Reversing desertification as a spatial resonance problem

Mau, Yair; Haim, Lev; Meron, Ehud

doi:10.1103/physreve.91.012903

Cited by 16 publications

(9 citation statements)

References 25 publications

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“…We modulate the infiltration rate, as in Eq (5) , to mimic stripes of removed soil crust that form a periodic configuration in the x direction with a wavenumber k f or wavelength L f = 2 π / k f . This is a spatial resonance problem [ 45 , 46 ] whereby a system that tends to self-organize in a periodic pattern with a wavenumber k 0 (wavelength L 0 ) is subjected to an external periodic force of a different wavenumber k f .…”

Section: Resultsmentioning

confidence: 99%

High-integrity human intervention in ecosystems: Tracking self-organization modes

et al. 2021

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Humans play major roles in shaping and transforming the ecology of Earth. Unlike natural drivers of ecosystem change, which are erratic and unpredictable, human intervention in ecosystems generally involves planning and management, but often results in detrimental outcomes. Using model studies and aerial-image analysis, we argue that the design of a successful human intervention form calls for the identification of the self-organization modes that drive ecosystem change, and for studying their dynamics. We demonstrate this approach with two examples: grazing management in drought-prone ecosystems, and rehabilitation of degraded vegetation by water harvesting. We show that grazing can increase the resilience to droughts, rather than imposing an additional stress, if managed in a spatially non-uniform manner, and that fragmental restoration along contour bunds is more resilient than the common practice of continuous restoration in vegetation stripes. We conclude by discussing the need for additional studies of self-organization modes and their dynamics.

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Section: Resultsmentioning

confidence: 99%

High-integrity human intervention in ecosystems: Tracking self-organization modes

et al. 2021

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“…An additional important aspect that bifurcation diagrams uncover is related to the existence of unstable solution branches. Tracking unstable solutions in bifurcation diagrams can be highly significant when the response of ecosystems to disturbances or human intervention is studied, as the appearance or disappearance of unstable solutions can dramatically affect the flow in phase space and, thus, the response [78]. These subtle aspects, which may have significant ecological implications, become apparent once a bifurcation diagram is calculated.…”

Section: Bifurcation Diagramsmentioning

confidence: 99%

Continuum Modeling of Discrete Plant Communities: Why Does It Work and Why Is It Advantageous?

et al. 2019

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Understanding ecosystem response to drier climates calls for modeling the dynamics of dryland plant populations, which are crucial determinants of ecosystem function, as they constitute the basal level of whole food webs. Two modeling approaches are widely used in population dynamics, individual (agent)-based models and continuum partial-differential-equation (PDE) models. The latter are advantageous in lending themselves to powerful methodologies of mathematical analysis, but the question of whether they are suitable to describe small discrete plant populations, as is often found in dryland ecosystems, has remained largely unaddressed. In this paper, we first draw attention to two aspects of plants that distinguish them from most other organisms-high phenotypic plasticity and dispersal of stress-tolerant seeds-and argue in favor of PDE modeling, where the state variables that describe population sizes are not discrete number densities, but rather continuous biomass densities. We then discuss a few examples that demonstrate the utility of PDE models in providing deep insights into landscape-scale behaviors, such as the onset of pattern forming instabilities, multiplicity of stable ecosystem states, regular and irregular, and the possible roles of front instabilities in reversing desertification. We briefly mention a few additional examples, and conclude by outlining the nature of the information we should and should not expect to gain from PDE model studies.

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“…If this is the case, a restoration strategy based on dashed patterns instead of banded vegetation could in some cases be more successful, or equally successful but more economic. 36 These predictions could be tested empirically.…”

Section: Ecological Implicationsmentioning

confidence: 99%

Striped pattern selection by advective reaction-diffusion systems: Resilience of banded vegetation on slopes

Siero¹,

Doelman²,

Eppinga³

et al. 2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

124

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For water-limited arid ecosystems, where water distribution and infiltration play a vital role, various models have been set up to explain vegetation patterning. On sloped terrains, vegetation aligned in bands has been observed ubiquitously. In this paper, we consider the appearance, stability, and bifurcations of 2D striped or banded patterns in an arid ecosystem model. We numerically show that the resilience of the vegetation bands is larger on steeper slopes by computing the stability regions (Busse balloons) of striped patterns with respect to 1D and transverse 2D perturbations. This is corroborated by numerical simulations with a slowly decreasing water input parameter. Here, long wavelength striped patterns are unstable against transverse perturbations, which we also rigorously prove on flat ground through an Evans function approach. In addition, we prove a "Squire theorem" for a class of two-component reaction-advection-diffusion systems that includes our model, showing that the onset of pattern formation in 2D is due to 1D instabilities in the direction of advection, which naturally leads to striped patterns. V C 2015 AIP Publishing LLC. This paper has been motivated by studies in one space dimension of a scaled phenomenological model for vegetation on possibly sloped planes in arid ecosystems. 53,60 One-dimensional patterns ideally represent striped patterns in two space dimensions by trivially extending them into a transversal direction. Such patterns are referred to as banded vegetation and have received considerable attention after reports of widespread observations. 8,58 Understanding the appearance and disappearance of vegetation bands may ultimately help prevent land degradation. The restriction to one space dimension may overestimate stability: patterns that are stable against 1D perturbations are not necessarily stable against all 2D perturbations. Natural questions to pose are:• Which of the 1D stable patterns extend to 2D stable striped patterns? • In case of destabilization by 2D perturbations, which mechanisms are responsible?In this paper, we answer these questions for the arid ecosystem model and determine the impact of slope induced advection of water. The influence of advection on striped pattern formation is studied in a more general setting. This approach provides a clear argumentation that is unobscured by model-specific details. Equally important, the results will be applicable to a wide range of models. Applicability to the arid ecosystem model is carefully checked though, assuring that the abstract requirements can in fact be met in practice.

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Reversing desertification as a spatial resonance problem

Cited by 16 publications

References 25 publications

High-integrity human intervention in ecosystems: Tracking self-organization modes

High-integrity human intervention in ecosystems: Tracking self-organization modes

Continuum Modeling of Discrete Plant Communities: Why Does It Work and Why Is It Advantageous?

Striped pattern selection by advective reaction-diffusion systems: Resilience of banded vegetation on slopes

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