Modeling spatial aggregation of finite populations.

Accurate description of spatial distribution of species is essential for correctly modeling macroecological patterns and thus to infer mechanisms of species coexistence. The Poisson and negative binomial distribution (NBD) are most widely used to respectively model random and aggregated distributions of species in infinitely large areas. As a finite version of the Poisson distribution, the binomial distribution is used to model random distribution of species populations in finite areas. Despite that spatial aggregation is the most widespread pattern and no species in nature are distributed in infinitely large areas, no model is currently available to describe spatial aggregation for species distributed in finite areas. Here we develop a finite counterpart of the NBD to model aggregated species in finite landscapes. Similar to the NBD, this new model also has a parameter k measuring spatial aggregation. When k --> infinity, this model becomes the binomial distribution; when study area approaches infinite, it becomes the NBD. This model was extensively evaluated against the distributions of over 300 tree species in a 50-ha stem-mapping plot from Barro Colorado Island, Panama. The results show that when sampling area is small (relative to the study area), the new model and the NBD are of little difference. But the former correctly models spatial distribution at the finite limit at which the NBD fails. We reveal serious theoretical pathologies by using infinite models to approximate finite distribution and show the theoretical and practical advantages for using the new finite model for modeling species-area relationships, species occupancy and spatial distribution of rare species.

Taking species abundance distributions beyond individuals.

The species abundance distribution (SAD) is one of the few universal patterns in ecology. Research on this fundamental distribution has primarily focused on the study of numerical counts, irrespective of the traits of individuals. Here we show that considering a set of Generalized Species Abundance Distributions (GSADs) encompassing several abundance measures, such as numerical abundance, biomass and resource use, can provide novel insights into the structure of ecological communities and the forces that organize them. We use a taxonomically diverse combination of macroecological data sets to investigate the similarities and differences between GSADs. We then use probability theory to explore, under parsimonious assumptions, theoretical linkages among them. Our study suggests that examining different GSADs simultaneously in natural systems may help with assessing determinants of community structure. Broadening SADs to encompass multiple abundance measures opens novel perspectives in biodiversity research and warrants future empirical and theoretical developments.

Incipient criticality in ecological communities.

In ecology, there have been attempts to establish links between the relative species abundance (RSA), the fraction of species in a community with a given abundance, and a power-law form of the species area relationship (SAR), the dependence of species richness on sampling area. However the SAR and other patterns in ecology often do not exhibit power-law behavior over an appreciable range of scales. This raises the question whether a scaling framework can be applied when the system under analysis does not exhibit power-law behavior. Here, we derive a general finite-size scaling framework applicable to such systems that can be used to identify incipient critical behavior and links the scale dependence of the RSA and the SAR. We confirm the generality of our theory by using data from a serpentine grassland plot, which exhibits a power-law SAR, and the Barro Colorado Island plot in Panama, whose SAR shows deviations from power-law behavior at every scale. Our results demonstrate that scaling provides a model-independent framework for analyzing and unifying ecological data and that, despite the absence of power laws, ecosystems are poised in the vicinity of a critical point.

The maximum entropy formalism and the idiosyncratic theory of biodiversity.

Why does the neutral theory, which is based on unrealistic assumptions, predict diversity patterns so accurately? Answering questions like this requires a radical change in the way we tackle them. The large number of degrees of freedom of ecosystems pose a fundamental obstacle to mechanistic modelling. However, there are tools of statistical physics, such as the maximum entropy formalism (MaxEnt), that allow transcending particular models to simultaneously work with immense families of models with different rules and parameters, sharing only well-established features. We applied MaxEnt allowing species to be ecologically idiosyncratic, instead of constraining them to be equivalent as the neutral theory does. The answer we found is that neutral models are just a subset of the majority of plausible models that lead to the same patterns. Small variations in these patterns naturally lead to the main classical species abundance distributions, which are thus unified in a single framework.

Non-neutral vegetation dynamics.

The neutral theory of biodiversity constitutes a reference null hypothesis for the interpretation of ecosystem dynamics and produces relatively simple analytical descriptions of basic system properties, which can be easily compared to observations. On the contrary, investigations in non-neutral dynamics have in the past been limited by the complexity arising from heterogeneous demographic behaviours and by the relative paucity of detailed observations of the spatial distribution of species diversity (beta-diversity): These circumstances prevented the development and testing of explicit non-neutral mathematical descriptions linking competitive strategies and observable ecosystem properties. Here we introduce an exact non-neutral model of vegetation dynamics, based on cloning and seed dispersal, which yields closed-form characterizations of beta-diversity. The predictions of the non-neutral model are validated using new high-resolution remote-sensing observations of salt-marsh vegetation in the Venice Lagoon (Italy). Model expressions of beta-diversity show a remarkable agreement with observed distributions within the wide observational range of scales explored (5 x 10(-1) m divided by 10(3) m). We also consider a neutral version of the model and find its predictions to be in agreement with the more limited characterization of beta-diversity typical of the neutral theory (based on the likelihood that two sites be conspecific or heterospecific, irrespective of the species). However, such an agreement proves to be misleading as the recruitment rates by propagules and by seed dispersal assumed by the neutral model do not reflect known species characteristics and correspond to averages of those obtained under the more general non-neutral hypothesis. We conclude that non-neutral beta-diversity characterizations are required to describe ecosystem dynamics in the presence of species-dependent properties and to successfully relate the observed patterns to the underlying processes.

The importance of demographic niches to tree diversity.

Most ecological hypotheses about species coexistence hinge on species differences, but quantifying trait differences across species in diverse communities is often unfeasible. We examined the variation of demographic traits using a global tropical forest data set covering 4500 species in 10 large-scale tree inventories. With a hierarchical Bayesian approach, we quantified the distribution of mortality and growth rates of all tree species at each site. This allowed us to test the prediction that demographic differences facilitate species richness, as suggested by the theory that a tradeoff between high growth and high survival allows species to coexist. Contrary to the prediction, the most diverse forests had the least demographic variation. Although demographic differences may foster coexistence, they do not explain any of the 16-fold variation in tree species richness observed across the tropics.

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.