Many ecological systems, such as shrublands in semi-arid ecosystems and mussel beds in the intertidal, exhibit striking spatial self-organized patterns. It has been suggested that the nature of local ecological interactions, such as the relative scales of competition and facilitation, can strongly influence the type of emerging spatial patterns, leading to

i) regular, periodic patches with a characteristic patch size, or to

ii) no characteristic scale of patchiness.

Regular patterns (periodic)

In ecosystems exhibiting periodic patterns, as the level of external stress increases, a predictable sequence of self-organized patterns based on ‘Turing instability’ occurs. In areas with no preferred orientation of the pattern, the shape of the patterns shifts from gaps to labyrinths and to spots as the system becomes more degraded. Thus, spotted vegetation patterns have been proposed to be an early warning signal of imminent desertification in drylands characterized by periodic patterns. In areas with band-like patterns, the wavelength increases as the system approaches a transition.

Irregular patterns (non-periodic)

In contrast to periodic patterns, there are cases where spatial processes give rise to non-periodic (irregular) patterns. In these cases, we can quantify the size of each patch and calculate the frequency of occurrence of different patch sizes. It is common practice to characterize the patchiness of these systems by a function that best describes the distribution of patch sizes. Irregular patterns may be characterized by a scale-free patch-size distribution, which means that there is no typical patch size in the ecosystem. Such a distribution may be well approximated by a pure power law or by other heavy-tailed functions, such as a log-normal, a stretched exponential or a power law with cutoff. It has been hypothesized that an increasing deviation from power-law distribution of patch sizes can signal increasing degradation.