Igor Volkov

Neutral theory and relative species abundance in ecology.

The theory of island biogeography 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 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 and an analytical solution for the distribution of the RSA both in the metacommunity (Fishers 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, 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, than the lognormal distribution.

Density dependence explains tree species abundance and diversity in tropical forests.

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. Here we show that the framework of the current neutral theory in ecology can easily be generalized to incorporate symmetric density dependence. 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. 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—empirical studies will be required to determine whether RSA patterns are due to one or the other mechanism, or to some combination of both.

Patterns of relative species abundance in rainforests and coral reefs

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.

Stochastic processes are key determinants of short-term evolution in influenza a virus.

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.

Inferring species interactions in tropical forests.

We present 2 distinct and independent approaches to deduce the effective interaction strengths between species and apply it to the 20 most abundant species in the long-term 50-ha plot on Barro Colorado Island, Panama. The first approach employs the principle of maximum entropy, and the second uses a stochastic birth–death model. Both approaches yield very similar answers and show that the collective effects of the pairwise interspecific interaction strengths are weak compared with the intraspecific interactions. Our approaches can be applied to other ecological communities in steady state to evaluate the extent to which interactions need to be incorporated into theoretical explanations for their structure and dynamics.

Applications of the principle of maximum entropy: from physics to ecology

There are numerous situations in physics and other disciplines which can be described at different levels of detail in terms of probability distributions. Such descriptions arise either intrinsically as in quantum mechanics, or because of the vast amount of details necessary for a complete description as, for example, in Brownian motion and in many-body systems. We show that an application of the principle of maximum entropy for estimating the underlying probability distribution can depend on the variables used for describing the system. The choice of characterization of the system carries with it implicit assumptions about fundamental attributes such as whether the system is classical or quantum mechanical or equivalently whether the individuals are distinguishable or indistinguishable. We show that the correct procedure entails the maximization of the relative entropy subject to known constraints and, additionally, requires knowledge of the behavior of the system in the absence of these constraints. We present an application of the principle of maximum entropy to understanding species diversity in ecology and introduce a new statistical ensemble corresponding to the distribution of a variable population of individuals into a set of species not defined a priori.

Spatial scaling in model plant communities.

We present an analytically tractable variant of the voter model that provides a quantitatively accurate description of Beta diversity (two-point correlation function) in two tropical forests. The model exhibits novel scaling behavior that leads to links between ecological measures such as relative species abundance and the species-area relationship.

Molecular dynamics simulations of crystallization of hard spheres.

We have carried out molecular dynamics simulations of the crystallization of hard spheres modeling colloidal systems that are studied in conventional and space-based experiments. We use microscopic probes to investigate the effects of gravitational forces, polydispersity, and of bounding walls on the phase structure. The simulations employed an extensive exclusive particle grid method and the type and degree of crystalline order was studied in two independent ways: by the structure factor, as in experiments, and through local rotational invariants. We present quantitative comparisons of the nucleation rates of monodisperse and polydisperse hard-sphere systems and benchmark them against experimental results. We show how the presence of bounding walls leads to wall-induced nucleation and rapid crystallization, and discuss the role of gravity on the dynamics of crystallization.

Statistical mechanics of ecological systems: Neutral theory and beyond

It is of societal importance to advance the understanding of emerging patterns of biodiversity from biological and ecological systems. The neutral theory offers a statistical-mechanical framework that relates key biological properties at the individual scale with macroecological properties at the community scale. This article surveys the quantitative aspects of neutral theory and its extensions for physicists who are interested in what important problems remain unresolved for studying ecological systems.

Neutral theory (communication arising): The stability of forest biodiversity

The unified neutral theory of biodiversity and biogeography1 provides a dynamic null hypothesis for the assembly of natural communities. It is also useful for understanding the influence of speciation, extinction, dispersal and ecological drift on patterns of relative species abundance, species–area relationships and phylogeny. Clark and McLachlan2 argue that neutral drift is inconsistent with the palaeorecord of stability in fossil pollen assemblages of the Holocene forests of southern Canada. We show here that their analysis is based on a partial misunderstanding of neutral theory and that their data alone cannot unambiguously test its validity.