Self-Replication of Localized Vegetation Patches in Scarce Environments

Nonreciprocal feedback induces migrating oblique and horizontal banded vegetation patterns in hyperarid landscapes

In hyperarid environments, vegetation is highly fragmented, with plant populations exhibiting non-random biphasic structures where regions of high biomass density are separated by bare soil. In the Atacama Desert of northern Chile, rainfall is virtually nonexistent, but fog pushed in from the interior sustains patches of vegetation in a barren environment. Tillandsia landbeckii, a plant with no functional roots, survives entirely on fog corridors as a water source. Their origin is attributed to interaction feedback among the ecosystem agents, which have different spatial scales, ultimately generating banded patterns as a self-organising response to resource scarcity. The interaction feedback between the plants can be nonreciprocal due to the fact that the fog flows in a well-defined direction. Using remote sensing analysis and mathematical modelling, we characterise the orientation angle of banded vegetation patterns with respect to fog direction and topographic slope gradient. We show that banded vegetation patterns can be either oblique or horizontal to the fog flow rather than topography. The initial and boundary conditions determine the type of the pattern. The bifurcation diagram for both patterns is established. The theoretical predictions are in agreement with observations from remote sensing image analysis.

The hidden order of Turing patterns in arid and semi-arid vegetation ecosystems

Vegetation Turing patterns play a critical role in the ecological functioning of arid and semi-arid ecosystems. However, the long-range spatial features of these patterns have been neglected compared to short-range features like patch shape and spatial wavelength. Drawing inspiration from hyperuniform structures in material science, we find that the arid and semi-arid vegetation Turing pattern exhibits long-range dispersion similar to hyperuniformity. As the degree of hyperuniformity of the vegetation Turing pattern increases, so does the water-use efficiency of the vegetation. This finding supports previous studies that suggest that Turing patterns represent a spatially optimized self-organization of ecosystems for water acquisition. The degree of hyperuniformity of Turing-type ecosystems exhibits significant critical slowing down near the tipping point, indicating that these ecosystems have non-negligible transient dynamical behavior. Reduced rainfall not only decreases the resilience of the steady state of the ecosystem but also slows down the rate of spatial optimization of water-use efficiency in long transient regimes. We propose that the degree of hyperuniformity indicates the spatial resilience of Turing-type ecosystems after strong, short-term disturbances. Spatially heterogeneous disturbances that reduce hyperuniformity lead to longer recovery times than spatially homogeneous disturbances that maintain hyperuniformity.

Topological defects law for migrating banded vegetation patterns in arid climates

Self-organization and pattern formation are ubiquitous processes in nature. We study the properties of migrating banded vegetation patterns in arid landscapes, usually presenting dislocation topological defects. Vegetation patterns with dislocations are investigated in three different ecosystems. We show through remote sensing data analysis and theoretical modeling that the number of dislocations N(x) decreases in space according to the law N ∼ log(x/B)/x, where x is the coordinate in the opposite direction to the water flow and B is a suitable constant. A sloped topography explains the origin of banded vegetation patterns with permanent dislocations. Theoretically, we considered well-established approaches to describe vegetation patterns. All the models support the law. This contrasts with the common belief that the dynamics of dislocations are transient. In addition, regimes with a constant distribution of defects in space are predicted. We analyze the different regimes depending on the aridity level and water flow speed. The reported decay law of defects can warn of imminent ecosystem collapse.

Effect of heterogeneous environmental conditions on labyrinthine vegetation patterns

Self-organization is a ubiquitous phenomenon in Nature due to the permanent balance between injection and dissipation of energy. The wavelength selection process is the main issue of pattern formation. Stripe, hexagon, square, and labyrinthine patterns are observed in homogeneous conditions. In systems with heterogeneous conditions, a single wavelength is not the rule. Large-scale self-organization of vegetation in arid environments can be affected by heterogeneities, such as interannual precipitation fluctuations, fire occurrences, topographic variations, grazing, soil depth distribution, and soil-moisture islands. Here, we investigate theoretically the emergence and persistence of vegetation labyrinthine patterns in ecosystems under deterministic heterogeneous conditions. Based on a simple local vegetation model with a space-varying parameter, we show evidence of perfect and imperfect labyrinthine patterns, as well as disordered vegetation self-organization. The intensity level and the correlation of the heterogeneities control the regularity of the labyrinthine self-organization. The phase diagram and the transitions of the labyrinthine morphologies are described with the aid of their global spatial features. We also investigate the local spatial structure of labyrinths. Our theoretical findings qualitatively agree with satellite images data of arid ecosystems that show labyrinthinelike textures without a single wavelength.

Flow characteristics of open channels based on patch distribution of partially discontinuous rigid combined vegetation

To clarify the flow characteristics of open channels under the combined distribution of vegetation in a patch, this study used the computational fluid dynamics tool FLUENT and the Reynolds stress model to design four combined and four discrete distribution modes under two different inundation states (submerged and non-submerged). The flow characteristics of longitudinally discontinuous rigid vegetation patches occupying half the width of the channel were numerically simulated. The numerical model is verified by indoor open channel flume experiments, and the obtained model data is in good agreement with the measured data. The results showed that: 1) The diameter of vegetation is an important factor affecting the wake structure. Under the submerged condition. 2)The submerged state, distribution pattern and combination form of vegetation are important factors that affect the distribution of flow velocity and change the structure of water flow. That is, the influence of vegetation distribution pattern on flow velocity and turbulence intensity under submerged condition is significantly weaker than that under non-submerged condition, and the flow velocity in non-vegetation area is significantly higher than that in vegetation area. The increase in the combined vegetation comprehensive stem thickness and the discrete degree resulted in an increase in the difference in flow velocity and turbulence intensity. 3) As the water flowed downstream, the flow velocity along the vegetated area continuously decreased, while it increased continuously along the non-vegetated area, and the difference in flow velocity between the two areas became more apparent. 4) The inundation state and combination characteristics of vegetation were important factors affecting the Reynolds stress of the channel location in the patch area.

Localised labyrinthine patterns in ecosystems

Self-organisation is a ubiquitous phenomenon in ecosystems. These systems can experience transitions from a uniform cover towards the formation of vegetation patterns as a result of symmetry-breaking instability. They can be either periodic or localised in space. Localised vegetation patterns consist of more or less circular spots or patches that can be either isolated or randomly distributed in space. We report on a striking patterning phenomenon consisting of localised vegetation labyrinths. This intriguing pattern is visible in satellite photographs taken in many territories of Africa and Australia. They consist of labyrinths which is spatially irregular pattern surrounded by either a homogeneous cover or a bare soil. The phenomenon is not specific to particular plants or soils. They are observed on strictly homogenous environmental conditions on flat landscapes, but they are also visible on hills. The spatial size of localized labyrinth ranges typically from a few hundred meters to ten kilometres. A simple modelling approach based on the interplay between short-range and long-range interactions governing plant communities or on the water dynamics explains the observations reported here.

Patchy landscapes in arid environments: Nonlinear analysis of the interaction-redistribution model

We consider a generic interaction-redistribution model of vegetation dynamics to investigate the formation of patchy vegetation in semi-arid and arid landscapes. First, we perform a weakly nonlinear analysis in the neighborhood of the symmetry-breaking instability. Following this analysis, we construct the bifurcation diagram of the biomass density. The weakly nonlinear analysis allows us to establish the condition under which the transition from super- to subcritical symmetry-breaking instability takes place. Second, we generate a random distribution of localized patches of vegetation numerically. This behavior occurs in regimes where a bare state coexists with a uniform biomass density. Field observations allow to estimate the total biomass density and the range of facilitative and competitive interactions.

On the repulsive interaction between localised vegetation patches in scarce environments

Fragmentation followed by desertification in water-limited resources and/or nutrient-poor ecosystems is a major risk to the biological productivity of vegetation. By using the vegetation interaction-redistribution model, we analyse the interaction between localised vegetation patches. Here we show analytically and numerically that the interaction between two or more patches is always repulsive. As a consequence, only a single localised vegetation patch is stable, and other localised bounded states or clusters of them are unstable. Following this, we discuss the impact of the repulsive nature of the interaction on the formation and the selection of vegetation patterns in fragmented ecosystems.

Evaluating the Potential of Multi-Seasonal CBERS-04 Imagery for Mapping the Quasi-Circular Vegetation Patches in the Yellow River Delta Using Random Forest

High-resolution satellite imagery enables decametric-scale quasi-circular vegetation patch (QVP) mapping, which greatly aids the monitoring of vegetation restoration projects and the development of theories in pattern evolution and maintenance research. This study analyzed the potential of employing five seasonal fused 5 m spatial resolution CBERS-04 satellite images to map QVPs in the Yellow River Delta, China, using the Random Forest (RF) classifier. The classification accuracies corresponding to individual and multi-season combined images were compared to understand the seasonal effect and the importance of optimal image timing and acquisition frequency for QVP mapping. For classification based on single season imagery, the early spring March imagery, with an overall accuracy (OA) of 98.1%, was proven to be more adequate than the other four individual seasonal images. The early spring (March) and winter (December) combined dataset produced the most accurate QVP detection results, with a precision rate of 66.3%, a recall rate of 43.9%, and an F measure of 0.528. For larger study areas, the gain in accuracy should be balanced against the increase in processing time and space when including the derived spectral indices in the RF classification model. Future research should focus on applying higher resolution imagery to QVP mapping.

Stabilizing a homoclinic stripe

For a large class of reaction-diffusion systems with large diffusivity ratio, it is well known that a two-dimensional stripe (whose cross-section is a one-dimensional homoclinic spike) is unstable and breaks up into spots. Here, we study two effects that can stabilize such a homoclinic stripe. First, we consider the addition of anisotropy to the model. For the Schnakenberg model, we show that (an infinite) stripe can be stabilized if the fast-diffusing variable (substrate) is sufficiently anisotropic. Two types of instability thresholds are derived: zigzag (or bending) and break-up instabilities. The instability boundaries subdivide parameter space into three distinct zones: stable stripe, unstable stripe due to bending and unstable due to break-up instability. Numerical experiments indicate that the break-up instability is supercritical leading to a 'spotted-stripe' solution. Finally, we perform a similar analysis for the Klausmeier model of vegetation patterns on a steep hill, and examine transition from spots to stripes.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)'.

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

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)'.

The Use of High-Resolution Historical Images to Analyse the Leopard Pattern in the Arid Area of La Alta Guajira, Colombia

A recent review of global arid areas supports the idea that there are two patterns to vegetation in arid lands. Patches of thick vegetation alternate with those with much less vegetation or none at all. There is a specific size, shape and spatial distribution that characterizes vegetation patterns in arid land ecosystems. In some places, the patches have irregular shapes; these are called spots or Leopard bush. This research project is based on a biophysical approach that integrates information collected in the field, high resolution historical satellite images and Geographical Information System technology. The results revealed that there were certain places in the landscape that facilitate the singular development of the vegetation. The Leopard pattern results from the interaction of various factors (fertility island, fragmentation of vegetation, anthropic influence, herbivorism). Specific characteristics that limit plant life forms are found in the area; since only certain resistant species develop, these form associations and in turn generate strategies to optimize resources. Eventually, this equilibrium is disturbed by human activities in the shape of ungulate livestock breeding and anthropogenic activities, resulting in a heterogeneity of soils and vegetation whose interaction generates the pattern.

Comparison of CBERS-04, GF-1, and GF-2 Satellite Panchromatic Images for Mapping Quasi-Circular Vegetation Patches in the Yellow River Delta, China

Vegetation in arid and semi-arid regions frequently exists in patches, which can be effectively mapped by remote sensing. However, not all satellite images are suitable to detect the decametric-scale vegetation patches because of low spatial resolution. This study compared the capability of the first Gaofen Satellite (GF-1), the second Gaofen Satellite (GF-2), and China-Brazil Earth Resource Satellite 4 (CBERS-04) panchromatic images for mapping quasi-circular vegetation patches (QVPs) with K-Means (KM) and object-based example-based feature extraction with support vector machine classification (OEFE) in the Yellow River Delta, China. Both approaches provide relatively high classification accuracy with GF-2. For all five images, the root mean square errors (RMSEs) for area, perimeter, and perimeter/area ratio were smaller using the KM than the OEFE, indicating that the results from the KM are more similar to ground truth. Although the mapped results of the QVPs from finer-spatial resolution images appeared more accurate, accuracy improvement in terms of QVP area, perimeter, and perimeter/area ratio was limited, and most of the QVPs detected only by finer-spatial resolution imagery had a more than 40% difference with the actual QVPs in these three parameters. Compared with the KM approach, the OEFE approach performed better for vegetation patch shape description. Coupling the CBERS-04 with the OEFE approach could suitably map the QVPs (overall accuracy 75.3%). This is important for ecological protection managers concerned about cost-effectiveness between image spatial resolution and mapping the QVPs.

Dissipative structures in biological systems: bistability, oscillations, spatial patterns and waves

The goal of this review article is to assess how relevant is the concept of dissipative structure for understanding the dynamical bases of non-equilibrium self-organization in biological systems, and to see where it has been applied in the five decades since it was initially proposed by Ilya Prigogine. Dissipative structures can be classified into four types, which will be considered, in turn, and illustrated by biological examples: (i) multistability, in the form of bistability and tristability, which involve the coexistence of two or three stable steady states, or in the form of birhythmicity, which involves the coexistence between two stable rhythms; (ii) temporal dissipative structures in the form of sustained oscillations, illustrated by biological rhythms; (iii) spatial dissipative structures, known as Turing patterns; and (iv) spatio-temporal structures in the form of propagating waves. Rhythms occur with widely different periods at all levels of biological organization, from neural, cardiac and metabolic oscillations to circadian clocks and the cell cycle; they play key roles in physiology and in many disorders. New rhythms are being uncovered while artificial ones are produced by synthetic biology. Rhythms provide the richest source of examples of dissipative structures in biological systems. Bistability has been observed experimentally, but has primarily been investigated in theoretical models in an increasingly wide range of biological contexts, from the genetic to the cell and animal population levels, both in physiological conditions and in disease. Bistable transitions have been implicated in the progression between the different phases of the cell cycle and, more generally, in the process of cell fate specification in the developing embryo. Turing patterns are exemplified by the formation of some periodic structures in the course of development and by skin stripe patterns in animals. Spatio-temporal patterns in the form of propagating waves are observed within cells as well as in intercellular communication. This review illustrates how dissipative structures of all sorts abound in biological systems.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)'.

Spontaneous motion of localized structures induced by parity symmetry breaking transition

We consider a paradigmatic nonvariational scalar Swift-Hohenberg equation that describes short wavenumber or large wavelength pattern forming systems. This work unveils evidence of the transition from stable stationary to moving localized structures in one spatial dimension as a result of a parity breaking instability. This behavior is attributed to the nonvariational character of the model. We show that the nature of this transition is supercritical. We characterize analytically and numerically this bifurcation scenario from which emerges asymmetric moving localized structures. A generalization for two-dimensional settings is discussed.

Dissipative structures and biological rhythms

Sustained oscillations abound in biological systems. They occur at all levels of biological organization over a wide range of periods, from a fraction of a second to years, and with a variety of underlying mechanisms. They control major physiological functions, and their dysfunction is associated with a variety of physiological disorders. The goal of this review is (i) to give an overview of the main rhythms observed at the cellular and supracellular levels, (ii) to briefly describe how the study of biological rhythms unfolded in the course of time, in parallel with studies on chemical oscillations, (iii) to present the major roles of biological rhythms in the control of physiological functions, and (iv) the pathologies associated with the alteration, disappearance, or spurious occurrence of biological rhythms. Two tables present the main examples of cellular and supracellular rhythms ordered according to their period, and their role in physiology and pathophysiology. Among the rhythms discussed are neural and cardiac rhythms, metabolic oscillations such as those occurring in glycolysis in yeast, intracellular Ca⁺⁺ oscillations, cyclic AMP oscillations in Dictyostelium amoebae, the segmentation clock that controls somitogenesis, pulsatile hormone secretion, circadian rhythms which occur in all eukaryotes and some bacteria with a period close to 24 h, the oscillatory dynamics of the enzymatic network driving the cell cycle, and oscillations in transcription factors such as NF-ΚB and tumor suppressors such as p53. Ilya Prigogine's concept of dissipative structures applies to temporal oscillations and allows us to unify within a common framework the various rhythms observed at different levels of biological organization, regardless of their period and underlying mechanism.