Maritan A

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.

Optimal paths and universality

Optimal paths in disordered systems are studied using two different models interpolating between weak and infinitely strong disorder. In one case, exact numerical methods are used to study the optimal path in a two-dimensional square lattice whereas a renormalization-group analysis is employed on hierarchical lattices in the other. The scaling behaviour is monitored as a function of parameters that tune the strength of the disorder. Two distinct scenarios are provided by the models: in the first, fractal behaviour occurs abruptly as soon as the disorder widens, while in the other it emerges as a limiting case of a self-affine regime.

Neutral theory: 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.

Phase diagrams of random-field Ising systems

We show that the random-field Ising model may be tuned to obtain two distinct scenarios of phase diagram topology. Explicit evidence for this is presented in a numerically exact analysis in three dimensions and on a Bethe lattice, which allows us to investigate the effects of temperature, coordination number, and asymmetry in the field distribution.

Interfacial geometry and overhanging configurations

Simple optimization and growth models are studied numerically and also using analytic arguments to assess the importance of overhanging configurations of the interface and differences between quenched and annealed disorder.