Local properties of patterned vegetation: quantifying endogenous and exogenous effects

Quantitatively monitoring the resilience of patterned vegetation in the Sahel

Patterning of vegetation in drylands is a consequence of localized feedback mechanisms. Such feedbacks also determine ecosystem resilience-i.e. the ability to recover from perturbation. Hence, the patterning of vegetation has been hypothesized to be an indicator of resilience, that is, spots are less resilient than labyrinths. Previous studies have made this qualitative link and used models to quantitatively explore it, but few have quantitatively analysed available data to test the hypothesis. Here we provide methods for quantitatively monitoring the resilience of patterned vegetation, applied to 40 sites in the Sahel (a mix of previously identified and new ones). We show that an existing quantification of vegetation patterns in terms of a feature vector metric can effectively distinguish gaps, labyrinths, spots, and a novel category of spot-labyrinths at their maximum extent, whereas NDVI does not. The feature vector pattern metric correlates with mean precipitation. We then explored two approaches to measuring resilience. First we treated the rainy season as a perturbation and examined the subsequent rate of decay of patterns and NDVI as possible measures of resilience. This showed faster decay rates-conventionally interpreted as greater resilience-associated with wetter, more vegetated sites. Second we detrended the seasonal cycle and examined temporal autocorrelation and variance of the residuals as possible measures of resilience. Autocorrelation and variance of our pattern metric increase with declining mean precipitation, consistent with loss of resilience. Thus, drier sites appear less resilient, but we find no significant correlation between the mean or maximum value of the pattern metric (and associated morphological pattern types) and either of our measures of resilience.

Ice needles weave patterns of stones in freezing landscapes

Patterned ground, defined by the segregation of stones in soil according to size, is one of the most strikingly self-organized characteristics of polar and high-alpine landscapes. The presence of such patterns on Mars has been proposed as evidence for the past presence of surface liquid water. Despite their ubiquity, the dearth of quantitative field data on the patterns and their slow dynamics have hindered fundamental understanding of the pattern formation mechanisms. Here, we use laboratory experiments to show that stone transport is strongly dependent on local stone concentration and the height of ice needles, leading effectively to pattern formation driven by needle ice activity. Through numerical simulations, theory, and experiments, we show that the nonlinear amplification of long wavelength instabilities leads to self-similar dynamics that resemble phase separation patterns in binary alloys, characterized by scaling laws and spatial structure formation. Our results illustrate insights to be gained into patterns in landscapes by viewing the pattern formation through the lens of phase separation. Moreover, they may help interpret spatial structures that arise on diverse planetary landscapes, including ground patterns recently examined using the rover Curiosity on Mars.

The effect of climate change on the resilience of ecosystems with adaptive spatial pattern formation

In a rapidly changing world, quantifying ecosystem resilience is an important challenge. Historically, resilience has been defined via models that do not take spatial effects into account. These systems can only adapt via uniform adjustments. In reality, however, the response is not necessarily uniform, and can lead to the formation of (self-organised) spatial patterns - typically localised vegetation patches. Classical measures of resilience cannot capture the emerging dynamics in spatially self-organised systems, including transitions between patterned states that have limited impact on ecosystem structure and productivity. We present a framework of interlinked phase portraits that appropriately quantifies the resilience of patterned states, which depends on the number of patches, the distances between them and environmental conditions. We show how classical resilience concepts fail to distinguish between small and large pattern transitions, and find that the variance in interpatch distances provides a suitable indicator for the type of imminent transition. Subsequently, we describe the dependency of ecosystem degradation based on the rate of climatic change: slow change leads to sporadic, large transitions, whereas fast change causes a rapid sequence of smaller transitions. Finally, we discuss how pre-emptive removal of patches can minimise productivity losses during pattern transitions, constituting a viable conservation strategy.

Spatiotemporal pattern formation in E. coli biofilms explained by a simple physical energy balance

While the biofilm growth mode conveys notable thriving advantages to bacterial populations, the mechanisms of biofilm formation are still strongly debated. Here, we investigate the remarkable spontaneous formation of regular spatial patterns during the growth of an Escherichia coli biofilm. These patterns reported here appear with non-motile bacteria, which excludes both chemotactic origins and other motility-based ones. We demonstrate that a minimal physical model based on phase separation describes them well. To confirm the predictive capacity of our model, we tune the cell-cell and cell-surface interactions using cells expressing different surface appendages. We further explain how F pilus-bearing cells enroll their wild type kindred, poorly piliated, into their typical pattern when mixed together. This work supports the hypothesis that purely physicochemical processes, such as the interplay of cell-cell and cell-surface interactions, can drive the emergence of a highly organized spatial structure that is potentially decisive for community fate and for biological functions.

Metastability as a Coexistence Mechanism in a Model for Dryland Vegetation Patterns

Vegetation patterns are a ubiquitous feature of water-deprived ecosystems. Despite the competition for the same limiting resource, coexistence of several plant species is commonly observed. We propose a two-species reaction-diffusion model based on the single-species Klausmeier model, to analytically investigate the existence of states in which both species coexist. Ecologically, the study finds that coexistence is supported if there is a small difference in the plant species' average fitness, measured by the ratio of a species' capabilities to convert water into new biomass to its mortality rate. Mathematically, coexistence is not a stable solution of the system, but both spatially uniform and patterned coexistence states occur as metastable states. In this context, a metastable solution in which both species coexist corresponds to a long transient (exceeding [Formula: see text] years in dimensional parameters) to a stable one-species state. This behaviour is characterised by the small size of a positive eigenvalue which has the same order of magnitude as the average fitness difference between the two species. Two mechanisms causing the occurrence of metastable solutions are established: a spatially uniform unstable equilibrium and a stable one-species pattern which is unstable to the introduction of a competitor. We further discuss effects of asymmetric interspecific competition (e.g. shading) on the metastability property.

Multistability of model and real dryland ecosystems through spatial self-organization

Spatial self-organization of dryland vegetation constitutes one of the most promising indicators for an ecosystem's proximity to desertification. This insight is based on studies of reaction-diffusion models that reproduce visual characteristics of vegetation patterns observed on aerial photographs. However, until now, the development of reliable early warning systems has been hampered by the lack of more in-depth comparisons between model predictions and real ecosystem patterns. In this paper, we combined topographical data, (remotely sensed) optical data, and in situ biomass measurements from two sites in Somalia to generate a multilevel description of dryland vegetation patterns. We performed an in-depth comparison between these observed vegetation pattern characteristics and predictions made by the extended-Klausmeier model for dryland vegetation patterning. Consistent with model predictions, we found that for a given topography, there is multistability of ecosystem states with different pattern wavenumbers. Furthermore, observations corroborated model predictions regarding the relationships between pattern wavenumber, total biomass, and maximum biomass. In contrast, model predictions regarding the role of slope angles were not corroborated by the empirical data, suggesting that inclusion of small-scale topographical heterogeneity is a promising avenue for future model development. Our findings suggest that patterned dryland ecosystems may be more resilient to environmental change than previously anticipated, but this enhanced resilience crucially depends on the adaptive capacity of vegetation patterns.

A topographic mechanism for arcing of dryland vegetation bands

Banded patterns consisting of alternating bare soil and dense vegetation have been observed in water-limited ecosystems across the globe, often appearing along gently sloped terrain with the stripes aligned transverse to the elevation gradient. In many cases, these vegetation bands are arced, with field observations suggesting a link between the orientation of arcing relative to the grade and the curvature of the underlying terrain. We modify the water transport in the Klausmeier model of water-biomass interactions, originally posed on a uniform hillslope, to qualitatively capture the influence of terrain curvature on the vegetation patterns. Numerical simulations of this modified model indicate that the vegetation bands arc convex-downslope when growing on top of a ridge, and convex-upslope when growing in a valley. This behaviour is consistent with observations from remote sensing data that we present here. Model simulations show further that whether bands grow on ridges, valleys or both depends on the precipitation level. A survey of three banded vegetation sites, each with a different aridity level, indicates qualitatively similar behaviour.

Signatures of human impact on self-organized vegetation in the Horn of Africa

In many dryland environments, vegetation self-organizes into bands that can be clearly identified in remotely-sensed imagery. The status of individual bands can be tracked over time, allowing for a detailed remote analysis of how human populations affect the vital balance of dryland ecosystems. In this study, we characterize vegetation change in areas of the Horn of Africa where imagery taken in the early 1950s is available. We find that substantial change is associated with steep increases in human activity, which we infer primarily through the extent of road and dirt track development. A seemingly paradoxical signature of human impact appears as an increase in the widths of the vegetation bands, which effectively increases the extent of vegetation cover in many areas. We show that this widening occurs due to altered rates of vegetation colonization and mortality at the edges of the bands, and conjecture that such changes are driven by human-induced shifts in plant species composition. Our findings suggest signatures of human impact that may aid in identifying and monitoring vulnerable drylands in the Horn of Africa.

Conservation of pattern as a tool for inference on spatial snapshots in ecological data

As climate change and other anthropogenic factors increase the uncertainty of vegetation ecosystem persistence, the ability to rapidly assess their dynamics is paramount. Vegetation and sessile communities form a variety of striking regular spatial patterns such as stripes, spots and labyrinths, that have been used as indicators of ecosystem current state, through qualitative analysis of simple models. Here we describe a new method for rigorous quantitative estimation of biological parameters from a single spatial snapshot. We formulate a synthetic likelihood through consideration of the expected change in the correlation structure of the spatial pattern. This then allows Bayesian inference to be performed on the model parameters, which includes providing parameter uncertainty. The method was validated against simulated data and then applied to real data in the form of aerial photographs of seagrass banding. The inferred parameters were found to be able to reproduce similar patterns to those observed and able to detect strength of spatial competition, competition-induced mortality and the local range of reproduction. This technique points to a way of performing rapid inference of spatial competition and ecological stability from a single spatial snapshots of sessile communities.

A morphometric analysis of vegetation patterns in dryland ecosystems

Vegetation in dryland ecosystems often forms remarkable spatial patterns. These range from regular bands of vegetation alternating with bare ground, to vegetated spots and labyrinths, to regular gaps of bare ground within an otherwise continuous expanse of vegetation. It has been suggested that spotted vegetation patterns could indicate that collapse into a bare ground state is imminent, and the morphology of spatial vegetation patterns, therefore, represents a potentially valuable source of information on the proximity of regime shifts in dryland ecosystems. In this paper, we have developed quantitative methods to characterize the morphology of spatial patterns in dryland vegetation. Our approach is based on algorithmic techniques that have been used to classify pollen grains on the basis of textural patterning, and involves constructing feature vectors to quantify the shapes formed by vegetation patterns. We have analysed images of patterned vegetation produced by a computational model and a small set of satellite images from South Kordofan (South Sudan), which illustrates that our methods are applicable to both simulated and real-world data. Our approach provides a means of quantifying patterns that are frequently described using qualitative terminology, and could be used to classify vegetation patterns in large-scale satellite surveys of dryland ecosystems.

When does colonisation of a semi-arid hillslope generate vegetation patterns?

Patterned vegetation occurs in many semi-arid regions of the world. Most previous studies have assumed that patterns form from a starting point of uniform vegetation, for example as a response to a decrease in mean annual rainfall. However an alternative possibility is that patterns are generated when bare ground is colonised. This paper investigates the conditions under which colonisation leads to patterning on sloping ground. The slope gradient plays an important role because of the downhill flow of rainwater. One long-established consequence of this is that patterns are organised into stripes running parallel to the contours; such patterns are known as banded vegetation or tiger bush. This paper shows that the slope also has an important effect on colonisation, since the uphill and downhill edges of an isolated vegetation patch have different dynamics. For the much-used Klausmeier model for semi-arid vegetation, the author shows that without a term representing water diffusion, colonisation always generates uniform vegetation rather than a pattern. However the combination of a sufficiently large water diffusion term and a sufficiently low slope gradient does lead to colonisation-induced patterning. The author goes on to consider colonisation in the Rietkerk model, which is also in widespread use: the same conclusions apply for this model provided that a small threshold is imposed on vegetation biomass, below which plant growth is set to zero. Since the two models are quite different mathematically, this suggests that the predictions are a consequence of the basic underlying assumption of water redistribution as the pattern generation mechanism.

Using wavelength and slope to infer the historical origin of semiarid vegetation bands

Landscape-scale patterns of vegetation occur worldwide at interfaces between semiarid and arid climates. They are important as potential indicators of climate change and imminent regime shifts and are widely thought to arise from positive feedback between vegetation and infiltration of rainwater. On gentle slopes the typical pattern form is bands (stripes), oriented parallel to the contours, and their wavelength is probably the most accessible statistic for vegetation patterns. Recent field studies have found an inverse correlation between pattern wavelength and slope, in apparent contradiction with the predictions of mathematical models. Here I show that this "contradiction" is based on a flawed approach to calculating the wavelength in models. When pattern generation is considered in detail, the theory is fully consistent with empirical results. For realistic parameters, degradation of uniform vegetation generates patterns whose wavelength increases with slope, whereas colonization of bare ground gives the opposite trend. Therefore, the empirical finding of an inverse relationship can be used, in conjunction with climate records, to infer the historical origin of the patterns. Specifically, for the African Sahel my results suggest that banded vegetation originated by the colonization of bare ground during circa 1760-1790 or since circa 1850.

Biogenic gradients in algal density affect the emergent properties of spatially self-organized mussel beds

Theoretical models highlight that spatially self-organized patterns can have important emergent effects on the functioning of ecosystems, for instance by increasing productivity and affecting the vulnerability to catastrophic shifts. However, most theoretical studies presume idealized homogeneous conditions, which are rarely met in real ecosystems. Using self-organized mussel beds as a case study, we reveal that spatial heterogeneity, resulting from the large-scale effects of mussel beds on their environment, significantly alters the emergent properties predicted by idealized self-organization models that assume homogeneous conditions. The proposed model explicitly considers that the suspended algae, the prime food for the mussels, are supplied by water flow from the seaward boundary of the bed, which causes in combination with consumption a gradual depletion of algae over the simulated domain. Predictions of the model are consistent with properties of natural mussel patterns observed in the field, featuring a decline in mussel biomass and a change in patterning. Model analyses reveal a fundamental change in ecosystem functioning when this self-induced algal depletion gradient is included in the model. First, no enhancement of secondary productivity of the mussels comparing with non-patterns states is predicted, irrespective of parameter setting; the equilibrium amount of mussels is entirely set by the input of algae. Second, alternate stable states, potentially present in the original (no algal gradient) model, are absent when gradual depletion of algae in the overflowing water layer is allowed. Our findings stress the importance of including sufficiently realistic environmental conditions when assessing the emergent properties of self-organized ecosystems.

Pattern formation in the geosciences

Pattern formation is a natural property of nonlinear and non-equilibrium dynamical systems. Geophysical examples of such systems span practically all observable length scales, from rhythmic banding of chemical species within a single mineral crystal, to the morphology of cusps and spits along hundreds of kilometres of coastlines. This article briefly introduces the general principles of pattern formation and argues how they can be applied to open problems in the Earth sciences. Particular examples are then discussed, which summarize the contents of the rest of this Theme Issue.

Phase separation explains a new class of self-organized spatial patterns in ecological systems

The origin of regular spatial patterns in ecological systems has long fascinated researchers. Turing's activator-inhibitor principle is considered the central paradigm to explain such patterns. According to this principle, local activation combined with long-range inhibition of growth and survival is an essential prerequisite for pattern formation. Here, we show that the physical principle of phase separation, solely based on density-dependent movement by organisms, represents an alternative class of self-organized pattern formation in ecology. Using experiments with self-organizing mussel beds, we derive an empirical relation between the speed of animal movement and local animal density. By incorporating this relation in a partial differential equation, we demonstrate that this model corresponds mathematically to the well-known Cahn-Hilliard equation for phase separation in physics. Finally, we show that the predicted patterns match those found both in field observations and in our experiments. Our results reveal a principle for ecological self-organization, where phase separation rather than activation and inhibition processes drives spatial pattern formation.