicted malaria cases exhibit a highly nonlinear response to warming, with a significant increase from the 1970s to the 1990s, although typical epidemic sizes are below those observed. These findings suggest that climate change has already played an important role in the exacerbation of malaria in this region. As the observed changes in malaria are even larger than those predicted by our model, other factors previously suggested to explain all of the increase in malaria may be enhancing the impact of climate change.