1
|
Escaff D. Anti-aligning interaction between active particles induces a finite wavelength instability: The dancing hexagons. Phys Rev E 2024; 109:024602. [PMID: 38491588 DOI: 10.1103/physreve.109.024602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2023] [Accepted: 01/11/2024] [Indexed: 03/18/2024]
Abstract
By considering a simple model for self-propelled particle interaction, we show that anti-aligning forces induce a finite wavelength instability. Consequently, the system exhibits pattern formation. The formed pattern involves, let us say, a choreographic movement of the active entities. At the level of particle density, the system oscillates between a stripe pattern and a hexagonal one. The underlying dynamics of these density oscillations consists of two counterpropagating and purely hexagonal traveling waves. They are assembling and disassembling a global hexagonal structure and a striped lineup of particles. This self-assembling process becomes quite erratic for long-time simulations, seeming aperiodic.
Collapse
Affiliation(s)
- Daniel Escaff
- Universidad de los Andes, Chile, Avenida Monseñor Álvaro del Portillo N° 12.455, Las Condes, Santiago 7620060, Chile
| |
Collapse
|
2
|
Wang C, Wang H, Yuan S. Precipitation governing vegetation patterns in an arid or semi-arid environment. J Math Biol 2023; 87:22. [PMID: 37395848 DOI: 10.1007/s00285-023-01954-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2022] [Revised: 05/15/2023] [Accepted: 06/15/2023] [Indexed: 07/04/2023]
Abstract
In an arid or semi-arid environment, precipitation plays a vital role in vegetation growth. Recent researches reveal that the response of vegetation growth to precipitation has a lag effect. To explore the mechanism behind the lag phenomenon, we propose and investigate a water-vegetation model with spatiotemporal nonlocal effects. It is shown that the temporal kernel function does not affect Turing bifurcation. For better understanding the influences of lag effect and nonlocal competition on the vegetation pattern formation, we choose some special kernel functions and obtain some insightful results: (i) Time delay does not trigger the vegetation pattern formation, but can postpone the evolution of vegetation. In addition, in the absence of diffusion, time delay can induce the occurrence of stability switches, while in the presence of diffusion, spatially nonhomogeneous time-periodic solutions may emerge, but there are no stability switches; (ii) The spatial nonlocal interaction may trigger the pattern onset for small diffusion ratio of water and vegetation, and can change the number and size of isolated vegetation patches for large diffusion ratio. (iii) The interaction between time delay and spatial nonlocal competition may induce the emergence of traveling wave patterns, so that the vegetation remains periodic in space, but is oscillating in time. These results demonstrate that precipitation can significantly affect the growth and spatial distribution of vegetation.
Collapse
Affiliation(s)
- Cuihua Wang
- University of Shanghai for Science and Technology, Shanghai, 200093, People's Republic of China
| | - Hao Wang
- Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G2G1, Canada
| | - Sanling Yuan
- University of Shanghai for Science and Technology, Shanghai, 200093, People's Republic of China.
| |
Collapse
|
3
|
Pal MK, Poria S. Role of herbivory in shaping the dryland vegetation ecosystem: Linking spiral vegetation patterns and nonlinear, nonlocal grazing. Phys Rev E 2023; 107:064403. [PMID: 37464659 DOI: 10.1103/physreve.107.064403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2022] [Accepted: 04/17/2023] [Indexed: 07/20/2023]
Abstract
Self-organized vegetation patterns are an amazing aspect of dryland ecosystems; in addition to being visually appealing, patterns control how these water-deprived systems react to escalating environmental stress. Although there is a wide variety of vegetation patterns, little is known about the mechanisms behind spiral patterns. The well-known models that explain other vegetation patterns such stripes, rings, and fairy circles cannot account for these spirals. Here we have adopted a modeling approach in which the interplay between herbivore grazing and vegetation is found to be the reason why spirals form. To comprehend the nonlinear dependence of grazing on the availability vegetation, we have introduced a grazing term that gets saturated when forage is abundant. To account for the impact of the spatial nonhomogeneity in vegetation layout, it is thought that grazing is dependent on mean vegetation density rather than density at a single site. Results show how the system dynamics is changed fundamentally depending on the different types of grazing response. Incorporation of nonlocality into the herbivore grazing leads to spiral-shaped vegetation patterns only in natural grazing scenarios; however, no patterning is seen in human controlled herbivory. Overall, our research points to the nonlocal, nonlinear grazing behavior of herbivores as one of the major driving forces for the development of spiral patterns.
Collapse
Affiliation(s)
- Mrinal Kanti Pal
- Department of Applied Mathematics, University of Calcutta, 92 APC Road, Kolkata-700009, India
| | - Swarup Poria
- Department of Applied Mathematics, University of Calcutta, 92 APC Road, Kolkata-700009, India
| |
Collapse
|
4
|
Conservative or dissipative? Two distinct processes for spatial pattern emergence. Proc Natl Acad Sci U S A 2023; 120:e2221117120. [PMID: 36696441 PMCID: PMC9945989 DOI: 10.1073/pnas.2221117120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
|
5
|
Phase-separation physics underlies new theory for the resilience of patchy ecosystems. Proc Natl Acad Sci U S A 2023; 120:e2202683120. [PMID: 36595670 PMCID: PMC9926271 DOI: 10.1073/pnas.2202683120] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
Spatial self-organization of ecosystems into large-scale (from micron to meters) patterns is an important phenomenon in ecology, enabling organisms to cope with harsh environmental conditions and buffering ecosystem degradation. Scale-dependent feedbacks provide the predominant conceptual framework for self-organized spatial patterns, explaining regular patterns observed in, e.g., arid ecosystems or mussel beds. Here, we highlight an alternative mechanism for self-organized patterns, based on the aggregation of a biotic or abiotic species, such as herbivores, sediment, or nutrients. Using a generalized mathematical model, we demonstrate that ecosystems with aggregation-driven patterns have fundamentally different dynamics and resilience properties than ecosystems with patterns that formed through scale-dependent feedbacks. Building on the physics theory for phase-separation dynamics, we show that patchy ecosystems with aggregation patterns are more vulnerable than systems with patterns formed through scale-dependent feedbacks, especially at small spatial scales. This is because local disturbances can trigger large-scale redistribution of resources, amplifying local degradation. Finally, we show that insights from physics, by providing mechanistic understanding of the initiation of aggregation patterns and their tendency to coarsen, provide a new indicator framework to signal proximity to ecological tipping points and subsequent ecosystem degradation for this class of patchy ecosystems.
Collapse
|
6
|
Sun GQ, Hou LF, Li L, Jin Z, Wang H. Spatial dynamics of a vegetation model with uptake-diffusion feedback in an arid environment. J Math Biol 2022; 85:50. [PMID: 36227425 DOI: 10.1007/s00285-022-01825-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2021] [Revised: 09/20/2022] [Accepted: 10/03/2022] [Indexed: 10/17/2022]
Abstract
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.
Collapse
Affiliation(s)
- Gui-Quan Sun
- Department of Mathematics, North University of China, Taiyuan, 030051, Shanxi, China.,Complex Systems Research Center, Shanxi University, Taiyuan, 030006, Shanxi, China
| | - Li-Feng Hou
- Complex Systems Research Center, Shanxi University, Taiyuan, 030006, Shanxi, China
| | - Li Li
- School of Computer and Information Technology, Shanxi University, Taiyuan, 030006, Shanxi, China.,Science and Technology on Electronic Test and Measurement Laboratory, North University of China, Taiyuan, 030051, Shanxi, China
| | - Zhen Jin
- Complex Systems Research Center, Shanxi University, Taiyuan, 030006, Shanxi, China
| | - Hao Wang
- Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, T6G 2G1, Canada.
| |
Collapse
|
7
|
High-integrity human intervention in ecosystems: Tracking self-organization modes. PLoS Comput Biol 2021; 17:e1009427. [PMID: 34587157 PMCID: PMC8504872 DOI: 10.1371/journal.pcbi.1009427] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2021] [Revised: 10/11/2021] [Accepted: 09/06/2021] [Indexed: 11/19/2022] Open
Abstract
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. Human intervention in ecosystems is motivated by various functional needs, such as provisioning ecosystem services, but often has unexpected detrimental outcomes. A major question in ecology is how to manage human intervention so as to achieve its goal without impairing ecosystem function. The main idea pursued here is the need to identify the inherent response ways of ecosystems to disturbances, and use them as road maps for conducting interventions. This approach is demonstrated mathematically using two contexts, grazing management and vegetation restoration, and compared to remote sensing data for the latter. Among the surprising insights obtained is the beneficial effect of grazing, in terms of resilience to droughts, that can be achieved by managing it non-uniformly in space.
Collapse
|
8
|
Sherratt JA, Liu QX, van de Koppel J. A Comparison of the "Reduced Losses" and "Increased Production" Models for Mussel Bed Dynamics. Bull Math Biol 2021; 83:99. [PMID: 34427781 PMCID: PMC8384834 DOI: 10.1007/s11538-021-00932-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2020] [Accepted: 07/20/2021] [Indexed: 11/02/2022]
Abstract
Self-organised regular pattern formation is one of the foremost examples of the development of complexity in ecosystems. Despite the wide array of mechanistic models that have been proposed to understand pattern formation, there is limited general understanding of the feedback processes causing pattern formation in ecosystems, and how these affect ecosystem patterning and functioning. Here we propose a generalised model for pattern formation that integrates two types of within-patch feedback: amplification of growth and reduction of losses. Both of these mechanisms have been proposed as causing pattern formation in mussel beds in intertidal regions, where dense clusters of mussels form, separated by regions of bare sediment. We investigate how a relative change from one feedback to the other affects the stability of uniform steady states and the existence of spatial patterns. We conclude that there are important differences between the patterns generated by the two mechanisms, concerning both biomass distribution in the patterns and the resilience of the ecosystems to disturbances.
Collapse
Affiliation(s)
- Jonathan A Sherratt
- Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK.
| | - Quan-Xing Liu
- State Key Laboratory of Estuarine and Coastal Research, School of Ecological and Environmental Sciences, East China Normal University, Shanghai, 200241, People's Republic of China
| | - Johan van de Koppel
- Department of Estuarine and Delta Systems, Royal Netherlands Institute for Sea Research and Utrecht University, PO Box 140, 4400 AC, Yerseke, The Netherlands
| |
Collapse
|
9
|
Abstract
Population-level scaling in ecological systems arises from individual growth and death with competitive constraints. We build on a minimal dynamical model of metabolic growth where the tension between individual growth and mortality determines population size distribution. We then separately include resource competition based on shared capture area. By varying rates of growth, death, and competitive attrition, we connect regular and random spatial patterns across sessile organisms from forests to ants, termites, and fairy circles. Then, we consider transient temporal dynamics in the context of asymmetric competition, such as canopy shading or large colony dominance, whose effects primarily weaken the smaller of two competitors. When such competition couples slow timescales of growth to fast competitive death, it generates population shocks and demographic oscillations similar to those observed in forest data. Our minimal quantitative theory unifies spatiotemporal patterns across sessile organisms through local competition mediated by the laws of metabolic growth, which in turn, are the result of long-term evolutionary dynamics.
Collapse
|
10
|
Eigentler L. Species coexistence in resource‐limited patterned ecosystems is facilitated by the interplay of spatial self‐organisation and intraspecific competition. OIKOS 2021. [DOI: 10.1111/oik.07880] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Affiliation(s)
- L. Eigentler
- Division of Molecular Microbiology, School of Life Sciences, Univ. of Dundee Dundee UK
- Maxwell Inst. for Mathematical Sciences, Dept of Mathematics, Heriot‐Watt Univ. Edinburgh UK
| |
Collapse
|
11
|
Eigentler L, Sherratt J. Spatial self-organisation enables species coexistence in a model for savanna ecosystems. J Theor Biol 2020; 487:110122. [DOI: 10.1016/j.jtbi.2019.110122] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2019] [Revised: 11/18/2019] [Accepted: 12/16/2019] [Indexed: 11/16/2022]
|
12
|
Effects of Land-Use Practices on Woody Plant Cover Dynamics in Sahelian Agrosystems in Burkina Faso since the 1970s–1980s Droughts. SUSTAINABILITY 2019. [DOI: 10.3390/su11215908] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The 1970s–1980s droughts in the Sahel caused a significant degradation of land and plant cover. To cope with this situation, populations have developed several biophysical and social adaptation practices. Many of these are agroforestry practices and contribute to the maintenance of agrosystems. Unfortunately, they remain insufficiently documented and their contributions to the resilience of agrosystems insufficiently evaluated. Many authors widely link the regreening in the Sahel after droughts to the resumption of rainfall. This study examines the contribution of agroforestry practices to the improvement of woody plant cover in the North of Burkina Faso after the 1970s–1980s droughts. The examination of practices is carried out by integrating the rainfall, soil, and geomorphology variables. Landsat images are used to detect changes in woody plant cover: increasing, decreasing, and no-change in the Enhanced Vegetation Index. In addition, 230 field observations, coupled with interviews conducted on the different categories of change, have allowed to characterize the biophysical environment and identify land-use practices. The results show a variability of vegetation index explained to 9% (R2 = 0.09) by rainfall. However, Chi-Squared independence tests show a strong dependence between changes in woody plant cover and geomorphology (p = 0.0018 *), land use, land cover (p = 0.0001 *), and land-use practices (p = 0.0001 *). Our results show that rainfall alone is not enough to explain the dynamics of agrosystems’ woody plant cover. Agricultural and social practices related to the dynamics of farmer perceptions play a key role.
Collapse
|
13
|
Continuum Modeling of Discrete Plant Communities: Why Does It Work and Why Is It Advantageous? MATHEMATICS 2019. [DOI: 10.3390/math7100987] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
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.
Collapse
|
14
|
Consolo G, Valenti G. Secondary seed dispersal in the Klausmeier model of vegetation for sloped semi-arid environments. Ecol Modell 2019. [DOI: 10.1016/j.ecolmodel.2019.02.009] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
|
15
|
Using Experimental Data and Information Criteria to Guide Model Selection for Reaction–Diffusion Problems in Mathematical Biology. Bull Math Biol 2019; 81:1760-1804. [DOI: 10.1007/s11538-019-00589-x] [Citation(s) in RCA: 44] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2018] [Accepted: 02/20/2019] [Indexed: 12/20/2022]
|
16
|
Fernandez-Oto C, Escaff D, Cisternas J. Spiral vegetation patterns in high-altitude wetlands. ECOLOGICAL COMPLEXITY 2019. [DOI: 10.1016/j.ecocom.2018.12.003] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
|
17
|
Gandhi P, Zelnik YR, Knobloch E. Spatially localized structures in the Gray-Scott model. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2018; 376:20170375. [PMID: 30420543 PMCID: PMC6232600 DOI: 10.1098/rsta.2017.0375] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 08/21/2018] [Indexed: 05/19/2023]
Abstract
Spatially localized structures in the one-dimensional Gray-Scott reaction-diffusion model are studied using a combination of numerical continuation techniques and weakly nonlinear theory, focusing on the regime in which the activator and substrate diffusivities are different but comparable. Localized states arise in three different ways: in a subcritical Turing instability present in this regime, and from folds in the branch of spatially periodic Turing states. They also arise from the fold of spatially uniform states. These three solution branches interconnect in complex ways. We use numerical continuation techniques to explore their global behaviour within a formulation of the model that has been used to describe dryland vegetation patterns on a flat terrain.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)'.
Collapse
Affiliation(s)
- Punit Gandhi
- Mathematical Biosciences Institute, Ohio State University, Columbus, OH 43210, USA
| | - Yuval R Zelnik
- Centre for Biodiversity Theory and Modelling, Theoretical and Experimental Ecology Station, CNRS and Paul Sabatier University, 09200 Moulis, France
| | - Edgar Knobloch
- Department of Physics, University of California, Berkeley, CA 94720, USA
| |
Collapse
|
18
|
Bastiaansen R, Jaïbi O, Deblauwe V, Eppinga MB, Siteur K, Siero E, Mermoz S, Bouvet A, Doelman A, Rietkerk M. Multistability of model and real dryland ecosystems through spatial self-organization. Proc Natl Acad Sci U S A 2018; 115:11256-11261. [PMID: 30322906 PMCID: PMC6217401 DOI: 10.1073/pnas.1804771115] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
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.
Collapse
Affiliation(s)
- Robbin Bastiaansen
- Mathematical Institute, Leiden University, 2300 RA Leiden, The Netherlands;
| | - Olfa Jaïbi
- Mathematical Institute, Leiden University, 2300 RA Leiden, The Netherlands
| | - Vincent Deblauwe
- International Institute of Tropical Agriculture, BP 2008 (Messa), Yaounde, Cameroon
- Center for Tropical Research, Institute of the Environment and Sustainability, University of California, Los Angeles, CA 90095
| | - Maarten B Eppinga
- Department of Environmental Sciences, Copernicus Institute, Utrecht University, 3508 TC Utrecht, The Netherlands
| | - Koen Siteur
- Department of Estuarine and Delta Systems, Royal Netherlands Institute for Sea Research and Utrecht University, 4401 NT Yerseke, The Netherlands
- Shanghai Key Laboratory for Urban Ecological Processes and Eco-Restoration, School of Ecological and Environmental Science, East China Normal University, 200241 Shanghai, China
- Center for Global Change and Ecological Forecasting, School of Ecological and Environmental Science, East China Normal University, 200241 Shanghai, China
| | - Eric Siero
- Institute for Mathematics, Carl von Ossietzky University Oldenburg, 26111 Oldenburg, Germany
| | - Stéphane Mermoz
- Centre d'Etudes Spatiales de la Biosphère, Université Toulouse III Paul Sabatier, Centre National d'Etudes Spatiales, Centre National de la Recherche Scientifique, Institut de Recherche pour le Développement, 31401 Toulouse, France
| | - Alexandre Bouvet
- Centre d'Etudes Spatiales de la Biosphère, Université Toulouse III Paul Sabatier, Centre National d'Etudes Spatiales, Centre National de la Recherche Scientifique, Institut de Recherche pour le Développement, 31401 Toulouse, France
| | - Arjen Doelman
- Mathematical Institute, Leiden University, 2300 RA Leiden, The Netherlands
| | - Max Rietkerk
- Department of Environmental Sciences, Copernicus Institute, Utrecht University, 3508 TC Utrecht, The Netherlands
| |
Collapse
|
19
|
Gowda K, Iams S, Silber M. Signatures of human impact on self-organized vegetation in the Horn of Africa. Sci Rep 2018; 8:3622. [PMID: 29483556 PMCID: PMC5827523 DOI: 10.1038/s41598-018-22075-5] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2017] [Accepted: 02/15/2018] [Indexed: 11/09/2022] Open
Abstract
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.
Collapse
Affiliation(s)
- Karna Gowda
- Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL, 60208, USA
| | - Sarah Iams
- Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
| | - Mary Silber
- Committee on Computational and Applied Mathematics, and Department of Statistics, University of Chicago, Chicago, IL, 60637, USA.
| |
Collapse
|
20
|
|
21
|
Zhang F, Zhang H, Evans MR, Huang T. Vegetation patterns generated by a wind driven sand-vegetation system in arid and semi-arid areas. ECOLOGICAL COMPLEXITY 2017. [DOI: 10.1016/j.ecocom.2017.02.005] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
22
|
Pringle RM, Tarnita CE. Spatial Self-Organization of Ecosystems: Integrating Multiple Mechanisms of Regular-Pattern Formation. ANNUAL REVIEW OF ENTOMOLOGY 2017; 62:359-377. [PMID: 28141964 DOI: 10.1146/annurev-ento-031616-035413] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Large-scale regular vegetation patterns are common in nature, but their causes are disputed. Whereas recent theory focuses on scale-dependent feedbacks as a potentially universal mechanism, earlier studies suggest that many regular spatial patterns result from territorial interference competition between colonies of social-insect ecosystem engineers, leading to hexagonally overdispersed nest sites and associated vegetation. Evidence for this latter mechanism is scattered throughout decades of disparate literature and lacks a unified conceptual framework, fueling skepticism about its generality in debates over the origins of patterned landscapes. We review these mechanisms and debates, finding evidence that spotted and gapped vegetation patterns generated by ants, termites, and other subterranean animals are globally widespread, locally important for ecosystem functioning, and consistent with models of intraspecific territoriality. Because these and other mechanisms of regular-pattern formation are not mutually exclusive and can coexist and interact at different scales, the prevailing theoretical outlook on spatial self-organization in ecology must expand to incorporate the dynamic interplay of multiple processes.
Collapse
Affiliation(s)
- Robert M Pringle
- Department of Ecology and Evolutionary Biology, Princeton University, Princeton, New Jersey 08544; ,
| | - Corina E Tarnita
- Department of Ecology and Evolutionary Biology, Princeton University, Princeton, New Jersey 08544; ,
| |
Collapse
|
23
|
Sherratt JA, Mackenzie JA. How does tidal flow affect pattern formation in mussel beds? J Theor Biol 2016; 406:83-92. [PMID: 27343625 DOI: 10.1016/j.jtbi.2016.06.025] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2016] [Revised: 06/06/2016] [Accepted: 06/20/2016] [Indexed: 10/21/2022]
Abstract
In the Wadden Sea, mussel beds self-organise into spatial patterns consisting of bands parallel to the shore. A leading explanation for this phenomenon is that mussel aggregation reduces losses from dislodgement and predation, because of the adherence of mussels to one another. Previous mathematical modelling has shown that this can lead to spatial patterning when it is coupled to the advection from the open sea of algae-the main food source for mussels in the Wadden Sea. A complicating factor in this process is that the advection of algae will actually oscillate with the tidal flow. This has been excluded from previous modelling studies, and the present paper concerns the implications of this oscillation for pattern formation. The authors initially consider piecewise constant ("square-tooth") oscillations in advection, which enables analytical investigation of the conditions for pattern formation. They then build on this to study the more realistic case of sinusoidal oscillations. Their analysis shows that future research on the details of pattern formation in mussel beds will require an in-depth understanding of how the tides affect long-range inhibition among mussels.
Collapse
Affiliation(s)
- Jonathan A Sherratt
- Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK.
| | - Jay A Mackenzie
- Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK.
| |
Collapse
|
24
|
The response of shrubland patterns' properties to rainfall changes and to the catastrophic removal of plants in semi-arid regions predicted by Reaction–Diffusion simulations. ECOL INFORM 2016. [DOI: 10.1016/j.ecoinf.2016.02.001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
|
25
|
Gowda K, Chen Y, Iams S, Silber M. Assessing the robustness of spatial pattern sequences in a dryland vegetation model. Proc Math Phys Eng Sci 2016; 472:20150893. [PMID: 27118924 DOI: 10.1098/rspa.2015.0893] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
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.
Collapse
Affiliation(s)
- Karna Gowda
- Department of Engineering Sciences and Applied Mathematics , Northwestern University , Evanston, IL 60208, USA
| | - Yuxin Chen
- Department of Engineering Sciences and Applied Mathematics , Northwestern University , Evanston, IL 60208, USA
| | - Sarah Iams
- Paulson School of Engineering and Applied Sciences , Harvard University , Cambridge, MA 02138, USA
| | - Mary Silber
- Department of Statistics , The University of Chicago , Chicago, IL 60637, USA
| |
Collapse
|
26
|
Pattern formation – A missing link in the study of ecosystem response to environmental changes. Math Biosci 2016; 271:1-18. [DOI: 10.1016/j.mbs.2015.10.015] [Citation(s) in RCA: 56] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2015] [Revised: 10/17/2015] [Accepted: 10/23/2015] [Indexed: 11/18/2022]
|
27
|
Cobbold CA, Lutscher F, Sherratt JA. Diffusion-driven instabilities and emerging spatial patterns in patchy landscapes. ECOLOGICAL COMPLEXITY 2015. [DOI: 10.1016/j.ecocom.2015.10.001] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
|
28
|
Sherratt JA. When does colonisation of a semi-arid hillslope generate vegetation patterns? J Math Biol 2015; 73:199-226. [PMID: 26547308 DOI: 10.1007/s00285-015-0942-8] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2015] [Revised: 09/05/2015] [Indexed: 10/22/2022]
Abstract
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.
Collapse
Affiliation(s)
- Jonathan A Sherratt
- Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK.
| |
Collapse
|