The simplest theories often have much merit and many limitations, and, in this vein, the value of neutral theory (NT) of biodiversity has been the subject of much debate over the past 15 years. NT was proposed at the turn of the century by Stephen Hubbell to explain several patterns observed in the organization of ecosystems. Among ecologists, it had a polarizing effect: There were a few ecologists who were enthusiastic, and there were a larger number who firmly opposed it. Physicists and mathematicians, instead, welcomed the theory with excitement. Indeed, NT spawned several theoretical studies that attempted to explain empirical data and predicted trends of quantities that had not yet been studied. While there are a few reviews of NT oriented toward ecologists, the goal here is to review the quantitative aspects of NT and its extensions for physicists who are interested in learning what NT is, what its successes are, and what important problems remain unresolved. Furthermore, this review could also be of interest to theoretical ecologists because many potentially interesting results are buried in the vast NT literature. It is proposed to make these more accessible by extracting them and presenting them in a logical fashion. The focus of this review is broader than NT: new, more recent approaches for studying ecological systems and how one might introduce realistic non-neutral models are also discussed.

We study how river networks, acting as environmental corridors for pathogens, affect the spreading of cholera epidemics. Specifically, we compare epidemiological data from the real world with the space‐time evolution of infected individuals predicted by a theoretical scheme based on reactive transport of infective agents through a biased network portraying actual river pathways. The data pertain to a cholera outbreak in South Africa which started in 2000 and affected in particular the KwaZulu‐Natal province. The epidemic lasted for 2 years and involved about 140,000 confirmed cholera cases. Hydrological and demographic data have also been carefully considered. The theoretical tools relate to recent advances in hydrochory, migration fronts, and infection spreading and are novel in that nodal reactions describe the dynamics of cholera. Transport through network links provides the coupling of the nodal dynamics of infected people, who are assumed to reside at the nodes. This proves a realistic scheme. We argue that the theoretical scheme is remarkably capable of predicting actual outbreaks and, indeed, that network structures play a controlling role in the actual, rather anisotropic propagation of infections, in analogy to spreading of species or to migration processes that also use rivers as ecological corridors.

In this Letter, we explore the dynamics of species abundances within ecological communities using the generalized Lotka-Volterra (GLV) model. At variance with previous approaches, we present an analysis of GLV dynamics with temporal stochastic fluctuations in interaction strengths between species. We develop a dynamical mean field theory (DMFT) tailored for scenarios with colored noise interactions, which we term annealed disorder, and simple functional responses. Our DMFT framework enables us to show that annealed disorder acts as an effective environmental noise; i.e., every species experiences a time-dependent environment shaped by the collective presence of all other species. We then derive analytical predictions for the species abundance distribution that well match empirical observations. Our results suggest that annealed disorder in interaction strengths favors species coexistence and leads to a large pool of very rare species in the systems, supporting the insurance theory of biodiversity. This Letter offers new insights not only into the modeling of large ecosystem dynamics but also proposes novel methodologies for examining ecological systems.