Banded Vegetation Patterns Research Articles

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.

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.

A Pulsed-Precipitation Model of Dryland Vegetation Pattern Formation

We develop a model for investigating the impact of rainstorm variability on the formation of banded vegetation patterns in dryland ecosystems. Water input, during rare rainstorms, is modeled as an instantaneous kick to the soil water. The redistribution, from surface water to soil moisture, accounts for the impact of vegetation on infiltration rate and downslope overland flow speed. These two positive feedbacks between water and biomass distributions act on the fast timescales of rain storms. During dry periods, a classic reaction-diffusion framework is used for the slow processes associated with soil water and biomass. This pulsed precipitation model predicts that the preferred spacing of the vegetation bands is determined by the characteristic distance that a storm pulse of water travels overland before infiltrating into the soil. In this way, the vegetation pattern is determined by the fast ecohydrological processes and may be attuned with its dryland precipitation pattern. We demonstrate how this modeling framework, suited for stochastic rain inputs, can be used to investigate possible collapse of a dryland pattern-forming ecosystem under different precipitation patterns with identical low annual mean. Model simulations suggest, for instance, that shorter rainy seasons and greater variability in storm depth may both hasten ecosystem collapse.

Stability analysis of periodic traveling waves in a model of vegetation patterns in semi-arid ecosystems

Banded vegetation pattern is a striking feature of self-organized ecosystems. In particular, vegetation patterns in semi-arid ecosystems are typical on hillsides, orienting parallel to the contours. The present study concerns a system of coupled reaction–advection–diffusion equations model for this phenomenon and studies the existence and stability of periodic traveling waves in a one-parameter family of solutions. Specifically, we consider a parameter region in which vegetation patterns occur and subdivide into stable and unstable regions as solutions of the model equations. Our numerical results show that the periodic traveling wave changes their stability by Eckhaus (sideband) bifurcation. We discuss the variations of the wavelength, wave speed as well as the conditions of the rainfall parameter by using linear analysis. We also explore how the solution patterns grow when the bifurcation parameter is changing slowly. In order to compare this result with the spatiotemporal pattern in the direct simulation, we show that when it passes a critical value of rainfall parameter a stable pattern becomes unstable and finally disappear. In addition, we investigate the existence and stability of periodic traveling waves as a function of water transport parameter.

A fast–slow model of banded vegetation pattern formation in drylands

From infiltration of water into the soil during rainstorms to seasonal plant growth and death, the ecohydrological processes that are thought to be relevant to the formation of banded vegetation patterns in drylands occur across multiple timescales. We propose a new fast–slow switching model in order to capture these processes on appropriate timescales within a conceptual modeling framework based on reaction–advection–diffusion equations. The fast system captures hydrological processes that occur on minute to hour timescales during and shortly after major rainstorms, assuming a fixed vegetation distribution. These include key feedbacks between vegetation biomass and downhill surface water transport, as well as between biomass and infiltration rate. The slow system acts between rain events, on a timescale of days to months, and evolves vegetation and soil moisture. Modeling processes at the appropriate timescales allows parameter values to be set by the actual processes they capture. This reduces the number of parameters that are chosen expressly to fit pattern characteristics, or to artificially slow down fast processes by the orders of magnitude required to align their timescales with the biomass dynamics. We explore the fast–slow switching model through numerical simulation on a one-dimensional hillslope, and find agreement with certain observations about the pattern formation phenomenon, including band spacing and upslope colonization rates. We also find that the predicted soil moisture dynamics are consistent with time series data that has been collected at a banded vegetation site. This fast–slow model framework introduces a tool for investigating the possible impact of changes to frequency and intensity of rain events in dryland ecosystems.

Intraspecific competition in models for vegetation patterns: Decrease in resilience to aridity and facilitation of species coexistence

Patterned vegetation is a characteristic feature of many dryland ecosystems. While plant densities on the ecosystem-wide scale are typically low, a spatial self-organisation principle leads to the occurrence of alternating patches of high biomass and patches of bare soil. Nevertheless, intraspecific competition dynamics other than competition for water over long spatial scales are commonly ignored in mathematical models for vegetation patterns. In this paper, I address the impact of local intraspecific competition on a modelling framework for banded vegetation patterns. Firstly, I show that in the context of a single-species model, neglecting local intraspecific competition leads to an overestimation of a patterned ecosystem’s resilience to increases in aridity. Secondly, in the context of a multispecies model, I argue that local intraspecific competition is a key element in the successful capture of species coexistence in model solutions representing a vegetation pattern. For both models, a detailed bifurcation analysis is presented to analyse the onset, existence and stability of patterns. Besides the strengths of local intraspecific competition, also the difference between two species has a significant impact on the bifurcation structure, providing crucial insights into the complex ecosystem dynamics. Predictions on future ecosystem dynamics presented in this paper, especially on pattern onset and pattern stability, can aid the development of conservation programs.

Connectivity-Mediated Ecohydrological Feedbacks and Regime Shifts in Drylands

Identified as essential mechanisms promoting alternative stable states, positive feedbacks have been the focus of most former studies on the potential for catastrophic shifts in drylands. Conversely, little is known about how negative feedbacks could counterbalance the effects of positive feedbacks. A decrease in vegetation cover increases the connectivity of bare-soil areas and entails a global loss of runoff-driven resources from the ecosystem but also a local increase in runoff transferred from bare-soil areas to vegetation patches. In turn, these global resource losses and local resource gains decrease and increase vegetation cover, respectively, resulting in a global positive and a local negative feedback loop. We propose that the interplay of these two interconnected ecohydrological feedbacks of opposite sign determines the vulnerability of dryland ecosystems to catastrophic shifts. To test this hypothesis, we developed a spatially explicit model and assessed the effects of varying combinations of feedback strengths on the dynamics, resilience, recovery potential, and spatial structure of the system. Increasing strengths of the local negative feedback relative to the global positive feedback decreased the risk of catastrophic shifts, facilitated recovery from a degraded state, and promoted the formation of banded vegetation patterns. Both feedbacks were most relevant at low vegetation cover due to the nonlinear increase in hydrological connectivity with decreasing vegetation. Our modelling results suggest that catastrophic shifts to degraded states are less likely in drylands with strong source–sink dynamics and/or strong response of vegetation growth to resource redistribution and that feedback manipulation can be useful to enhance dryland restoration.

The influence of infiltration feedback on the characteristic of banded vegetation pattern on hillsides of semiarid area.

The formation and characteristics are two important topics in the study of vegetation pattern. In this paper, we focus on the influence of infiltration feedback of surface runoff on the formation and characteristics of banded vegetation pattern on hillsides of semiarid area. Firstly, it is shown that the infiltration feedback of surface runoff is an important formation mechanics of the banded vegetation pattern in semiarid area. Then it is found that the patterns formed within the reasonable parameter space are periodic both in space and time and the wave speed of the periodic vegetation stripes become larger with the increase of the infiltration feedback strength, while the wavelength is negatively correlated with the infiltration feedback strength. At last, it is shown that the mean productivity of grass pattern is lower than that of homogeneous steady state when the infiltration feedback is weak and it is larger than that with stronger infiltration feedback.

Existence of Periodic Traveling Waves in the Klausmeier Model of Desertification and its Modification: A Comparative Study

Self-organized and spatially periodic banded vegetation patterns have been observed in many semi-arid ecosystems. In order to understand the mechanism of these patterns, we consider a system of reaction-advection-diffusion equations in a two-variable model of desertification. This work deals with the investigation of the existence of periodic traveling waves in a one-parameter family of solutions. In addition, we investigate the existence of periodic traveling waves as a function of water transport parameter in the model.
 GANIT J. Bangladesh Math. Soc.Vol. 38 (2018) 27-46

Long-distance seed dispersal affects the resilience of banded vegetation patterns in semi-deserts

Landscape-scale vegetation stripes (tiger bush) observed on the gentle slopes of semi-arid regions are useful indicators of future ecosystem degradation and catastrophic shifts towards desert. Mathematical models like the Klausmeier model—a set of coupled partial differential equations describing vegetation and water densities in space and time—are central to understanding their formation and development. One assumption made for mathematical simplicity is the local dispersal of seeds via a diffusion term. In fact, a large amount of work focuses on fitting dispersal ‘kernels’, probability density functions for seed dispersal distance, to empirical data of different species and modes of dispersal. In this paper, we address this discrepancy by analysing an extended Klausmeier model that includes long-distance seed dispersal via a non-local convolution term in place of diffusion, and assessing its effect on the resilience of striped patterns. Many authors report a slow uphill migration of stripes; but others report no detectable migration speed. We show that long-distance seed dispersal permits the formation of patterns with a very slow (possibly undetectable) migration speed, and even stationary patterns which could explain the inconsistencies in the empirical data. In general, we show that the resilience of patterns to reduced rainfall may vary significantly depending on the rate of seed dispersal and the width of the dispersal kernel, and compare a selection of ecologically relevant kernels to examine the variation in pattern resilience.

Advection and Autocatalysis as Organizing Principles for Banded Vegetation Patterns

We motivate and analyze a simple model for the formation of banded vegetation patterns. The model incorporates a minimal number of ingredients for vegetation growth in semi-arid landscapes. It allows for comprehensive analysis and sheds new light onto phenomena such as the migration of vegetation bands and the interplay between their upper and lower edges. The key ingredient is the formulation as a closed reaction-diffusion system, thus introducing a conservation law that both allows for analysis and provides ready intuition and understanding through analogies with characteristic speeds of propagation and shock waves.

Analysis of a model for banded vegetation patterns in semi-arid environments with nonlocal dispersal.

Vegetation patterns are a characteristic feature of semi-arid regions. On hillsides these patterns occur as stripes running parallel to the contours. The Klausmeier model, a coupled reaction-advection-diffusion system, is a deliberately simple model describing the phenomenon. In this paper, we replace the diffusion term describing plant dispersal by a more realistic nonlocal convolution integral to account for the possibility of long-range dispersal of seeds. Our analysis focuses on the rainfall level at which there is a transition between uniform vegetation and pattern formation. We obtain results, valid to leading order in the large parameter comparing the rate of water flow downhill to the rate of plant dispersal, for a negative exponential dispersal kernel. Our results indicate that both a wider dispersal of seeds and an increase in dispersal rate inhibit the formation of patterns. Assuming an evolutionary trade-off between these two quantities, mathematically motivated by the limiting behaviour of the convolution term, allows us to make comparisons to existing results for the original reaction-advection-diffusion system. These comparisons show that the nonlocal model always predicts a larger parameter region supporting pattern formation. We then numerically extend the results to other dispersal kernels, showing that the tendency to form patterns depends on the type of decay of the kernel.

The effect of landform variation on vegetation patterning and related sediment dynamics

AbstractSemi‐arid ecosystems are often spatially self‐organized in typical patterns of vegetation bands with high plant cover interspersed with bare soil areas, also known as ‘tiger bush’. In modelling studies, most often, straight planar slopes were used to analyse vegetation patterning. The effect of slope steepness has been investigated widely, and some studies investigated the effects of microtopography and hillslope orientation. However, at the larger catchment scale, the overall form of the landscape may affect vegetation patterning and these more complex landscapes are much more prevalent than straight slopes. Hence, our objective was to determine the effect of landform variation on vegetation patterning and sediment dynamics. We linked two well‐established models that simulate (a) plant growth, death and dispersal of vegetation, and (b) erosion and sedimentation dynamics. The model was tested on a straight planar hillslope and then applied to (i) a set of simple synthetic topographies with varying curvature and (ii) three more complex, real‐world landscapes of distinct morphology. Results show banded vegetation patterning on all synthetic topographies, always perpendicular to the slope gradient. Interestingly, we also found that movement of bands – a debated phenomenon – seems to be dependent on curvature. Vegetation banding was simulated on the slopes of the alluvial fan and along the valley slopes of the dissected and rolling landscapes. In all landscapes, local valleys developed a full vegetation cover induced by water concentration, which is consistent with observations worldwide. Finally, banded vegetation patterns were found to reduce erosion significantly as compared to other vegetation configurations. © 2018 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.

Formation of banded vegetation patterns resulted from interactions between sediment deposition and vegetation growth

This research investigates the formation of banded vegetation patterns on hillslopes affected by interactions between sediment deposition and vegetation growth. The following two perspectives in the formation of these patterns are taken into consideration: (a) increased sediment deposition from plant interception, and (b) reduced plant biomass caused by sediment accumulation. A spatial model is proposed to describe how the interactions between sediment deposition and vegetation growth promote self-organization of banded vegetation patterns. Based on theoretical and numerical analyses of the proposed spatial model, vegetation bands can result from a Turing instability mechanism. The banded vegetation patterns obtained in this research resemble patterns reported in the literature. Moreover, measured by sediment dynamics, the variation of hillslope landform can be described. The model predicts how treads on hillslopes evolve with the banded patterns. Thus, we provide a quantitative interpretation for coevolution of vegetation patterns and landforms under effects of sediment redistribution.

Vegetation patterns generated by a wind driven sand-vegetation system in arid and semi-arid areas

Wind has been proposed as a driving factor in determining vegetation patterns, but there are few dynamic models that include both vegetation and wind. In this paper, we present a dynamic model to investigate how a vegetation pattern is generated and affected by wind. In the model, the effects of prevailing wind and non-prevailing wind on sand and vegetation are modeled respectively as advection terms and diffusion terms. With these considerations and proper parameter values that satisfy Turing bifurcation conditions, labyrinth and banded vegetation patterns are obtained in two situations of wind. By changing wind transportation capacity, we simulate the adaptation process from one vegetation pattern to another. With environmental changes of large amplitude, the width of vegetation bands varies while the wavelength can increase but does not decrease in our simulation. Then we describe the difference between simulated patterns and real patterns. And in the discussion, we explain the mechanism that forming patterns and the consistency of this research with other studies.

Matching ecohydrological processes and scales of banded vegetation patterns in semiarid catchments

AbstractWhile the claim that water‐carbon interactions result in spatially coherent vegetation patterning is rarely disputed in many arid and semiarid regions, the significance of the detailed water pathways and other high frequency variability remain an open question. How the short temporal scale meteorological fluctuations form the long‐term spatial variability of available soil water in complex terrains due to the various hydrological, land surface, and vegetation dynamic feedbacks frames the scope of the work here. Knowledge of the detailed mechanistic feedbacks among soil, plants, and the atmosphere will lead to advances in our understanding of plant water availability in arid and semiarid ecosystems and will provide insights for future model development concerning vegetation pattern formation. In this study, quantitative estimates of water fluxes and vegetation productivity are provided for a semiarid ecosystem with established vegetation bands on hillslopes using numerical simulations. A state‐of‐the‐science process based ecohydrological model is used, which resolves hydrological and plant physiological processes at the relevant space and time scales, for relatively small periods (e.g., decades) of mature ecosystems (i.e., spatially static vegetation distribution). To unfold the mechanisms that shape the spatial distribution of soil moisture, plant productivity and the relevant surface/subsurface and atmospheric water fluxes, idealized hillslope numerical experiments are constructed, where the effects of soil type, slope steepness, and overland flow accumulation area are quantified. Those mechanisms are also simulated in the presence of complex topography features on landscapes. The main results are (a) short temporal scale meteorological variability and accurate representation of the scales at which each ecohydrological process operates are crucial for the estimation of the spatial variability of soil water availability to the plant root zone; (b) water fluxes such as evapotranspiration, infiltration, runoff‐run‐on, and subsurface soil water movement have a dynamic short temporal scale behavior that determines the long‐term spatial organization of plant soil water availability in ecosystems with established vegetation patterns; and (c) hypotheses concerning the hydrological responses that can lead to vegetation pattern formation have to accommodate realistic and physically based representations of the fast dynamics of key ecohydrological fluxes.

DIVERSE PRODUCTIVE ROADSIDES: ECOLOGICALLY INTEGRATING AGRICULTURE INTO OUR HIGHWAY SYSTEM

The extensive under-used area of roadsides along public highways could readily provide valuable environmental, economic, and cultural benefits for society. Furthermore, local food sources are an increasing priority as energy and environmental costs of long-distance transport increase. This article highlights the central goals and principles for introducing food production in roadsides. Seven types of roadside cultivation are considered: market vegetables, grain, fodder, orchard, biofuel, compost, and livestock. Principles important for incorporating food production into roadsides include: location relative to adjacent land uses; wildlife movement and biodiversity; site topography and hydrology; and arrangement of crops based on roadside pollutant concentrations. Potential problems and their solutions are examined, such as: a swale and remediation system for stormwater and aerial pollutants; a banded vegetation pattern with inedible crops close to the road and edible crops farther from the road; and strategically locating trees to narrow the perceived highway width for enhanced driver safety. Major benefits of roadside production include providing additional farmland for farmers, vegetation design that facilitates wildlife movement and reduces the effects of habitat fragmentation, a cultural symbol of productivity in a highly visible landscape, local food for markets and eateries, carbon sequestration, and multi-use right-of-way biodiversity and landscape management. A case study uses the goals and principles pinpointed to outline a specific design strategy for inserting diverse agriculture along 30km of highway (MA I-495) outside Boston, Massachusetts (USA). Now, widespread designs and pilot projects are needed to initiate the next generation of our roadsides, where public appreciation for local food production, multiple uses of infrastructure, and the landscape's wildlife heritage become the norm.

Vegetation patterns and desertification waves in semi-arid environments: Mathematical models based on local facilitation in plants

In semi-arid regions, infiltration of rain water into the soil issignificantly higher in vegetated areas than for bare ground. However,quantitative data on the dependence of infiltration capacityon plant biomass is very limited. In this paper, we use asimple reaction-diffusion-advection model to investigate the effectsof varying the strength of this dependence. We begin by studying theformation of banded vegetation patterns on gentle slopes ('tigerbush'), which is a hallmark of semi-deserts. We calculate therange of rainfall parameter values over which such patterns occur,using numerical continuation methods.We then consider interfaces between vegetationand bare ground, showing that the vegetated region either expands orcontracts depending on whether the rainfall parameter is above orbelow a critical value. We conclude by discussing themathematical questions raised by our work.

Determinants and dynamics of banded vegetation pattern migration in arid climates

Dense vegetation bands aligned to contour levels and alternating at regular intervals with relatively barren interbands have been reported at the margins of all tropical deserts. Since their discovery in the 1950s, it has been supposed that these vegetation bands migrate upslope, forming a space–time cyclic pattern. Evidence to date has been relatively sparse and indirect, and observations have remained conflicting. Unequivocal photographic evidence of upslope migration (a few decimeters per year) is provided here for three independent dryland areas exhibiting periodic banded pattern: (1) the U.S. northeastern Chihuahuan Desert, (2) the Somalian Haud, and (3) the Mediterranean steppes of eastern Morocco. Migration speeds, averaged through time and space using Fourier cross‐spectral analysis, are shown to be directly proportional to pattern scale (wavelength). A sequence of aerial photographs of the Chihuahuan Desert showed that migration was not continuous, but intermittent in response to fluctuating weather regimes. The rates at which bands expanded upslope and contracted downslope were better predicted by the change in annual rainfall than by its average level. However, the migration of banded patterns cannot be considered as systematic because in our observations of three other banded systems located in the Somalian Haud, central Australia, and western New South Wales, migration was undetectable at the available image resolution. In each of the six sites under study, the modal value of band orientation axes was verified to be approximately orthogonal to the steepest slope. Our results underscore the importance of taking both the spatial structure and the past climate sequence into account for understanding vegetation dynamics in arid to semiarid ecosystems. In addition, we show how Fourier spectral analysis applied to historical series of optical images can serve to quantify landscape dynamics at a decadal time scale.

Wavelet Transform Analysis of Tiger Bush Landscape in Niger Valley

A series of wavelet analysis techniques are applied to observe the reduction in the banded vegetation pattern of Niger valley, to select the best suited wavelet pattern to describe the changes in Vegetation. The best fit pattern was found to be Mexican Hat transform. Using the Mexican hat transform on the vegetation pattern, significant clumping of vegetation was found due to the heavy fragmentation use by humans for firewood and other fuel use.