Localized states qualitatively change the response of ecosystems to varying conditions and local disturbances

Transitions between dissipative localized structures in the simplified Gilad-Meron model for dryland plant ecology

Spatially extended patterns and multistability of possible different states are common in many ecosystems, and their combination has an important impact on their dynamical behaviors. One potential combination involves tristability between a patterned state and two different uniform states. Using a simplified version of the Gilad-Meron model for dryland ecosystems, we study the organization, in bifurcation terms, of the localized structures arising in tristable regimes. These states are generally related to the concept of wave front locking and appear in the form of spots and gaps of vegetation. We find that the coexistence of localized spots and gaps, within tristable configurations, yields the appearance of hybrid states. We also study the emergence of spatiotemporal localized states consisting of a portion of a periodic pattern embedded in a uniform Hopf-like oscillatory background in a subcritical Turing-Hopf dynamical regime.

Spatial dynamics of a vegetation model with uptake-diffusion feedback in an arid environment

Vegetation patterns with a variety of structures is amazing phenomena in arid or semi-arid areas, which can identify the evolution law of vegetation and are typical signals of ecosystem functions. Many achievements have been made in this respect, yet the mechanisms of uptake-diffusion feedback on the pattern structures of vegetation is not fully understood. To well reveal the influences of parameters perturbation on the pattern formation of vegetation, we give a comprehensive analysis on a vegetation-water model in the forms of reaction-diffusion equation which is posed by Zelnik et al. (Proc Natl Acad Sci 112:12,327-12,331, 2015). We obtain the exact parameters range for stationary patterns and show the dynamical behaviors near the bifurcation point based on nonlinear analysis. It is found that the model has the properties of spot, labyrinth and gap patterns. Moreover, water diffusion rate prohibits the growth of vegetation while shading parameter promotes the increase of vegetation biomass. Our results show that gradual transitions from uniform state to gap pattern can occur for suitable value of parameters which may induce the emergence of desertification.

Unified framework for localized patterns in reaction-diffusion systems; the Gray-Scott and Gierer-Meinhardt cases

A recent study of canonical activator-inhibitor Schnakenberg-like models posed on an infinite line is extended to include models, such as Gray-Scott, with bistability of homogeneous equilibria. A homotopy is studied that takes a Schnakenberg-like glycolysis model to the Gray-Scott model. Numerical continuation is used to understand the complete sequence of transitions to two-parameter bifurcation diagrams within the localized pattern parameter regime as the homotopy parameter varies. Several distinct codimension-two bifurcations are discovered including cusp and quadruple zero points for homogeneous steady states, a degenerate heteroclinic connection and a change in connectedness of the homoclinic snaking structure. The analysis is repeated for the Gierer-Meinhardt system, which lies outside the canonical framework. Similar transitions are found under homotopy between bifurcation diagrams for the case where there is a constant feed in the active field, to it being in the inactive field. Wider implications of the results are discussed for other pattern-formation systems arising as models of natural phenomena. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.

The Impact of Roads on the Redistribution of Plants and Associated Arthropods in a Hyper-Arid Ecosystem

The construction of vehicular roads likely affects the distribution of natural resources. Although the effects of roads on different ecosystem aspects have been extensively studied, studies in arid and, particularly, in hyper-arid ecosystems are scarce. In drylands, where water is the main limiting factor, the effect of roads on the redistribution of water may have strong subsequent effects on the ecosystem, especially when roads cross natural water flow paths. To fill this knowledge gap, we studied the effects of a road that runs across a slope on the distribution of plants and animals in a hyper-arid environment. Changes in shrub cover, below and above the road, were quantified by remote sensing and image classification, while plant-associated arthropods were vacuum-sampled from shrub canopies and from open (inter-shrub) areas. We found that the spatial distribution of shrubs, a vital resource facilitating many other organisms, was affected by the road, with an increase in the shrub cover immediately above the road and a decrease below it. Arthropod abundance generally followed shrub cover, but the exact pattern depended on the specific group sampled. While some arthropod groups (e.g., aphids, parasitic wasps and barklice) thrived under the disturbed conditions above the road, other arthropod groups (e.g., mites and true bugs) were less abundant in the disturbed patches. Our results highlight the strong effects of human-made structures on the distribution of flora and fauna in arid ecosystems.

Formation of localized states in dryland vegetation: Bifurcation structure and stability

We study theoretically the emergence of localized states of vegetation close to the onset of desertification. These states are formed through the locking of vegetation fronts, connecting a uniform vegetation state with a bare soil state, which occurs nearby the Maxwell point of the system. To study these structures we consider a universal model of vegetation dynamics in drylands, which has been obtained as the normal form for different vegetation models. Close to the Maxwell point localized gaps and spots of vegetation exist and undergo collapsed snaking. The presence of gaps strongly suggest that the ecosystem may undergo a recovering process. In contrast, the presence of spots may indicate that the ecosystem is close to desertification.

Spatio-Temporal Land-Use Changes and the Response in Landscape Pattern to Hemeroby in a Resource-Based City

Hemeroby is an integrated indicator used to measure the impact and degree of all human interventions on ecological components or ecosystems. The constant exploitation of resources is a strong interference of human beings to the natural environment. With the depletion of non-renewable resources, some cities with resource exploitation as their main industry—“resource-based cities”—are facing great development pressure. In order to quantify the impact of human disturbance on the natural environment and provide some scientific support for policy makers of the resource-based city, we used remote sensing images and landscape pattern metrics, introduced the synthetic hemeroby index model and analyzed the relationship between human disturbance and landscape pattern during 1990–2017. The results showed that: (1) The hemeroby in Daqing continued to rise during 1990–2017, and the main factor was the continuous expansion of the construction land and the reclamation of farmland. (2) In the areas with different hemeroby, there were significant differences in landscape pattern. In the areas with high-level hemeroby, the heterogeneity of landscape pattern was low, the aggregation among patches was high, and the shape of patches was regular, whereas the landscape pattern in the areas with medium-level hemeroby was just opposite. Although the heterogeneity of landscape pattern and the aggregation among patches were high in the areas with low-level hemeroby, the complexity of landscape was low and the shape of patches was regular. (3) In the temporal dimension, the increase of hemeroby contributed to the complexity of patch shape, the decrease of the aggregation among patches, and the fragmentation of landscape pattern. In the spatial dimension, the response in landscape pattern to human disturbance was relatively insensitive in the areas with low-level hemeroby, and this response was basically same in the high-level hemeroby and the whole study areas.

Continuum Modeling of Discrete Plant Communities: Why Does It Work and Why Is It Advantageous?

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.

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.

Effects of Hydraulic Soil Properties on Vegetation Pattern Formation in Sloping Landscapes

Current models of vegetation pattern formation rely on a system of weakly nonlinear reaction-diffusion equations that are coupled by their source terms. While these equations, which are used to describe a spatiotemporal planar evolution of biomass and soil water, qualitatively capture the emergence of various types of vegetation patterns in arid environments, they are phenomenological and have a limited predictive power. We ameliorate these limitations by deriving the vertically averaged Richards' equation to describe flow (as opposed to "diffusion") of water in partially saturated soils. This establishes conditions under which this nonlinear equation reduces to its weakly nonlinear reaction-diffusion counterpart used in the previous models, thus relating their unphysical parameters (e.g., diffusion coefficient) to the measurable soil properties (e.g., hydraulic conductivity) used to parameterize the Richards equation. Our model is valid for both flat and sloping landscapes and can handle arbitrary topography and boundary conditions. The result is a model that relates the environmental conditions (e.g., precipitation rate, runoff and soil properties) to formation of multiple patterns observed in nature (such as stripes, labyrinth and spots).