Self-organized critical forest-fire model on large scales

Finite-size scaling of critical avalanches

We examine probability distribution for avalanche sizes observed in self-organized critical systems. While a power-law distribution with a cutoff because of finite system size is typical behavior, a systematic investigation reveals that it may also decrease with increasing the system size at a fixed avalanche size. We implement the scaling method and identify scaling functions. The data collapse ensures a correct estimation of the critical exponents and distinguishes two exponents related to avalanche size and system size. Our simple analysis provides striking implications. While the exact value for avalanches size exponent remains elusive for the prototype sandpile on a square lattice, we suggest the exponent should be 1. The simulation results represent that the distribution shows a logarithmic system size dependence, consistent with the normalization condition. We also argue that for the train or Oslo sandpile model with bulk drive, the avalanche size exponent is slightly less than 1, which differs significantly from the previous estimate of 1.11.

Shocks generate crossover behavior in lattice avalanches

A spatial avalanche model is introduced, in which avalanches increase stability in the regions where they occur. Instability is driven globally by a driving process that contains shocks. The system is typically subcritical, but the shocks occasionally lift it into a near- or supercritical state from which it rapidly retreats due to large avalanches. These shocks leave behind a signature-a distinct power-law crossover in the avalanche size distribution. The model is inspired by landslide field data, but the principles may be applied to any system that experiences stabilizing failures, possesses a critical point, and is subject to an ongoing process of destabilization that includes occasional dramatic destabilizing events.

Propagation of local interactions create global gap structure and dynamics in a tropical rainforest

Gap dynamics in tropical forests are of interest because an understanding of them can help to predict canopy structure and biodiversity. We present a simple cellular automaton model that is capable of capturing many of the trends seen in the canopy gap pattern of a complex tropical rainforest on the Barro Colorado Island (BCI) using a single set of model parameters. We fit the global and local densities, the cluster size distributions, and two correlation functions, for gaps, gap formations, and gap closures determined from a spatial map of the forest (1983-1984). To the best of our knowledge, this is the first report that the cluster size distributions of gap formations and closures in the BCI are both power laws. An important element in the model is that when a transition from gap to non-gap (closure), or vice versa (formation), occurs, this transition is allowed to expand into adjacent cells in order to make different cluster sizes of transitions. Model results are in excellent agreement with reported field data. The propagation of local interactions is necessary in order to obtain the complex dynamics of the gap pattern. We also establish a connection between the global and local densities via the neighborhood-dependent transition rates and the effective global transition rates.

Lattice geometry, gap formation and scale invariance in forests

The geometry of the lattice used in ecological modeling is important because of the local nature of ecological interactions. The latter can generate complex behavior such as criticality (scale-invariance). In this work, we implement two slightly different forest disturbance models on three lattices, each with square, triangular and hexagonal symmetry, in order to study the effect of geometry. We calculate the density distribution of gaps in a forest and find bumps in the distribution at sizes that depend on lattice geometry. Similar bumps were observed in real data but remained unexplainable. We suggest that these bumps provide information about the geometry and scale of ecological interactions. We also found an effect of geometry on the conditions under which criticality appears in model forests. These conditions appear to be more biologically realistic, and also linked to the likelihood of local disturbance propagation. The scaling exponent of the gap-size distribution, however, was found to be independent of both model and geometry, a hallmark of universality.