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 towards ecologists, our goal here is to review the quantitative aspects of NT and its extensions for physicists who are inter- problems remain unresolved. Furthermore, we hope that this review could also be of interest to theoretical ecologists because many potentially interesting results are buried in the vast NT literature. We propose to make these more accessible by extracting them and presenting them in a logical fashion. The focus of this review is broader than NT: we also discuss new, more recent approaches for studying ecological systems and how one might introduce realistic non-neutral models. CONTENTS

The assembly of an ecosystem such as a tropical forest depends crucially on the species interaction network, and the deduction of its rules is a formidably complex problem. In spite of this, many recent studies using Hubbell's neutral theory of biodiversity and biogeography have demonstrated that the resulting emergent macroscopic behaviour of the ecosystem at or near a stationary state shows a surprising simplicity reminiscent of many physical systems. Indeed the symmetry postulate, that the effective birth and death rates are species-independent within a single trophic level, allows one to make analytical predictions for various static distributions such as the relative species abundance, beta-diversity and the species-area relationship. In contrast, there have only been a few studies of the dynamics and stability of tropical rain forests. Here we consider the dynamical behaviour of a community, and benchmark it against the exact predictions of a neutral model near or at stationarity. In addition to providing a description of the relative species abundance, our analysis leads to a quantitative understanding of the species turnover distribution and extinction times, and a measure of the temporal scales of neutral evolution. Our model gives a very good description of the large quantity of data collected in Barro Colorado Island in Panama in the period 1990-2000 with just three ecologically relevant parameters and predicts the dynamics of extinction of the existing species.

[1] 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.

Abstract. The measurement and prediction of species' populations at different spatial scales is crucial to spatial ecology as well as conservation biology. An efficient yet challenging goal to achieve such population estimates consists of recording empirical species' presence and absence at a specific regional scale and then trying to predict occupancies at finer scales. So far the majority of the methods have been based on particular species' distributional features deemed to be crucial for downscaling occupancy. However, only a minority of them have dealt explicitly with specific spatial features. Here we employ a wide class of spatial point processes, the shot noise Cox processes (SNCP), to model species occupancies at different spatial scales and show that species' spatial aggregation is crucial for predicting population estimates at fine scales starting from coarser ones. These models are formulated in continuous space and locate points regardless of the arbitrary resolution that one employs to study the spatial pattern. We compare the performances of nine models, calibrated at regional scales and demonstrate that a very simple class of SNCP, the Thomas process, is able to outperform other published models in predicting occupancies down to areas four orders of magnitude smaller than the ones employed for the parameterization. We conclude by explaining the ability of the approach to infer spatially explicit information from spatially implicit measures, the potential of the framework to combine niche and spatial models, and the possibility of reversing the method to allow upscaling.

The dynamics of two competing species in a finite size community is one of the most studied problems in population genetics and community ecology. Stochastic fluctuations lead, inevitably, to the extinction of one of the species, but the relevant timescale depends on the underlying dynamics. The persistence time of the community has been calculated for neutral models, where the only drive of the system is drift (demographic stochasticity) and for models with strong selection. Following recent analyses that stress the importance of environmental stochasticity in empirical systems, we present here a general theory of persistence time of two-species community where drift, environmental variations and time independent selective advantage are all taken into account.

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Summary 1.A key challenge for both ecological researchers and biodiversity managers is the measurement and prediction of species richness across spatial scales. Typically, biodiversity is assessed at fine scales (e.g. in quadrats or transects) for practical reasons, but often we are interested in coarser-scale (field, regional, global) diversity issues. Moreover, the pressures affecting biodiversity patterns are often scale specific, making multiscale assessment a crucial methodological priority. As species richness is not additive, it is difficult to translate from the scale of measurement to the scale(s) of interest. A number of methods have been proposed to tackle this problem, but most are too model specific or too rigid to allow general application. Here, we present a general framework (and a specific implementation of it) that allows such scale translations to be performed. 2. Building on the intrinsic relationships among patterns of species richness, abundance and spatial turnover, we introduce a framework that links and predicts the profile of the species-area relationship and the speciesabundance distributions across scales when a limited number of fine-scale scattered samples are available. Using the correlation in species' abundances between pairs of samples as a function of the distance between them, we are able to link the effects of aggregation, similarity decay, species richness and species abundances across scales. 3. Our approach allows one to draw inferences about biodiversity scaling under very general assumptions pertaining to the nature of interactions, the geographical distributions of individuals and ecological processes. 4. We demonstrate the accuracy of our predictions using data from two well-studied forest stands and also demonstrate the potential value of such methods by examining the effects of management on farmland insects across scales. The framework has important applications to biodiversity research and conservation practice.

We provide a framework to upscale biodiversity in tropical forests from local samples of species richness and abundances.