Observation and modelling of vegetation spirals and arcs in isotropic environmental conditions: dissipative structures in arid landscapes

Abstract

We report for the first time on the formation of spirals like vegetation patterns in isotropic and uniform environmental conditions. The vegetation spirals are not waves and they do not rotate. They belong to the class of dissipative structures found out of equilibrium. Isolated or interacting spirals and arcs observed in South America (Bolivia) and North Africa (Morocco) are interpreted as a result of curvature instability that affects the circular shape of localized patches. The biomass exhibits a dynamical behaviour with arcs that transform into spirals. Interpretation of observations and of the predictions provided by the theory is illustrated by recent measurements of peculiar plant morphology (the alfa plant, or Stipa tenacissima L.) originated from northwestern Africa and the southern part of the Iberian Peninsula. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)’.

From nonequilibrium initial conditions to steady dryland vegetation patterns: How trajectories matter

“…The driest IHCs ( ) decay into bare states before three years have elapsed. Slightly wetter IHC ( ) evolve into transient ring patterns –supporting other modelling evidence (Bonanomi et al, ; Fernandez‐Oto et al, ; Sheffer et al, ; Tlidi et al, ; Yizhaq et al, )– which slowly break down into spotted, hybrid‐spotted and spiral patterns. In the central cases ( ) the biomass peaks smoothly develop into vegetation spots.…”

“…Patterns resulting in rather classical periodic patterns (e.g., mm) are the consequence of the well‐establish Turing instability mechanism of pattern generation (Meron, ). The new hybrid patterns (e.g., mm for mm day , and mm for mm day ) are likely the result not of Turing instability but of excitable behaviour (Fernandez‐Oto et al, ; Meron, ; Tlidi et al, ). Excitable behaviour means that a small perturbation or stimulus—that is, the IHC—can generate a strong and propagating response throughout the system and is a phenomenon typical of systems far from equilibrium (Lindner, García‐Ojalvo, Neiman, & Schimansky‐Geier, ). The patterns remain transient after years and even by years for all IHCs including plantless equilibrium.…”

“…Observed patterns have been reported not to coincide with simulated steady‐state patterns (Meron, ). Ring and spiral patterns have been identified as transient (Bonanomi et al, ; Fernandez‐Oto, Escaff, & Cisternas, ; Sheffer, Yizhaq, Shachak, & Meron, ; Tlidi et al, ; Yizhaq et al, ), likely triggered by excitable behaviour (Fernandez‐Oto et al, ; Tlidi et al, ). Discrete rainfall events have been observed to produce transients (Baudena et al, ).…”

Vegetation ring formation by water overland flow in water‐limited environments: Field measurements and mathematical modelling

“…Water‐limited environments are inherently patchy and exhibit a mixture of bare soil and vegetation patches. These ecosystems are defined by self‐organization processes, in which positive biomass–water feedbacks operate at subpatch scales whereas long‐term negative feedbacks induce vegetation patterns at landscape scales (Meron, ; Tlidi et al, ). Much effort has been devoted to modelling water‐limited landscapes and understanding self‐organized patchiness (Borgogno, D'Odorico, Laio, & Ridolfi, ; Deblauwe, Barbier, Couteron, Lejeune, & Bogaert, ; Getzin et al, ; Gilad, von Hardenberg, Provenzale, Shachak, & Meron, , ; Rietkerk, Dekker, De Ruiter, & Van de Koppel, ; Rietkerk & Van de Koppel, ; Yizhaq, Stavi, Shachak, & Bel, ; Zelnik, Meron, & Bel, ).…”

“…Much effort has been devoted to modelling water‐limited landscapes and understanding self‐organized patchiness (Borgogno, D'Odorico, Laio, & Ridolfi, ; Deblauwe, Barbier, Couteron, Lejeune, & Bogaert, ; Getzin et al, ; Gilad, von Hardenberg, Provenzale, Shachak, & Meron, , ; Rietkerk, Dekker, De Ruiter, & Van de Koppel, ; Rietkerk & Van de Koppel, ; Yizhaq, Stavi, Shachak, & Bel, ; Zelnik, Meron, & Bel, ). Very few model studies, however, have been devoted to patterns that emerge at the single‐patch scale, such as spots, rings, crescent‐like shapes, and spirals, and to the biomass–water relationships associated with them (Couteron et al, ; Fernandez‐Oto, Escaff, & Cisternas, ; Meron, Yizhaq, & Gilad, ; Sheffer et al, ; Sheffer, Yizhaq, Gilad, Shachak, & Meron, ; Tlidi et al, ; Tlidi, Lefever, & Vladimirov, ). Model studies of self‐organized patchiness, at both the patch and landscape scales, are important for understanding the relationships among spatial heterogeneity, community structure, and ecosystem functioning (Nathan, Osem, Shachak, & Meron, ).…”