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.