Phenotypic plasticity: A missing element in the theory of vegetation pattern formation.

Regular spatial patterns of vegetation are a common sight in drylands. Their formation is a population-level response to water stress that increases water availability for the few via partial plant mortality. At the individual level, plants can also adapt to water stress by changing their phenotype. Phenotypic plasticity of individual plants and spatial patterning of plant populations have extensively been studied independently, but the likely interplay between the two robust mechanisms has remained unexplored. In this paper, we incorporate phenotypic plasticity into a multi-level theory of vegetation pattern formation and use a fascinating ecological phenomenon, the Namibian "fairy circles," to demonstrate the need for such a theory. We show that phenotypic changes in the root structure of plants, coupled with pattern-forming feedback within soil layers, can resolve two puzzles that the current theory fails to explain: observations of multi-scale patterns and the absence of theoretically predicted large-scale stripe and spot patterns along the rainfall gradient. Importantly, we find that multi-level responses to stress unveil a wide variety of more effective stress-relaxation pathways, compared to single-level responses, implying a previously underestimated resilience of dryland ecosystems.

Evidence for scale-dependent root-antation feedback and its role in halting the spread of a pantropical shrub into an endemic sedge.

Vegetation pattern formation is a widespread phenomenon in resource-limited environments, but the driving mechanisms are largely unconfirmed empirically. Combining results of field studies and mathematical modeling, empirical evidence for a generic pattern-formation mechanism is demonstrated with the clonal shrub Guilandina bonduc L. (hereafter Guilandina) on the Brazilian island of Trindade. The mechanism is associated with water conduction by laterally spread roots and root augmentation as the shoot grows-a crucial element in the positive feedback loop that drives spatial patterning. Assuming precipitation-dependent root-shoot relations, the model accounts for the major vegetation landscapes on Trindade Island, substantiating lateral root augmentation as the driving mechanism of Guilandina patterning. Guilandina expands into surrounding communities dominated by the Trindade endemic, Cyperus atlanticus Hemsl. (hereafter Cyperus). It appears to do so by decreasing the water potential in soils below Cyperus through its dense lateral roots, leaving behind a patchy Guilandina-only landscape. We use this system to highlight a novel form of invasion, likely to apply to many other systems where the invasive species is pattern-forming. Depending on the level of water stress, the invasion can take two distinct forms: (i) a complete invasion at low stress that culminates in a patchy Guilandina-only landscape through a spot-replication process, and (ii) an incomplete invasion at high stress that begins but does not spread, forming isolated Guilandina spots of fixed size, surrounded by bare-soil halos, in an otherwise uniform Cyperus grassland. Thus, drier climates may act selectively on pattern-forming invasive species, imposing incomplete invasion and reducing the negative effects on native species.

Dryland mechanisms could widely control ecosystem functioning in a drier and warmer world.

Responses of terrestrial ecosystems to climate change have been explored in many regions worldwide. While continued drying and warming may alter process rates and deteriorate the state and performance of ecosystems, it could also lead to more fundamental changes in the mechanisms governing ecosystem functioning. Here we argue that climate change will induce unprecedented shifts in these mechanisms in historically wetter climatic zones, towards mechanisms currently prevalent in dry regions, which we refer to as 'dryland mechanisms'. We discuss 12 dryland mechanisms affecting multiple processes of ecosystem functioning, including vegetation development, water flow, energy budget, carbon and nutrient cycling, plant production and organic matter decomposition. We then examine mostly rare examples of the operation of these mechanisms in non-dryland regions where they have been considered irrelevant at present. Current and future climate trends could force microclimatic conditions across thresholds and lead to the emergence of dryland mechanisms and their increasing control over ecosystem functioning in many biomes on Earth.

Linking spatial self-organization to community assembly and biodiversity.

Temporal shifts to drier climates impose environmental stresses on plant communities that may result in community reassembly and threatened ecosystem services, but also may trigger self-organization in spatial patterns of biota and resources, which act to relax these stresses. The complex relationships between these counteracting processes - community reassembly and spatial self-organization - have hardly been studied. Using a spatio-temporal model of dryland plant communities and a trait-based approach, we study the response of such communities to increasing water-deficit stress. We first show that spatial patterning acts to reverse shifts from fast-growing species to stress-tolerant species, as well as to reverse functional-diversity loss. We then show that spatial self-organization buffers the impact of further stress on community structure. Finally, we identify multistability ranges of uniform and patterned community states and use them to propose forms of non-uniform ecosystem management that integrate the need for provisioning ecosystem services with the need to preserve community structure.

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

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.

Belowground feedbacks as drivers of spatial self-organization and community assembly.

Vegetation patterning in water-limited and other resource-limited ecosystems highlights spatial self-organization processes as potentially key drivers of community assembly. These processes provide insight into predictable landscape-level relationships between organisms and their abiotic environment in the form of regular and irregular patterns of biota and resources. However, two aspects have largely been overlooked; the roles played by plant - soil-biota feedbacks and allelopathy in spatial self-organization, and their potential contribution, along with plant-resource feedbacks, to community assembly through spatial self-organization. Here, we expand the drivers of spatial self-organization from a focus on plant-resource feedbacks to include plant - soil-biota feedbacks and allelopathy, and integrate concepts of nonlinear physics and community ecology to generate a new hypothesis. According to this hypothesis, below-ground processes can affect community assemblages through two types of spatial self-organization, global and local. The former occurs simultaneously across whole ecosystems, leading to self-organized patterns of biota, allelochemicals and resources, and niche partitioning. The latter occurs locally in ecotones, and determines ecotone structure and motion, invasion dynamics, and species coexistence. Studies of the two forms of spatial self-organization are important for understanding the organization of plant communities in drier climates which are likely to involve spatial patterning or re-patterning. Such studies are also important for developing new practices of ecosystem management, based on local manipulations at ecotones, to slow invasion dynamics or induce transitions from transitive to intransitive networks of interspecific interactions which increase species diversity.

The role of spatial self-organization in the design of agroforestry systems.

The development of sustainable agricultural systems in drylands is currently a crucial issue in the context of mitigating the outcomes of population growth under the conditions of climatic changes. The need to meet the growing demand for food, fodder, and fuel, together with the hazards due to climate change, requires cross-disciplinary studies of ways to increase livelihood while minimizing the impact on the environment. Practices of agroforestry systems, in which herbaceous species are intercropped between rows of woody species plantations, have been shown to mitigate several of the predicaments of climatic changes. Focusing on agroforestry in drylands, we address the question of how we can improve the performance of agroforestry systems in those areas. As vegetation in drylands tends to self-organize in various patterns, it seems essential to explore the various patterns that agroforestry systems tend to form and their impact on the performance of these systems in terms of biomass production, resilience to droughts, and water use efficiency. We use a two-soil-layers vegetation model to study the relationship between deep-rooted woody vegetation and shallow herbaceous vegetation, and explore how self-organization in different spatial patterns influences the performance of agroforestry systems. We focus on three generic classes of patterns, spots, gaps, and stripes, assess these patterns using common metrics for agroforestry systems, and examine their resilience to droughts. We show that in contrast to the widespread practice of planting the woody and herbaceous species in alternating rows, that is, in a stripe pattern, planting the woody species in hexagonal spot patterns may increase the system's resilience to droughts. Furthermore, hexagonal spot patterns reduce the suppression of herbs growth by the woody vegetation, therefore maintaining higher crop yields. We conclude by discussing some limitations of this study and their significance.

Organizing principles for vegetation dynamics.

Plants and vegetation play a critical-but largely unpredictable-role in global environmental changes due to the multitude of contributing processes at widely different spatial and temporal scales. In this Perspective, we explore approaches to master this complexity and improve our ability to predict vegetation dynamics by explicitly taking account of principles that constrain plant and ecosystem behaviour: natural selection, self-organization and entropy maximization. These ideas are increasingly being used in vegetation models, but we argue that their full potential has yet to be realized. We demonstrate the power of natural selection-based optimality principles to predict photosynthetic and carbon allocation responses to multiple environmental drivers, as well as how individual plasticity leads to the predictable self-organization of forest canopies. We show how models of natural selection acting on a few key traits can generate realistic plant communities and how entropy maximization can identify the most probable outcomes of community dynamics in space- and time-varying environments. Finally, we present a roadmap indicating how these principles could be combined in a new generation of models with stronger theoretical foundations and an improved capacity to predict complex vegetation responses to environmental change.

Spatial heterogeneity may form an inverse camel shaped Arnol'd tongue in parametrically forced oscillations.

Frequency locking in forced oscillatory systems typically organizes in "V"-shaped domains in the plane spanned by the forcing frequency and amplitude, the so-called Arnol'd tongues. Here, we show that if the medium is spatially extended and monotonically heterogeneous, e.g., through spatially dependent natural frequency, the resonance tongues can also display "U" and "W" shapes; we refer to the latter as an "inverse camel" shape. We study the generic forced complex Ginzburg-Landau equation for damped oscillations under parametric forcing and, using linear stability analysis and numerical simulations, uncover the mechanisms that lead to these distinct resonance shapes. Additionally, we study the effects of discretization by exploring frequency locking of oscillator chains. Since we study a normal-form equation, the results are model-independent near the onset of oscillations and, therefore, applicable to inherently heterogeneous systems in general, such as the cochlea. The results are also applicable to controlling technological performances in various contexts, such as arrays of mechanical resonators, catalytic surface reactions, and nonlinear optics.

A model study of terraced riverbeds as novel ecosystems.

Riverbed terracing has been introduced in ancient times to retain water and soil, to reduce hydrological connectivity and erosion and to increase primary and secondary productivity of agro-ecological systems. These presently abandoned human-made landscapes have become novel ecosystems and a potential source of ecosystem services to humans in drylands. We use a mathematical-modeling approach to study factors that regulate terraced riverbeds and affect community and ecosystem attributes such as productivity, functional diversity and resilience to droughts. We introduce a model that captures the relationships between rainfall pattern, runoff coupling between adjacent terraces, and vegetation growth, taking into account competition for water and light. We found that a large number of weak rainfall events results in lower total biomass and functional diversity across the terraced riverbed compared with a few strong rainfall events. We further analyzed the filtering of species traits from pools of functional groups that make different tradeoffs between investment in above-ground biomass to capture canopy resources and investment in below-ground biomass to capture soil resources. Pools characterized by concave tradeoffs give rise to higher functional diversity, lower biomass production and lower resilience to droughts, as compared with convex pools. New empirical studies are needed to test these model predictions.

Period doubling as an indicator for ecosystem sensitivity to climate extremes.

The predictions for a warmer and drier climate and for increased likelihood of climate extremes raise high concerns about the possible collapse of dryland ecosystems, and about the formation of new drylands where native species are less tolerant to water stress. Using a dryland-vegetation model for plant species that display different tradeoffs between fast growth and tolerance to droughts, we find that ecosystems subjected to strong seasonal variability, typical for drylands, exhibit a temporal period-doubling route to chaos that results in early collapse to bare soil. We further find that fast-growing plants go through period doubling sooner and span wider chaotic ranges than stress-tolerant plants. We propose the detection of period-doubling signatures in power spectra as early indicators of ecosystem collapse that outperform existing indicators in their ability to warn against climate extremes and capture the heightened vulnerability of newly-formed drylands. The proposed indicator is expected to apply to other types of ecosystems, such as consumer-resource and predator-prey systems. We conclude by delineating the conditions ecosystems should meet in order for the proposed indicator to apply.

Front Instabilities Can Reverse Desertification.

Degradation processes in living systems often take place gradually by front propagation. An important context of such processes is loss of biological productivity in drylands or desertification. Using a dryland-vegetation model, we analyze the stability and dynamics of desertification fronts, identify linear and nonlinear front instabilities, and highlight the significance of these instabilities in inducing self-recovery. The results are based on the derivation and analysis of a universal amplitude equation for pattern-forming living systems for which nonuniform instabilities cannot emerge from the nonviable (zero) state. The results may therefore be applicable to other contexts of animate matter where degradation processes occur by front propagation.

Interplay between exogenous and endogenous factors in seasonal vegetation oscillations.

A fundamental question in ecology is whether vegetation oscillations are merely a result of periodic environmental variability, or rather driven by endogenous factors. We address this question using a mathematical model of dryland vegetation subjected to annual rainfall periodicity. We show that while spontaneous oscillations do not exist in realistic parameter ranges, resonant response to periodic precipitation is still possible due to the existence of damped oscillatory modes. Using multiple time-scale analysis, in a restricted parameter range, we find that these endogenous modes can be pumped by the exogenous precipitation forcing to form sustained oscillations. The oscillations amplitude shows a resonance peak that depends on model parameters representing species traits and mean annual precipitation. Extending the study to bistability ranges of uniform vegetation and bare soil, we investigate numerically the implications of resonant oscillations for ecosystem function. We consider trait parameters that represent species with damped oscillatory modes and species that lack such modes, and compare their behaviors. We find that the former are less resilient to droughts, suffer from larger declines in their biomass production as the precipitation amplitude is increased, and, in the presence of spatial disturbances, are likely to go through abrupt collapse to bare soil, rather than gradual, domino-like collapse.

Molding the asymmetry of localized frequency-locking waves by a generalized forcing and implications to the inner ear.

Frequency locking to an external forcing frequency is a well-known phenomenon. In the auditory system, it results in a localized traveling wave, the shape of which is essential for efficient discrimination between incoming frequencies. An amplitude equation approach is used to show that the shape of the localized traveling wave depends crucially on the relative strength of additive versus parametric forcing components; the stronger the parametric forcing, the more asymmetric is the response profile and the sharper is the traveling-wave front. The analysis qualitatively captures the empirically observed regions of linear and nonlinear responses and highlights the potential significance of parametric forcing mechanisms in shaping the resonant response in the inner ear.

Implications of tristability in pattern-forming ecosystems.

Many ecosystems show both self-organized spatial patterns and multistability of possible states. The combination of these two phenomena in different forms has a significant impact on the behavior of ecosystems in changing environments. One notable case is connected to tristability of two distinct uniform states together with patterned states, which has recently been found in model studies of dryland ecosystems. Using a simple model, we determine the extent of tristability in parameter space, explore its effects on the system dynamics, and consider its implications for state transitions or regime shifts. We analyze the bifurcation structure of model solutions that describe uniform states, periodic patterns, and hybrid states between the former two. We map out the parameter space where these states exist, and note how the different states interact with each other. We further focus on two special implications with ecological significance, breakdown of the snaking range and complex fronts. We find that the organization of the hybrid states within a homoclinic snaking structure breaks down as it meets a Maxwell point where simple fronts are stationary. We also discover a new series of complex fronts between the uniform states, each with its own velocity. We conclude with a brief discussion of the significance of these findings for the dynamics of regime shifts and their potential control.

Desertification by front propagation?

Understanding how desertification takes place in different ecosystems is an important step in attempting to forecast and prevent such transitions. Dryland ecosystems often exhibit patchy vegetation, which has been shown to be an important factor on the possible regime shifts that occur in arid regions in several model studies. In particular, both gradual shifts that occur by front propagation, and abrupt shifts where patches of vegetation vanish at once, are a possibility in dryland ecosystems due to their emergent spatial heterogeneity. However, recent theoretical work has suggested that the final step of desertification - the transition from spotted vegetation to bare soil - occurs only as an abrupt shift, but the generality of this result, and its underlying origin, remain unclear. We investigate two models that detail the dynamics of dryland vegetation using a markedly different functional structure, and find that in both models the final step of desertification can only be abrupt. Using a careful numerical analysis, we show that this behavior is associated with the disappearance of confined spot-pattern domains as stationary states, and identify the mathematical origin of this behavior. Our findings show that a gradual desertification to bare soil due to a front propagation process can not occur in these and similar models, and opens the question of whether these dynamics can take place in nature.

Discovery of fairy circles in Australia supports self-organization theory.

Vegetation gap patterns in arid grasslands, such as the "fairy circles" of Namibia, are one of nature's greatest mysteries and subject to a lively debate on their origin. They are characterized by small-scale hexagonal ordering of circular bare-soil gaps that persists uniformly in the landscape scale to form a homogeneous distribution. Pattern-formation theory predicts that such highly ordered gap patterns should be found also in other water-limited systems across the globe, even if the mechanisms of their formation are different. Here we report that so far unknown fairy circles with the same spatial structure exist 10,000 km away from Namibia in the remote outback of Australia. Combining fieldwork, remote sensing, spatial pattern analysis, and process-based mathematical modeling, we demonstrate that these patterns emerge by self-organization, with no correlation with termite activity; the driving mechanism is a positive biomass-water feedback associated with water runoff and biomass-dependent infiltration rates. The remarkable match between the patterns of Australian and Namibian fairy circles and model results indicate that both patterns emerge from a nonuniform stationary instability, supporting a central universality principle of pattern-formation theory. Applied to the context of dryland vegetation, this principle predicts that different systems that go through the same instability type will show similar vegetation patterns even if the feedback mechanisms and resulting soil-water distributions are different, as we indeed found by comparing the Australian and the Namibian fairy-circle ecosystems. These results suggest that biomass-water feedbacks and resultant vegetation gap patterns are likely more common in remote drylands than is currently known.

Pattern formation--A missing link in the study of ecosystem response to environmental changes.

Environmental changes can affect the functioning of an ecosystem directly, through the response of individual life forms, or indirectly, through interspecific interactions and community dynamics. The feasibility of a community-level response has motivated numerous studies aimed at understanding the mutual relationships between three elements of ecosystem dynamics: the abiotic environment, biodiversity and ecosystem function. Since ecosystems are inherently nonlinear and spatially extended, environmental changes can also induce pattern-forming instabilities that result in spatial self-organization of life forms and resources. This, in turn, can affect the relationships between these three elements, and make the response of ecosystems to environmental changes far more complex. Responses of this kind can be expected in dryland ecosystems, which show a variety of self-organizing vegetation patterns along the rainfall gradient. This paper describes the progress that has been made in understanding vegetation patterning in dryland ecosystems, and the roles it plays in ecosystem response to environmental variability. The progress has been achieved by modeling pattern-forming feedbacks at small spatial scales and up-scaling their effects to large scales through model studies. This approach sets the basis for integrating pattern formation theory into the study of ecosystem dynamics and addressing ecologically significant questions such as the dynamics of desertification, restoration of degraded landscapes, biodiversity changes along environmental gradients, and shrubland-grassland transitions.