Mathematical models of vegetation pattern formation in ecohydrology

Abstract

Highly organized vegetation patterns can be found in a number of landscapes around the world. In recent years, several authors have investigated the processes underlying vegetation pattern formation. Patterns that are induced neither by heterogeneity in soil properties nor by the local topography are generally explained as the result of spatial self‐organization resulting from “symmetry‐breaking instability” in nonlinear systems. In this case, the spatial dynamics are able to destabilize the homogeneous state of the system, leading to the emergence of stable heterogeneous configurations. Both deterministic and stochastic mechanisms may explain the self‐organized vegetation patterns observed in nature. After an extensive analysis of deterministic theories, we review noise‐induced mechanisms of pattern formation and provide some examples of applications relevant to the environmental sciences.

Local properties of patterned vegetation: quantifying endogenous and exogenous effects

“…Patterns have been observed in dryland vegetation [5], in bogs and wetlands [6,7], in mussel beds [8], termite mounds [4] and other systems [9]. In many cases, ecological patterns form an intermediate realization between environmental states in which the entire landscape is either colonized or bare.…”

“…Vegetation pattern formation in dryland ecosystems is a global phenomenon, ranging from random distributions of bare soil and vegetation canopies [12] to highly organized spatial distributions with identifiable length scales and orientations [1,5,13]. Intermediate cases such as power-law (scale-free) clustering [14][15][16], and dendritic structures in which vegetation concentrates along drainage lines [17,18] are also observed.…”

“…The formation of periodic vegetation patterns is strongly linked to the coupling of (i) water redistribution to the vicinity of plants and (ii) competition between individual plants for access to this water resource [3,5,27,28]. The dynamics of patterned vegetation systems has formed a focus of ecohydrological and nonlinear dynamics research, motivated by the increasingly welldemonstrated connection between pattern morphology and desertification risk [1,11,29,30]; and by the inherently interesting nonlinear dynamics of these systems [3,31].…”

Transitions between patterned states in vegetation models for semiarid ecosystems

“…These patterns appear ubiquitously in semi-arid ecosystems, where water is a limiting resource for vegetation growth. Examples include the regular stripe patterns that form on gradual slopes, and the spot, gap, and labyrinth patterns that form on flat terrain [1] (see Figure 1). Flat terrain patterns are observed to be long-lived steady states and are thought to be self-organized phenomena that result from a symmetry-breaking instability in the underlying ecosystem dynamics [2][3][4][5].…”

Periodic versus scale-free patterns in dryland vegetation

“…Models of this kind have been proposed and used to explain the emergence of periodic vegetation patterns and their changes along environmental gradients (Borgogno et al 2009). As many of these models capture the essential ingredients of overland water flow, soil-water dynamics and water-limited biomass growth, they should account for scale-free patterns too, provided these patterns are results of endogenous self-organization.…”