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Tree-grass coexistence is a defining feature of savanna ecosystems, which play an important role in supporting biodiversity and human populations worldwide. While recent advances have clarified many of the underlying processes, how these mechanisms interact to shape ecosystem dynamics under environmental stress is not yet understood. Here, we present and analyse a minimalistic spatially extended model of tree-grass dynamics in dry savannas. We incorporate tree facilitation of grasses through shading and grass competing with trees for water, both varying with tree life stage. Our model shows that these mechanisms lead to grass-tree coexistence and bistability between savanna and grassland states. Moreover, the model predicts vegetation patterns consisting of trees and grasses, particularly under harsh environmental conditions, which can persist in situations where a non-spatial version of the model predicts ecosystem collapse from savanna to grassland instead (a phenomenon called ‘Turing-evades-tipping’). Additionally, we identify a novel ‘Turing-triggers-tipping’ mechanism, where unstable pattern formation drives tipping events that are overlooked when spatial dynamics are not included. These transient patterns act as early warning signals for ecosystem transitions, offering a critical window for intervention. Further theoretical and empirical research is needed to determine when spatial patterns prevent tipping or drive collapse.

Drylands are pattern-forming systems showing self-organized vegetation patchiness, multiplicity of stable states and fronts separating domains of alternative stable states. Pattern dynamics, induced by droughts or disturbances, can result in desertification shifts from patterned vegetation to bare soil. Pattern formation theory suggests various scenarios for such dynamics: an abrupt global shift involving a fast collapse to bare soil, a gradual global shift involving the expansion and coalescence of bare-soil domains and an incipient shift to a hybrid state consisting of stationary bare-soil domains in an otherwise periodic pattern. Using models of dryland vegetation, we address the question of which of these scenarios can be realized. We found that the models can be split into two groups: models that exhibit multiplicity of periodic-pattern and bare-soil states, and models that exhibit, in addition, multiplicity of hybrid states. Furthermore, in all models, we could not identify parameter regimes in which bare-soil domains expand into vegetated domains. The significance of these findings is that, while models belonging to the first group can only exhibit abrupt shifts, models belonging to the second group can also exhibit gradual and incipient shifts. A discussion of open problems concludes the paper.

A particular sequence of patterns, ‘gaps→labyrinth→spots’, occurs with decreasing precipitation in previously reported numerical simulations of partial differential equation dryland vegetation models. These observations have led to the suggestion that this sequence of patterns can serve as an early indicator of desertification in some ecosystems. Because parameter values in the vegetation models can take on a range of plausible values, it is important to investigate whether the pattern sequence prediction is robust to variation. For a particular model, we find that a quantity calculated via bifurcation-theoretic analysis appears to serve as a proxy for the pattern sequences that occur in numerical simulations across a range of parameter values. We find in further analysis that the quantity takes on values consistent with the standard sequence in an ecologically relevant limit of the model parameter values. This suggests that the standard sequence is a robust prediction of the model, and we conclude by proposing a methodology for assessing the robustness of the standard sequence in other models and formulations.

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.

We construct far-from-onset radially symmetric spot and gap solutions in a two-component dryland ecosystem model of vegetation pattern formation on flat terrain, using spatial dynamics and geometric singular perturbation theory. We draw connections between the geometry of the spot and gap solutions with that of traveling and stationary front solutions in the same model. In particular, we demonstrate the instability of spots of large radius by deriving an asymptotic relationship between a critical eigenvalue associated with the spot and a coefficient which encodes the sideband instability of a nearby stationary front. Furthermore, we demonstrate that spots are unstable to a range of perturbations of intermediate wavelength in the angular direction, provided the spot radius is not too small. Our results are accompanied by numerical simulations and spectral computations.

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.

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

Globally, treeline ecotones vary from abrupt lines to extended zones of increasingly small, stunted and/or dispersed trees. These spatial patterns contain information about the processes that control treeline dynamics. Describing these patterns consistently along ecologically meaningful dimensions is needed for generalizing hypotheses and knowledge about controlling processes and expected treeline shifts globally. However, existing spatial categorizations of treelines are very loosely defined, leading to ambiguities in their use and interpretation. To help better understand treeline‐forming processes, we present a new framework for describing alpine treeline ecotones, focusing on hillside‐scale patterns, using pattern dimensions with distinct indicative values: 1) the spatial pattern in the x‐y plane: a) decline in tree cover, and b) change in the level of clustering. Variation along these dimensions results in more or less ‘discrete' or ‘diffuse' treelines with or without islands. These patterns mainly indicate demographic processes: establishment and mortality. 2) Changes in tree stature: a) decline in tree height, and b) change in tree shape. Variation along these dimensions results in more or less ‘abrupt' or ‘gradual' treelines with or without the formation of environmental krummholz. These patterns mainly indicate growth and dieback processes. Additionally, tree population structure can help distinguish alternative hypotheses about pattern formation, while analysing the functional composition of the ecotonal vegetation is essential to understand community‐level processes, controlled by species‐specific demographic processes. Our graphical representation of this framework can be used to place any treeline pattern in the proposed multi‐dimensional space to guide hypotheses on underlying processes and associated dynamics. To quantify the dimensions and facilitate comparative research, we advocate a joint effort in gathering and analysing spatial patterns from treelines globally. The improved recognition of treeline patterns should allow more effective comparative research and monitoring and advance our understanding of treeline‐forming processes and vegetation dynamics in response to climate warming.

Functioning of many resource-limited ecosystems is facilitated through spatial patterns. Patterns can indicate ecosystems productivity and resilience, but the interpretation of a pattern requires good understanding of its structure and underlying biophysical processes. Regular patterns are understood to form autogenously through self-organization, for which exogenous heterogeneities are negligible. This has been corroborated by reaction-diffusion models which generate highly regular patterns in idealized homogeneous environments. However, such model-generated patterns are considerably more regular than natural patterns, which indicates that the concept of autogenous pattern formation is incomplete. Models can generate patterns which appear more natural when they incorporate exogenous random spatial heterogeneities (noise), such as microtopography or spatially varying soil properties. However, the mechanism through which noise influences the pattern formation has not been explained so far. Recalling that irregular patterns can form through stochastic processes, we propose that regular patterns can form through stochastic processes as well, where spatial noise is filtered through scale-dependent biophysical feedbacks. First, we demonstrate that the pattern formation in nonlinear reaction-diffusion models is highly sensitive to noise. We then propose simple stochastic processes which can explain why and how random exogenous heterogeneity influences the formation of regular and irregular patterns. Finally, we derive linear filters which reproduce the spatial structure and visual appearance of natural patterns well. Our work contributes to a more holistic understanding of spatial pattern formation in self-organizing ecosystems.

Tectonic activity impacts the environment; therefore, identifying the influence of active faulting on environmental factors, such as soil development and vegetation growth patterns, is valuable in better understanding ecosystem functions. Here, we illustrate how tectonic activity and the lithology of bedrock influence temporal and spatial patterns of vegetation and soil parameters in a fault-controlled river basin. The Mara River basin lies in a region of previously unrecognised active normal faulting, dominated by the Utimbara and Isuria faults, resulting in areas of relative uplift, subsidence and tilting. Faulting leads to spatially variable erosion and soil formation rates as well as disruption and modification of drainage systems. On a small scale, steep escarpments cast shade and provide shelter. All of these factors might be expected to exert controls on ecosystem dynamics on a range of lengths and timescales. Here, we investigate tectonic controls on ecological processes in the Mara River basin using TanDEM-X and Sentinel-2 data. We use high-resolution digital elevation models (DEMs) to map the Utimbara and Isuria faults and to measure the height of the escarpments (up to 400 m) along the length of the faults. Total fault offset can be estimated by correlating Neogene phonolite lavas (thought to be 3.5–4.5 Myr old) on either side of the faults. If the age is correct, slip rates can be estimated to be on the order of 0.1 mm yr−1. Analysis of DEMs also reveals the presence of recent earthquake scarps in the hanging-wall sediments of the main faults and extensive alluvial fan formation on the hanging wall. Low mountain front sinuosity values and the presence of steep escarpments also suggest recent activity. Drainage is displaced across the fault traces, and, in one area, it is possible to map the lateral channel migration of the Mara River due to hanging-wall tilting. We used a 5-year normalised difference vegetation index (NDVI) time series, the clay mineral ratio (CMR) and a moisture stress index (MSI) to investigate spatiotemporal vegetation patterns and soil formation. Whilst lithology does exert some control, as expected, we observed that the downthrown hanging wall of the faults, especially directly adjacent to the escarpment, is consistently associated with a higher degree of vegetation, wetland formation and clay distribution. Analysis of spectral indices shows that the overall spatial pattern of vegetation cover is seasonally low in the flat plains and perennially high in the vicinity of more complex, tectonically influenced structures. The NDVI highlights several locations with permanently healthy vegetation along the escarpment which extend downslope for several kilometres. Our study shows that in the Mara River basin, active normal faulting is an important stabiliser of vegetation growth patterns, likely caused by favourable hydrological and pedological conditions along the escarpments; tectonic activity has a direct beneficial influence on ecological processes in this climatically sensitive region.