The theory of island biogeography 1 asserts that an island or a local community approaches an equilibrium species richness as a result of the interplay between the immigration of species from the much larger metacommunity source area and local extinction of species on the island (local community). Hubbell 2 generalized this neutral theory to explore the expected steady-state distribution of relative species abundance (RSA) in the local community under restricted immigration. Here we present a theoretical framework for the unified neutral theory of biodiversity 2 and an analytical solution for the distribution of the RSA both in the metacommunity (Fisher's log series) and in the local community, where there are fewer rare species. Rare species are more extinction-prone, and once they go locally extinct, they take longer to re-immigrate than do common species. Contrary to recent assertions 3 , we show that the analytical solution provides a better fit, with fewer free parameters, to the RSA distribution of tree species on Barro Colorado Island, Panama 4 , than the lognormal distribution 5,6 .The neutral theory in ecology 2,7 seeks to capture the influence of speciation, extinction, dispersal and ecological drift on the RSA under the assumption that all species are demographically alike on a per capita basis. This assumption, while only an approximation 8-10 , appears to provide a useful description of an ecological community on some spatial and temporal scales 2,7 . More significantly, it allows the development of a tractable null theory for testing hypotheses about community assembly rules. However, until now, there has been no analytical derivation of the expected equilibrium distribution of RSA in the local community, and fits to the theory have required simulations 2 with associated problems of convergence times, unspecified stopping rules, and precision 3 .The dynamics of the population of a given species is governed by generalized birth and death events (including speciation, immigration and emigration). Let b n,k and d n,k represent the probabilities of birth and death, respectively, in the kth species with n individuals with b 21;k ¼ d 0;k ¼ 0: Let p n,k (t) denote the probability that the kth species contains n individuals at time t. In the simplest scenario, the time evolution of p n,k (t) is regulated by the master equation 11-13 dp n;k ðtÞ dt ¼ p nþ1;k ðtÞd nþ1;k þ p n21;k ðtÞb n21;k 2 p n;k ðtÞðb n;k þ d n;k Þ ð 1Þ which leads to the steady-state or equilibrium solution, denoted by P:for n . 0 and where P 0,k can be deduced from the normalization condition P n P n;k ¼ 1: Note that there is no requirement of Box 1Derivation of the RSA of the local communityWe study the dynamics within a local community following the mathematical framework of McKane et al. 27 , who studied a mean-field stochastic model for species-rich communities. In our context, the dynamical rules 2 governing the stochastic processes in the community are:(1) With probability 1-m, pick two individuals at random from the local communi...

A formidable many-body problem in ecology is to understand the complex of factors controlling patterns of relative species abundance (RSA) in communities of interacting species. Unlike many problems in physics, the nature of the interactions in ecological communities is not completely known. Although most contemporary theories in ecology start with the basic premise that species interact, here we show that a theory in which all interspecific interactions are turned off leads to analytical results that are in agreement with RSA data from tropical forests and coral reefs. The assumption of non-interacting species leads to a sampling theory for the RSA that yields a simple approximation at large scales to the exact theory. Our results show that one can make significant theoretical progress in ecology by assuming that the effective interactions among species are weak in the stationary states in species-rich communities such as tropical forests and coral reefs.A variety of patterns have been observed in the RSA distributions, which are measures of the number of species having a given number of individuals, of ecological communities. In particular, tropical forests'"^ and coral reefs'""' exhibit contrasting RSA patterns. In tropical-tree communities there are fewer rare species in the local community than in the metacommunity, whereas the opposite pattern is found in coral reefs. Reference 6 reported log-series-like RSA distributions in local communities, and log-normal-like RSA distributions when a geographically widespread set of coral-reef communities was pooled to estimate the RSA distribution for the metacommunity. In contrast, local tropical-tree communities exhibit log-normal-like RSA distributions, which become more log-series-like at large landscape scales'"'. The log-series RSA distribution has a larger proportion of rare species than the log-normal. Here we consider two distinct types of community structure: first, a relatively small semi-isolated local community surrounded by a very large metacommunity acting as a source of immigrants, as in HubbelFs theory', and, second, spatially isolated island communities whose assemblage acts as the metacommunity*'. For the tropical forest, the timescale for species turnover in the metacommunity is very long compared to the characteristic timescale for immigration, leading to an effectively frozen metacommunity acting as a backdrop for immigration. In coral reefs, in contrast, each local community receives immigrants from all the surrounding semi-isolated local communities, within each of which the species abundances are not frozen in time. We present a simple unified theory for understanding the RSA patterns of tropical forests and coral reefs. Coral reefsConsider a metacommunity consisting of many small semi-isolated local communities, each of which receives immigrants from other local communities. Because of the isolation of the local communities from each other, changes in the RSA distribution of the aggregated metacommunity may be assumed to occur more rapidly th...

The recurrent patterns in the commonness and rarity of species in ecological communities-the relative species abundance-have puzzled ecologists for more than half a century 1,2 . Here we show that the framework of the current neutral theory in ecology [3][4][5][6][7][8][9][10] can easily be generalized to incorporate symmetric density dependence [11][12][13][14] . We can calculate precisely the strength of the rare-species advantage that is needed to explain a given RSA distribution. Previously, we demonstrated that a mechanism of dispersal limitation also fits RSA data well 3,4 . Here we compare fits of the dispersal and density-dependence mechanisms for empirical RSA data on tree species in six New and Old World tropical forests and show that both mechanisms offer sufficient and independent explanations. We suggest that RSA data cannot by themselves be used to discriminate among these explanations of RSA patterns 15 -empirical studies will be required to determine whether RSA patterns are due to one or the other mechanism, or to some combination of both.Ecologists have long sought to explain the high levels of tree diversity that often occur in tropical forests. One aspect of this challenge is to understand the evolutionary origin and maintenance of this diversity on large spatial and temporal scales 16 . Another is to understand how such extraordinarily high alpha (local) tree diversity can be maintained on very local scales in particular tropical forests. For example, there are over a thousand tree species in a 52-hectare plot in Borneo (Lambir, Sarawak, Table 1). Numerous mechanisms have been proposed to explain tropical tree species coexistence on local scales; many of these hypotheses invoke density-and frequencydependent mechanisms. Two of the most prominent of these hypotheses are the Janzen-Connell hypothesis 11,12 and the ChessonWarner hypothesis 13 .The Janzen-Connell hypothesis is that seeds that disperse farther away from the maternal parent are more likely to escape mortality from host-specific predators or pathogens. This spatially structured mortality disfavours the population growth of locally abundant species relative to uncommon species by reducing the probability of species' self-replacement in the same location in the next generation.The Chesson-Warner hypothesis is that a rare-species reproductive advantage arises when species have similar per capita rates of mortality but reproduce asynchronously, and there are overlapping generations. Processes that hold the abundance of a common species in check inevitably lead to rare-species advantage because the space or resources freed up by density-dependent deaths are then exploited by less-common species. Therefore, among-species frequency dependence is the community-level consequence of within-species density dependence, and thus they are two different manifestations of the same phenomenon. There is accumulating empirical evidence that such density-and frequency-dependent processes may play a large part in maintaining the diversity of tropical t...

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

Understanding the evolutionary dynamics of influenza A virus is central to its surveillance and control. While immune-driven antigenic drift is a key determinant of viral evolution across epidemic seasons, the evolutionary processes shaping influenza virus diversity within seasons are less clear. Here we show with a phylogenetic analysis of 413 complete genomes of human H3N2 influenza A viruses collected between 1997 and 2005 from New York State, United States, that genetic diversity is both abundant and largely generated through the seasonal importation of multiple divergent clades of the same subtype. These clades cocirculated within New York State, allowing frequent reassortment and generating genome-wide diversity. However, relatively low levels of positive selection and genetic diversity were observed at amino acid sites considered important in antigenic drift. These results indicate that adaptive evolution occurs only sporadically in influenza A virus; rather, the stochastic processes of viral migration and clade reassortment play a vital role in shaping short-term evolutionary dynamics. Thus, predicting future patterns of influenza virus evolution for vaccine strain selection is inherently complex and requires intensive surveillance, whole-genome sequencing, and phenotypic analysis.