Sandro Azaele

Dynamical evolution of ecosystems.

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, β-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.

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.

Daily streamflow analysis based on a two-scaled gamma pulse model

In this paper, we develop a simple analysis method to infer some properties of the watershed processes from daily streamflow data. The method is built on a simple streamflow model with a link to rainfall stochasticity, which characterizes the streamflow as a series of overlapping gamma distribution-shaped pulses. The key premise of the method is that the complex streamflow processes can be effectively captured by simply dividing streamflow into two regimes. Specifically in this method, the gamma pulse model is applied separately to low- and high-flow regimes. We demonstrate the application of the method to five watersheds and show that it is capable of capturing at least two important statistical properties of streamflow, namely the probability density function and the autocorrelation function for wide ranges of values (i.e., from low to large flows and time lags, respectively).

On neutral metacommunity patterns of river basins at different scales of aggregation

Neutral metacommunity models for spatial biodiversity patterns are implemented on river networks acting as ecological corridors at different resolution. Coarse-graining elevation fields (under the constraint of preserving the basin mean elevation) produce a set of reconfigured drainage networks. The hydrologic assumption made implies uniform runoff production such that each link has the same habitat capacity. Despite the universal scaling properties shown by river basins regardless of size, climate, vegetation, or exposed lithology, we find that species richness at local and regional scales exhibits resolution-dependent behavior. In addition, we investigate species-area relationships and rank-abundance patterns. The slopes of the species-area relationships, which are consistent over coarse-graining resolutions, match those found in real landscapes in the case of long-distance dispersal. The rank-abundance patterns are independent of the resolution over a broad range of dispersal length. Our results confirm that strong interactions occur between network structure and the dispersal of species and that under the assumption of neutral dynamics, these interactions produce resolution-dependent biodiversity patterns that diverge from expectations following from universal geomorphic scaling laws. Both in theoretical and in applied ecology studying how patterns change in resolution is relevant for understanding how ecological dynamics work in fragmented landscape and for sampling and biodiversity management campaigns, especially in consideration of climate change.

Spatial aggregation and the species–area relationship across scales

There has been a considerable effort to understand and quantify the spatial distribution of species across different ecosystems. Relative species abundance (RSA), beta diversity and species-area relationship (SAR) are among the most used macroecological measures to characterize plants communities in forests. In this paper we introduce a simple phenomenological model based on Poisson cluster processes which allows us to exactly link RSA and beta diversity to SAR. The framework is spatially explicit and accounts for the spatial aggregation of conspecific individuals. Under the simplifying assumption of neutral theory, we derive an analytical expression for the SAR which reproduces tri-phasic behavior as sample area increases from local to continental scales, explaining how the tri-phasic behavior can be understood in terms of simple geometric arguments. We also find an expression for the endemic area relationship (EAR) and for the scaling of the RSA.

Predicting spatial similarity of freshwater fish biodiversity

A major issue in modern ecology is to understand how ecological complexity at broad scales is regulated by mechanisms operating at the organismic level. What specific underlying processes are essential for a macroecological pattern to emerge? Here, we analyze the analytical predictions of a general model suitable for describing the spatial biodiversity similarity in river ecosystems, and benchmark them against the empirical occurrence data of freshwater fish species collected in the Mississippi–Missouri river system. Encapsulating immigration, emigration, and stochastic noise, and without resorting to species abundance data, the model is able to reproduce the observed probability distribution of the Jaccard similarity index at any given distance. In addition to providing an excellent agreement with the empirical data, this approach accounts for heterogeneities of different subbasins, suggesting a strong dependence of biodiversity similarity on their respective climates. Strikingly, the model can also predict the actual probability distribution of the Jaccard similarity index for any distance when considering just a relatively small sample. The proposed framework supports the notion that simplified macroecological models are capable of predicting fundamental patterns—a theme at the heart of modern community ecology.

The effect of environmental stochasticity on species richness in neutral communities.

Environmental stochasticity is known to be a destabilizing factor, increasing abundance fluctuations and extinction rates of populations. However, the stability of a community may benefit from the differential response of species to environmental variations due to the storage effect. This paper provides a systematic and comprehensive discussion of these two contradicting tendencies, using the metacommunity version of the recently proposed time-average neutral model of biodiversity which incorporates environmental stochasticity and demographic noise and allows for extinction and speciation. We show that the incorporation of demographic noise into the model is essential to its applicability, yielding realistic behavior of the system when fitness variations are relatively weak. The dependence of species richness on the strength of environmental stochasticity changes sign when the correlation time of the environmental variations increases. This transition marks the point at which the storage effect no longer succeeds in stabilizing the community.

Spontaneously broken neutral symmetry in an ecological system.

Spontaneous symmetry breaking plays a fundamental role in many areas of condensed matter and particle physics. A fundamental problem in ecology is the elucidation of the mechanisms responsible for biodiversity and stability. Neutral theory, which makes the simplifying assumption that all individuals (such as trees in a tropical forest)--regardless of the species they belong to--have the same prospect of reproduction, death, etc., yields gross patterns that are in accord with empirical data. We explore the possibility of birth and death rates that depend on the population density of species, treating the dynamics in a species-symmetric manner. We demonstrate that dynamical evolution can lead to a stationary state characterized simultaneously by both biodiversity and spontaneously broken neutral symmetry.

Absence of detailed balance in ecology

Living systems are typically characterized by irreversible processes. A condition equivalent to the reversibility is the detailed balance, whose absence is an obstacle for analytically solving ecological models. We revisit a promising model with an elegant field-theoretic analytic solution and show that the theoretical analysis is invalid because of an implicit assumption of detailed balance. A signature of the difficulties is evident in the inconsistencies appearing in the many-point correlation functions and in the analytical formula for the species area relationship.

Potential impacts of precipitation change on large-scale patterns of tree diversity

Forests are globally important ecosystems host to outstanding biological diversity. Widespread efforts have addressed the impacts of climate change on biodiversity in these ecosystems. We show that a metacommunity model founded on basic ecological processes offers direct linkage from large-scale forcing, such as precipitation, to tree diversity patterns of the Mississippi-Missouri River System and its subregions. We quantify changes in tree diversity patterns under various projected precipitation patterns, resulting in a range of responses. Uncertainties accompanying global climate models necessitate the use of scenarios of biodiversity. Here we present results from scenarios with the largest losses and gains in tree diversity. Our results suggest that species losses under scenarios with the most dramatic contractions tend to be greater in magnitude, spatial extent, and statistical significance than gains under alternative scenarios. These findings are expected to have important implications for conservation policy and resource management.