1
|
Li L, Pang YZ, Sun GQ, Ruan S. Impact of climate change on vegetation patterns in Altay Prefecture, China. MATHEMATICAL MEDICINE AND BIOLOGY : A JOURNAL OF THE IMA 2024; 41:53-80. [PMID: 38421157 DOI: 10.1093/imammb/dqae002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2023] [Revised: 12/18/2023] [Accepted: 02/20/2024] [Indexed: 03/02/2024]
Abstract
Altay Prefecture, a typical arid region in northwestern China, has experienced the climate transition from warming-drying to warming-wetting since 1980s and has attracted widespread attention. Nonetheless, it is still unclear how climate change has influenced the distribution of vegetation in this region. In this paper, a reaction-diffusion model of the climate-vegetation system is proposed to study the impact of climate change (precipitation, temperature and carbon dioxide concentration) on vegetation patterns in Altay Prefecture. Our results indicate that the tendency of vegetation growth in Altay Prefecture improved gradually from 1985 to 2010. Under the current climate conditions, the increase of precipitation results in the change of vegetation pattern structures, and eventually vegetation coverage tends to be uniform. Moreover, we found that there exists an optimal temperature where the spot vegetation pattern structure remains stable. Furthermore, the increase in carbon dioxide concentration induces vegetation pattern transition. Based on four climate change scenarios of the Coupled Model Intercomparison Project Phase 6 (CMIP6), we used the power law range (PLR) to predict the optimal scenario for the sustainable development of the vegetation ecosystem in Altay Prefecture.
Collapse
Affiliation(s)
- Li Li
- School of Computer and Information Technology, Shanxi University, Taiyuan 030006, Shanxi, China
| | - Yi-Zhi Pang
- Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, China
| | - Gui-Quan Sun
- Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, China
- Department of Mathematics, North University of China, Taiyuan 030051, Shanxi, China
| | - Shigui Ruan
- Department of Mathematics, University of Miami, Coral Gables, FL 33146, USA
| |
Collapse
|
2
|
Wang C, Yuan S, Wang H. The impact of water storage capacity on plant dynamics in arid environments: A stoichiometric modeling approach. Math Biosci 2024; 369:109147. [PMID: 38266704 DOI: 10.1016/j.mbs.2024.109147] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2023] [Revised: 10/05/2023] [Accepted: 01/17/2024] [Indexed: 01/26/2024]
Abstract
Plants in arid environments have evolved many strategies to resist drought. Among them, the developed water storage tissue is an essential characteristic of xerophytes. To clarify the role of water storage capacity in plant performance, we originally formulate a stoichiometric model to describe the interaction between plants and water with explicit water storage. Via an ecological reproductive index, we explore the effects of precipitation and water storage capacity on plant dynamics. The model possesses saddle-node bifurcation and forward or backward bifurcation, and the latter may lead to the emergence of alternative stable states between a stable survival state and a stable extinction state. Numerical simulations illustrate the persistence and resilience of plants regulated by soil conditions, precipitation and water storage capacity. Our findings contribute to the botanical theory in the perspectives of environmental change and plant water storage traits.
Collapse
Affiliation(s)
- Cuihua Wang
- University of Shanghai for Science and Technology, Shanghai, 200093, China
| | - Sanling Yuan
- University of Shanghai for Science and Technology, Shanghai, 200093, China.
| | - Hao Wang
- Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G2G1, Canada
| |
Collapse
|
3
|
Abrantes GH, Gücker B, Chaves RC, Boëchat IG, Figueredo CC. Epilithic biofilms provide large amounts of nitrogen to tropical mountain landscapes. Environ Microbiol 2023; 25:3592-3603. [PMID: 37816630 DOI: 10.1111/1462-2920.16515] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2023] [Accepted: 09/19/2023] [Indexed: 10/12/2023]
Abstract
We show that epilithic biofilms are a relevant nitrogen (N) source in a rocky mountain range in Brazil. During different seasons, we quantified nitrate, ammonium, dissolved organic N (DON) and total dissolved N (TDN) leached by a simulated short rain event. We quantified the epilithic autotrophic biomass by taxonomic groups and its correlation with leached N. We hypothesized that leached N would be correlated to heterocystous cyanobacteria biomass since they are more efficient N2 fixers. We estimated a landscape N supply of 8.5 kg.ha-1 .year-1 considering the mean precipitation in the region. TDN in leachate was mainly composed of DON (83.8% ± 22%), followed by nitrate (12.1% ± 3%) and ammonium (5% ± 5%). The autotrophic epilithic community was mainly composed of non-heterocystous (Gloeocapsopsis) and heterocystous cyanobacteria (Scytonema and Stigonema), except for a site more commonly affected by fire events that showed a dominance of Chlorophyta. Biogeochemical upscaling was facilitated by the fact that N leaching was not different among sites or related to autotrophic epilithic biomass or assemblage composition. In conclusion, the capacity of epilithic biofilms to provide N to surrounding systems is an ecosystem service that underscores the necessity to conserve them and their habitats.
Collapse
Affiliation(s)
| | - Björn Gücker
- Department of Geosciences, Federal University of São João del-Rei, São João del-Rei, Brazil
| | - Ronaldo César Chaves
- Department of Botany, Federal University of Minas Gerais, Belo Horizonte, Brazil
| | - Iola Gonçalves Boëchat
- Department of Geosciences, Federal University of São João del-Rei, São João del-Rei, Brazil
| | | |
Collapse
|
4
|
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
|
5
|
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
|
6
|
Al Saadi F, Parra-Rivas P. Transitions between dissipative localized structures in the simplified Gilad-Meron model for dryland plant ecology. CHAOS (WOODBURY, N.Y.) 2023; 33:033129. [PMID: 37003806 DOI: 10.1063/5.0133576] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2022] [Accepted: 02/15/2023] [Indexed: 06/19/2023]
Abstract
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.
Collapse
Affiliation(s)
- Fahad Al Saadi
- Department of Systems Engineering, Military Technological College, Muscat, Oman
| | - Pedro Parra-Rivas
- Dipartimento di Ingegneria dell'Informazione, Elettronica e Telecomunicazioni, Sapienza Universitá di Roma, via Eudossiana 18, 00184 Rome, Italy
| |
Collapse
|
7
|
Eigentler L, Sherratt JA. Long-range seed dispersal enables almost stationary patterns in a model for dryland vegetation. J Math Biol 2023; 86:15. [PMID: 36528665 PMCID: PMC9759510 DOI: 10.1007/s00285-022-01852-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2022] [Revised: 09/15/2022] [Accepted: 12/01/2022] [Indexed: 12/23/2022]
Abstract
Spatiotemporal patterns of vegetation are a ubiquitous feature of semi-arid ecosystems. On sloped terrain, vegetation patterns occur as stripes perpendicular to the contours. Field studies report contrasting long-term dynamics between different observation sites; some observe slow uphill migration of vegetation bands while some report stationary patterns. In this paper, we show that long-range seed dispersal provides a mechanism that enables the occurrence of both migrating and stationary patterns. We utilise a nonlocal PDE model in which seed dispersal is accounted for by a convolution term. The model represents vegetation patterns as periodic travelling waves and numerical continuation shows that both migrating and almost stationary patterns are stable if seed dispersal distances are sufficiently large. We use a perturbation theory approach to obtain analytical confirmation of the existence of almost stationary patterned solutions and provide a biological interpretation of the phenomenon.
Collapse
Affiliation(s)
- L. Eigentler
- Division of Molecular Microbiology, School of Life Sciences, University of Dundee, Dundee, DD1 5EH UK ,Mathematics, School of Science and Engineering, University of Dundee, Dundee, DD1 4HN UK
| | - J. A. Sherratt
- Maxwell Institute for Mathematical Sciences, Department of Mathematics, Heriot-Watt University, Edinburgh, EH14 4AS UK
| |
Collapse
|
8
|
Consolo G, Grifó G, Valenti G. Dryland vegetation pattern dynamics driven by inertial effects and secondary seed dispersal. Ecol Modell 2022. [DOI: 10.1016/j.ecolmodel.2022.110171] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
9
|
Sun GQ, Li L, Li J, Liu C, Wu YP, Gao S, Wang Z, Feng GL. Impacts of climate change on vegetation pattern: Mathematical modeling and data analysis. Phys Life Rev 2022; 43:239-270. [PMID: 36343569 DOI: 10.1016/j.plrev.2022.09.005] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2022] [Accepted: 09/07/2022] [Indexed: 11/27/2022]
Abstract
Climate change has become increasingly severe, threatening ecosystem stability and, in particular, biodiversity. As a typical indicator of ecosystem evolution, vegetation growth is inevitably affected by climate change, and therefore has a great potential to provide valuable information for addressing such ecosystem problems. However, the impacts of climate change on vegetation growth, especially the spatial and temporal distribution of vegetation, are still lacking of comprehensive exposition. To this end, this review systematically reveals the influences of climate change on vegetation dynamics in both time and space by dynamical modeling the interactions of meteorological elements and vegetation growth. Moreover, we characterize the long-term evolution trend of vegetation growth under climate change in some typical regions based on data analysis. This work is expected to lay a necessary foundation for systematically revealing the coupling effect of climate change on the ecosystem.
Collapse
Affiliation(s)
- Gui-Quan Sun
- Department of Mathematics, North University of China, Taiyuan, 030051, China; Complex Systems Research Center, Shanxi University, Taiyuan, 030006, China; Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai, 519082, China.
| | - Li Li
- School of Computer and Information Technology, Shanxi University, Taiyuan, 030006, China
| | - Jing Li
- School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan, 030006, China
| | - Chen Liu
- Center for Ecology and Environmental Sciences, Northwestern Polytechnical University, Xi'an, 710072, China
| | - Yong-Ping Wu
- College of Physics Science and Technology, Yangzhou University, Yangzhou, 225002, China
| | - Shupeng Gao
- School of Mechanical Engineering and School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University, Xian, 710072, China
| | - Zhen Wang
- School of Mechanical Engineering and School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University, Xian, 710072, China.
| | - Guo-Lin Feng
- College of Physics Science and Technology, Yangzhou University, Yangzhou, 225002, China; Laboratory for Climate Studies, National Climate Center, China Meteorological Administration, Beijing, 100081, China.
| |
Collapse
|
10
|
Pal MK, Poria S. Effect of nonlocal grazing on dry-land vegetation dynamics. Phys Rev E 2022; 106:054407. [PMID: 36559433 DOI: 10.1103/physreve.106.054407] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2022] [Accepted: 09/22/2022] [Indexed: 06/17/2023]
Abstract
Dry-land ecosystems have become a matter of grave concern, due to the growing threat of land degradation and bioproductivity loss. Self-organized vegetation patterns are a remarkable characteristic of these ecosystems; apart from being visually captivating, patterns modulate the system response to increasing environmental stress. Empirical studies hinted that herbivory is one the key regulatory mechanisms behind pattern formation and overall ecosystem functioning. However, most of the mathematical models have taken a mean-field strategy to grazing; foraging has been considered to be independent of spatial distribution of vegetation. To this end, an extended version of the celebrated plant-water model due to Klausmeier has been taken as the base here. To encompass the effect of heterogeneous vegetation distribution on foraging intensity and subsequent impact on entire ecosystem, grazing is considered here to depend on spatially weighted average vegetation density instead of density at a particular point. Moreover, varying influence of vegetation at any location over gazing elsewhere is incorporated by choosing a suitable averaging function. A comprehensive analysis demonstrates that inclusion of spatial nonlocality alters the understanding of system dynamics significantly. The grazing ecosystem is found to be more resilient to increasing aridity than it was anticipated to be in earlier studies on nonlocal grazing. The system response to rising environmental pressure is also observed to vary depending on the grazer. Obtained results also suggest the possibility of multistability due to the history dependence of the system response. Overall, this work indicates that the spatial heterogeneity in grazing intensity has a decisive role to play in the functioning of water-limited ecosystems.
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
|
11
|
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
|
12
|
Consolo G, Curró C, Grifó G, Valenti G. Oscillatory periodic pattern dynamics in hyperbolic reaction-advection-diffusion models. Phys Rev E 2022; 105:034206. [PMID: 35428106 DOI: 10.1103/physreve.105.034206] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2021] [Accepted: 01/24/2022] [Indexed: 11/07/2022]
Abstract
In this work we consider a quite general class of two-species hyperbolic reaction-advection-diffusion system with the main aim of elucidating the role played by inertial effects in the dynamics of oscillatory periodic patterns. To this aim, first, we use linear stability analysis techniques to deduce the conditions under which wave (or oscillatory Turing) instability takes place. Then, we apply multiple-scale weakly nonlinear analysis to determine the equation which rules the spatiotemporal evolution of pattern amplitude close to criticality. This investigation leads to a cubic complex Ginzburg-Landau (CCGL) equation which, owing to the functional dependence of the coefficients here involved on the inertial times, reveals some intriguing consequences. To show in detail the richness of such a scenario, we present, as an illustrative example, the pattern dynamics occurring in the hyperbolic generalization of the extended Klausmeier model. This is a simple two-species model used to describe the migration of vegetation stripes along the hillslope of semiarid environments. By means of a thorough comparison between analytical predictions and numerical simulations, we show that inertia, apart from enlarging the region of the parameter plane where wave instability occurs, may also modulate the key features of the coherent structures, solution of the CCGL equation. In particular, it is proven that inertial effects play a role, not only during transient regime from the spatially-homogeneous steady state toward the patterned state, but also in altering the amplitude, the wavelength, the angular frequency, and even the stability of the phase-winding solutions.
Collapse
Affiliation(s)
- Giancarlo Consolo
- Department of Mathematical, Computer, Physical and Earth Sciences, University of Messina (Italy) V.le F. Stagno D'Alcontres 31, I-98166 Messina, Italy
| | - Carmela Curró
- Department of Mathematical, Computer, Physical and Earth Sciences, University of Messina (Italy) V.le F. Stagno D'Alcontres 31, I-98166 Messina, Italy
| | - Gabriele Grifó
- Department of Mathematical, Computer, Physical and Earth Sciences, University of Messina (Italy) V.le F. Stagno D'Alcontres 31, I-98166 Messina, Italy
| | - Giovanna Valenti
- Department of Engineering, University of Messina (Italy) C.da di Dio, I-98166 Messina, Italy
| |
Collapse
|
13
|
A First Study of Urginea maritima Rings: A Case Study from Southern Jordan. LAND 2022. [DOI: 10.3390/land11020285] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
Vegetation rings are a common pattern in water-limited environments and mostly occur in clonal plants. This study presents, for the first time, rings of the geophyte species Urginea maritima. The rings, typically 40–90 cm in diameter, are abundant in the sandy environment of Little Petra and Wadi Rum, in the southern Jordanian drylands. Soil properties were studied in the rings’ center, periphery, and matrix. Soil-water volumetric content was significantly higher in the rings’ periphery than in the center and matrix. The soil organic carbon was highest in the periphery, intermediate in the center, and lowest in the matrix. At the same time, the soil texture, hydraulic conductivity, and gravimetric moisture content at the hygroscopic level were similar in the three microenvironments. According to the results, a possible ring formation mechanism is the soil-water uptake mechanism, which results in competition between the plants at the periphery and those in the center and is generally attributed to plants with large lateral root zones. Numerical simulations of a mathematical model implemented in this study support the soil-water uptake mechanism. A second possible mechanism is negative plant-soil feedback due to the accumulation of dead biomass and its consequent decomposition, with the resultant release of autotoxic compounds. It is possible that several mechanisms occur simultaneously and synergistically affect the formation of U. maritima rings.
Collapse
|
14
|
Stavi I, Yizhaq H, Osem Y, Argaman E. Positive impacts of livestock and wild ungulate routes on functioning of dryland ecosystems. Ecol Evol 2021; 11:13684-13691. [PMID: 34707810 PMCID: PMC8525128 DOI: 10.1002/ece3.8147] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2020] [Revised: 09/01/2021] [Accepted: 09/06/2021] [Indexed: 11/18/2022] Open
Abstract
Livestock grazing is often perceived as being detrimental to the quality and functioning of dryland ecosystems. For example, a study in a semiarid Kenyan savanna proposed that cattle form bare spaces throughout the landscape, which indicate ecosystem degradation. Other studies, conducted in north-eastern Spain, where climatic conditions range between semiarid and Mediterranean subhumid, reported that sheep and goat trails have increased the emergence of rill erosion processes. Sometimes, this negative perception is extended to include wild, large ungulate herbivores as well. Here, we challenge this perception by highlighting the generally nonadverse and even ameliorative impacts of moderate animal rate on geoecosystem functioning of hilly drylands. Specifically, trampling routes (also known as treading paths, livestock terracettes, cattle trails, migration tracks, cowtours, etc.) formed across hillslopes by grazing animals-being either domesticated livestock or native large herbivores-transform the original two-phase vegetation mosaic of shrubby patches and interpatch spaces into a three-phase mosaic. The animal routes increase the complexity of ecosystem, by strengthening the spatial redistribution of water and soil resources at the patch scale and decreasing hydrological connectivity at the hillslope scale. As a consequence, the animal routes improve functioning of hilly drylands and increase their resilience to long-term droughts and climatic change. Therefore, instead of viewing the animal routes as degraded spots, they should be perceived at a wider perspective that allows to properly understand their overall role in sustaining dryland geoecosystems.
Collapse
Affiliation(s)
- Ilan Stavi
- Dead Sea and Arava Science CenterYotvataIsrael
- Eilat CampusBen‐Gurion University of the NegevEilatIsrael
| | - Hezi Yizhaq
- Department of Solar Energy and Environmental PhysicsBlaustein Institutes for Desert ResearchBen‐Gurion University of the NegevEilatIsrael
| | - Yagil Osem
- Department of Natural ResourcesInstitute of Plant SciencesVolcani CenterRishon LeZionIsrael
| | - Eli Argaman
- Soil Erosion Research StationMinistry of Agriculture & Rural DevelopmentBet DaganIsrael
| |
Collapse
|
15
|
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
|
16
|
Bera BK, Tzuk O, Bennett JJR, Meron E. Linking spatial self-organization to community assembly and biodiversity. eLife 2021; 10:e73819. [PMID: 34570698 PMCID: PMC8497052 DOI: 10.7554/elife.73819] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2021] [Accepted: 09/19/2021] [Indexed: 11/29/2022] Open
Abstract
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.
Collapse
Affiliation(s)
- Bidesh K Bera
- Department of Solar Energy and Environmental Physics, BIDR, Ben-Gurion University of the NegevSede Boqer CampusIsrael
| | - Omer Tzuk
- Physics Department, Ben-Gurion University of the NegevBeer ShevaIsrael
| | - Jamie JR Bennett
- Department of Solar Energy and Environmental Physics, BIDR, Ben-Gurion University of the NegevSede Boqer CampusIsrael
| | - Ehud Meron
- Department of Solar Energy and Environmental Physics, BIDR, Ben-Gurion University of the NegevSede Boqer CampusIsrael
- Physics Department, Ben-Gurion University of the NegevBeer ShevaIsrael
| |
Collapse
|
17
|
Geodiversity impacts plant community structure in a semi-arid region. Sci Rep 2021; 11:15259. [PMID: 34315939 PMCID: PMC8316420 DOI: 10.1038/s41598-021-94698-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2021] [Accepted: 07/14/2021] [Indexed: 02/07/2023] Open
Abstract
Geodiversity refers to the variety of geological and physical elements as well as to geomorphological processes of the earth surface. Heterogeneity of the physical environment has an impact on plant diversity. In recent years, the relations between geodiversity and biodiversity has gained attention in conservation biology, especially in the context of climate change. In this study, we assessed the spatial and temporal change in plant's community structure in a semi-arid region, Sayeret Shaked Long Term Ecosystem Research (LTER) station, Israel. Vegetation surveys were conducted on different hillslopes, either with or without rock covers in order to study the spatial trends of hillslope geodiversity. The surveys were conducted for two consecutive years (2016 and 2017), of which the second year was drier and hotter and therefore permitted to investigate the temporal change of plant's community structure. The results of the spatial trends show that (1) geodiversity increases vegetation biodiversity and promotes perennial plants and those of the temporal change show that (2) the positive effect of geodiversity on plants' community structure and species richness is greater in the drier year than that in a wetter year. The main insight is that in these drylands, hillslopes with higher geodiversity appear to buffer the effect of drier years, and supported a more diverse plant community than lower geodiversity hillslopes.
Collapse
|
18
|
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
|
19
|
Garlaschi S, Gupta D, Maritan A, Azaele S. Ginzburg-Landau amplitude equation for nonlinear nonlocal models. Phys Rev E 2021; 103:022210. [PMID: 33736032 DOI: 10.1103/physreve.103.022210] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2020] [Accepted: 01/21/2021] [Indexed: 11/07/2022]
Abstract
Regular spatial structures emerge in a wide range of different dynamics characterized by local and/or nonlocal coupling terms. In several research fields this has spurred the study of many models, which can explain pattern formation. The modulations of patterns, occurring on long spatial and temporal scales, cannot be captured by linear approximation analysis. Here, we show that, starting from a general model with long range couplings displaying patterns, the spatiotemporal evolution of large-scale modulations at the onset of instability is ruled by the well-known Ginzburg-Landau equation, independently of the details of the dynamics. Hence, we demonstrate the validity of such equation in the description of the behavior of a wide class of systems. We introduce a mathematical framework that is also able to retrieve the analytical expressions of the coefficients appearing in the Ginzburg-Landau equation as functions of the model parameters. Such framework can include higher order nonlocal interactions and has much larger applicability than the model considered here, possibly including pattern formation in models with very different physical features.
Collapse
Affiliation(s)
- Stefano Garlaschi
- Dipartimento di Fisica e Astronomia "Galileo Galilei", Università degli Studi di Padova, via Marzolo 8, 35131 Padova, Italy
| | - Deepak Gupta
- Dipartimento di Fisica e Astronomia "Galileo Galilei", Università degli Studi di Padova, via Marzolo 8, 35131 Padova, Italy
| | - Amos Maritan
- Dipartimento di Fisica e Astronomia "Galileo Galilei", Università degli Studi di Padova, via Marzolo 8, 35131 Padova, Italy
| | - Sandro Azaele
- Dipartimento di Fisica e Astronomia "Galileo Galilei", Università degli Studi di Padova, via Marzolo 8, 35131 Padova, Italy
| |
Collapse
|
20
|
Eigentler L, Sherratt JA. An integrodifference model for vegetation patterns in semi-arid environments with seasonality. J Math Biol 2020; 81:875-904. [PMID: 32888058 PMCID: PMC7519009 DOI: 10.1007/s00285-020-01530-w] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2019] [Revised: 03/04/2020] [Indexed: 11/26/2022]
Abstract
Vegetation patterns are a characteristic feature of semi-deserts occurring on all continents except Antarctica. In some semi-arid regions, the climate is characterised by seasonality, which yields a synchronisation of seed dispersal with the dry season or the beginning of the wet season. We reformulate the Klausmeier model, a reaction–advection–diffusion system that describes the plant–water dynamics in semi-arid environments, as an integrodifference model to account for the temporal separation of plant growth processes during the wet season and seed dispersal processes during the dry season. The model further accounts for nonlocal processes involved in the dispersal of seeds. Our analysis focusses on the onset of spatial patterns. The Klausmeier partial differential equations (PDE) model is linked to the integrodifference model in an appropriate limit, which yields a control parameter for the temporal separation of seed dispersal events. We find that the conditions for pattern onset in the integrodifference model are equivalent to those for the continuous PDE model and hence independent of the time between seed dispersal events. We thus conclude that in the context of seed dispersal, a PDE model provides a sufficiently accurate description, even if the environment is seasonal. This emphasises the validity of results that have previously been obtained for the PDE model. Further, we numerically investigate the effects of changes to seed dispersal behaviour on the onset of patterns. We find that long-range seed dispersal inhibits the formation of spatial patterns and that the seed dispersal kernel’s decay at infinity is a significant regulator of patterning.
Collapse
Affiliation(s)
- Lukas Eigentler
- Department of Mathematics, Maxwell Institute for Mathematical Sciences, Heriot Watt University, Edinburgh, EH14 4AS UK
- Division of Molecular Microbiology, School of Life Sciences, University of Dundee, Dundee, DD1 5EH UK
- Division of Mathematics, School of Science and Engineering, University of Dundee, Dundee, DD1 4HN UK
| | - Jonathan A. Sherratt
- Department of Mathematics, Maxwell Institute for Mathematical Sciences, Heriot Watt University, Edinburgh, EH14 4AS UK
| |
Collapse
|
21
|
Messaoudi M, Clerc MG, Berríos-Caro E, Pinto-Ramos D, Khaffou M, Makhoute A, Tlidi M. Patchy landscapes in arid environments: Nonlinear analysis of the interaction-redistribution model. CHAOS (WOODBURY, N.Y.) 2020; 30:093136. [PMID: 33003924 DOI: 10.1063/5.0011010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2020] [Accepted: 08/24/2020] [Indexed: 06/11/2023]
Abstract
We consider a generic interaction-redistribution model of vegetation dynamics to investigate the formation of patchy vegetation in semi-arid and arid landscapes. First, we perform a weakly nonlinear analysis in the neighborhood of the symmetry-breaking instability. Following this analysis, we construct the bifurcation diagram of the biomass density. The weakly nonlinear analysis allows us to establish the condition under which the transition from super- to subcritical symmetry-breaking instability takes place. Second, we generate a random distribution of localized patches of vegetation numerically. This behavior occurs in regimes where a bare state coexists with a uniform biomass density. Field observations allow to estimate the total biomass density and the range of facilitative and competitive interactions.
Collapse
Affiliation(s)
- M Messaoudi
- Faculté des Sciences, Université Libre de Bruxelles (U.L.B), CP 231, Campus Plaine, B-1050 Bruxelles, Belgium
| | - M G Clerc
- Departamento de Física and Millennium Institute for Research in Optics, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile
| | - E Berríos-Caro
- Departamento de Física and Millennium Institute for Research in Optics, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile
| | - D Pinto-Ramos
- Departamento de Física and Millennium Institute for Research in Optics, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile
| | - M Khaffou
- Faculté des Sciences, Université Moulay Ismail, Dynamique des Systémes Complexes et Simulation Numérique, B.P. 11201, Zitoune, Meknès, Morocco
| | - A Makhoute
- Faculté des Sciences, Université Libre de Bruxelles (U.L.B), CP 231, Campus Plaine, B-1050 Bruxelles, Belgium
| | - M Tlidi
- Faculté des Sciences, Université Libre de Bruxelles (U.L.B), CP 231, Campus Plaine, B-1050 Bruxelles, Belgium
| |
Collapse
|
22
|
Tzuk O, Uecker H, Meron E. The role of spatial self-organization in the design of agroforestry systems. PLoS One 2020; 15:e0236325. [PMID: 32692773 PMCID: PMC7373287 DOI: 10.1371/journal.pone.0236325] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2019] [Accepted: 07/03/2020] [Indexed: 11/19/2022] Open
Abstract
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.
Collapse
Affiliation(s)
- Omer Tzuk
- Department of Physics, Ben-Gurion University of the Negev, Beer Sheva, Israel
- * E-mail:
| | - Hannes Uecker
- Institut für Mathematik, Universität Oldenburg, Oldenburg, Germany
| | - Ehud Meron
- Department of Physics, Ben-Gurion University of the Negev, Beer Sheva, Israel
- Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Beersheba, Israel
| |
Collapse
|
23
|
Parra-Rivas P, Fernandez-Oto C. Formation of localized states in dryland vegetation: Bifurcation structure and stability. Phys Rev E 2020; 101:052214. [PMID: 32575306 DOI: 10.1103/physreve.101.052214] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2019] [Accepted: 04/27/2020] [Indexed: 11/07/2022]
Abstract
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.
Collapse
Affiliation(s)
- P Parra-Rivas
- Service OPERA-photonics, Universit libre de Bruxelles, 50 Avenue F. D. Roosevelt, CP 194/5, B-1050 Bruxelles, Belgium.,Laboratory of Dynamics in Biological Systems, Department of Cellular and Molecular Medicine, University of Leuven, B-3000 Leuven, Belgium
| | - C Fernandez-Oto
- Complex Systems Group, Facultad de Ingenieria y Ciencias Aplicadas, Universidad de los Andes, Av. Mon. Alvaro del Portillo 12455 Santiago, Chile
| |
Collapse
|
24
|
Liautaud K, Barbier M, Loreau M. Ecotone formation through ecological niche construction: the role of biodiversity and species interactions. ECOGRAPHY 2020; 43:714-723. [PMID: 33304029 PMCID: PMC7116457 DOI: 10.1111/ecog.04902] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Rapid changes in species composition, also known as ecotones, can result from various causes including rapid changes in environmental conditions, or physiological thresholds. The possibility that ecotones arise from ecological niche construction by ecosystem engineers has received little attention. In this study, we investigate how the diversity of ecosystem engineers, and their interactions, can give rise to ecotones. We build a spatially explicit dynamical model that couples a multispecies community and its abiotic environment. We use numerical simulations and analytical techniques to determine the biotic and abiotic conditions under which ecotone emergence is expected to occur, and the role of biodiversity therein. We show that the diversity of ecosystem engineers can lead to indirect interactions through the modification of their shared environment. These interactions, which can be either competitive or mutualistic, can lead to the emergence of discrete communities in space, separated by sharp ecotones where a high species turnover is observed. Considering biodiversity is thus critical when studying the influence of species-environment interactions on the emergence of ecotones. This is especially true for the wide range of species that have small to moderate effects on their environment. Our work highlights new mechanisms by which biodiversity loss could cause significant changes in spatial community patterns in changing environments.
Collapse
Affiliation(s)
- Kevin Liautaud
- Centre for Biodiversity Theory and Modelling, Theoretical and Experimental Ecology Station, UMR 5321, CNRS and Paul Sabatier Univ., Moulis, France
| | - Matthieu Barbier
- Centre for Biodiversity Theory and Modelling, Theoretical and Experimental Ecology Station, UMR 5321, CNRS and Paul Sabatier Univ., Moulis, France
| | - Michel Loreau
- Centre for Biodiversity Theory and Modelling, Theoretical and Experimental Ecology Station, UMR 5321, CNRS and Paul Sabatier Univ., Moulis, France
| |
Collapse
|
25
|
Demir E, Yaman YI, Basaran M, Kocabas A. Dynamics of pattern formation and emergence of swarming in Caenorhabditis elegans. eLife 2020; 9:52781. [PMID: 32250243 PMCID: PMC7202895 DOI: 10.7554/elife.52781] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2019] [Accepted: 04/05/2020] [Indexed: 01/10/2023] Open
Abstract
Many animals collectively form complex patterns to tackle environmental difficulties. Several biological and physical factors, such as animal motility, population densities, and chemical cues, play significant roles in this process. However, very little is known about how sensory information interplays with these factors and controls the dynamics of pattern formation. Here, we study the direct relation between oxygen sensing, pattern formation, and emergence of swarming in active Caenorhabditis elegans aggregates. We find that when thousands of animals gather on food, bacteria-mediated decrease in oxygen level slows down the animals and triggers motility-induced phase separation. Three coupled factors—bacterial accumulation, aerotaxis, and population density—act together and control the entire dynamics. Furthermore, we find that biofilm-forming bacterial lawns including Bacillus subtilis and Pseudomonas aeruginosa strongly alter the collective dynamics due to the limited diffusibility of bacteria. Additionally, our theoretical model captures behavioral differences resulting from genetic variations and oxygen sensitivity.
Collapse
Affiliation(s)
- Esin Demir
- Bio-Medical Sciences and Engineering Program, Koç University, Sarıyer, Istanbul, Turkey
| | - Y Ilker Yaman
- Department of Physics, Koç University, Sarıyer, Istanbul, Turkey
| | - Mustafa Basaran
- Bio-Medical Sciences and Engineering Program, Koç University, Sarıyer, Istanbul, Turkey
| | - Askin Kocabas
- Bio-Medical Sciences and Engineering Program, Koç University, Sarıyer, Istanbul, Turkey.,Department of Physics, Koç University, Sarıyer, Istanbul, Turkey.,Koç University Surface Science and Technology Center, Koç University, Sarıyer, Istanbul, Turkey.,Koç University Research Center for Translational Medicine, Koç University, Sarıyer, Istanbul, Turkey
| |
Collapse
|
26
|
Eigentler L. Intraspecific competition in models for vegetation patterns: Decrease in resilience to aridity and facilitation of species coexistence. ECOLOGICAL COMPLEXITY 2020. [DOI: 10.1016/j.ecocom.2020.100835] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
|
27
|
Bastiaansen R, Doelman A, Eppinga MB, Rietkerk M. The effect of climate change on the resilience of ecosystems with adaptive spatial pattern formation. Ecol Lett 2020; 23:414-429. [PMID: 31912954 PMCID: PMC7028049 DOI: 10.1111/ele.13449] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2019] [Revised: 08/12/2019] [Accepted: 11/29/2019] [Indexed: 12/01/2022]
Abstract
In a rapidly changing world, quantifying ecosystem resilience is an important challenge. Historically, resilience has been defined via models that do not take spatial effects into account. These systems can only adapt via uniform adjustments. In reality, however, the response is not necessarily uniform, and can lead to the formation of (self-organised) spatial patterns - typically localised vegetation patches. Classical measures of resilience cannot capture the emerging dynamics in spatially self-organised systems, including transitions between patterned states that have limited impact on ecosystem structure and productivity. We present a framework of interlinked phase portraits that appropriately quantifies the resilience of patterned states, which depends on the number of patches, the distances between them and environmental conditions. We show how classical resilience concepts fail to distinguish between small and large pattern transitions, and find that the variance in interpatch distances provides a suitable indicator for the type of imminent transition. Subsequently, we describe the dependency of ecosystem degradation based on the rate of climatic change: slow change leads to sporadic, large transitions, whereas fast change causes a rapid sequence of smaller transitions. Finally, we discuss how pre-emptive removal of patches can minimise productivity losses during pattern transitions, constituting a viable conservation strategy.
Collapse
Affiliation(s)
| | - Arjen Doelman
- Mathematical InstituteLeiden University2300 RALeidenThe Netherlands
| | | | - Max Rietkerk
- Department of Environmental SciencesCopernicus InstituteUtrecht University3508 TCUtrechtThe Netherlands
| |
Collapse
|
28
|
Conde-Pueyo N, Vidiella B, Sardanyés J, Berdugo M, Maestre FT, de Lorenzo V, Solé R. Synthetic Biology for Terraformation Lessons from Mars, Earth, and the Microbiome. Life (Basel) 2020; 10:E14. [PMID: 32050455 PMCID: PMC7175242 DOI: 10.3390/life10020014] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2019] [Revised: 01/27/2020] [Accepted: 02/03/2020] [Indexed: 12/17/2022] Open
Abstract
What is the potential for synthetic biology as a way of engineering, on a large scale, complex ecosystems? Can it be used to change endangered ecological communities and rescue them to prevent their collapse? What are the best strategies for such ecological engineering paths to succeed? Is it possible to create stable, diverse synthetic ecosystems capable of persisting in closed environments? Can synthetic communities be created to thrive on planets different from ours? These and other questions pervade major future developments within synthetic biology. The goal of engineering ecosystems is plagued with all kinds of technological, scientific and ethic problems. In this paper, we consider the requirements for terraformation, i.e., for changing a given environment to make it hospitable to some given class of life forms. Although the standard use of this term involved strategies for planetary terraformation, it has been recently suggested that this approach could be applied to a very different context: ecological communities within our own planet. As discussed here, this includes multiple scales, from the gut microbiome to the entire biosphere.
Collapse
Affiliation(s)
- Nuria Conde-Pueyo
- ICREA-Complex Systems Lab, Universitat Pompeu Fabra, Plaça de la Mercè, 10, 08002 Barcelona, Spain; (B.V.); (M.B.)
- Institut de Biologia Evolutiva, UPF-CSIC, 08003 Barcelona, Spain
| | - Blai Vidiella
- ICREA-Complex Systems Lab, Universitat Pompeu Fabra, Plaça de la Mercè, 10, 08002 Barcelona, Spain; (B.V.); (M.B.)
- Institut de Biologia Evolutiva, UPF-CSIC, 08003 Barcelona, Spain
| | - Josep Sardanyés
- Centre de Recerca Matemàtica, Campus UAB Edifici C, 08193 Bellaterra, Barcelona, Spain;
- Barcelona Graduate School of Mathematics (BGSMath), Campus UAB Edifici C, 08193 Bellaterra, Barcelona, Spain
| | - Miguel Berdugo
- ICREA-Complex Systems Lab, Universitat Pompeu Fabra, Plaça de la Mercè, 10, 08002 Barcelona, Spain; (B.V.); (M.B.)
- Institut de Biologia Evolutiva, UPF-CSIC, 08003 Barcelona, Spain
- Departamento de Ecología and Instituto Multidisciplinar para el Estudio del Medio “Ramon Margalef”, Universidad de Alicante, Carr. de San Vicente del Raspeig, s/n, 03690 San Vicente del Raspeig, Alicante, Spain;
| | - Fernando T. Maestre
- Departamento de Ecología and Instituto Multidisciplinar para el Estudio del Medio “Ramon Margalef”, Universidad de Alicante, Carr. de San Vicente del Raspeig, s/n, 03690 San Vicente del Raspeig, Alicante, Spain;
| | - Victor de Lorenzo
- Systems and Synthetic Biology Program, Centro Nacional de Biotecnología (CNB-CSIC), Campus de Cantoblanco, 28049 Madrid, Spain;
| | - Ricard Solé
- ICREA-Complex Systems Lab, Universitat Pompeu Fabra, Plaça de la Mercè, 10, 08002 Barcelona, Spain; (B.V.); (M.B.)
- Institut de Biologia Evolutiva, UPF-CSIC, 08003 Barcelona, Spain
- Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA
| |
Collapse
|
29
|
Sun J, Li X, Chen N, Wang Y, Song G. Regular pattern formation regulates population dynamics: Logistic growth in cellular automata. Ecol Modell 2020. [DOI: 10.1016/j.ecolmodel.2019.108878] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
30
|
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]
|
31
|
Long-distance seed dispersal affects the resilience of banded vegetation patterns in semi-deserts. J Theor Biol 2019; 481:151-161. [DOI: 10.1016/j.jtbi.2018.10.002] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2018] [Revised: 09/27/2018] [Accepted: 10/01/2018] [Indexed: 11/18/2022]
|
32
|
Dor‐Haim S, Orenstein DE, Shachak M. Web of interactions among diversity approaches to identify ecosystem essential variables: Negev Highlands case study. Ecosphere 2019. [DOI: 10.1002/ecs2.2906] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022] Open
Affiliation(s)
- Shayli Dor‐Haim
- The Jacob Blaustein Institutes for Desert Research Ben‐Gurion University of the Negev Beer‐Sheva Israel
- Dead Sea and Arava Science Center Masada Israel
| | - Daniel E. Orenstein
- Faculty of Architecture and Town Planning Technion – Israel Institute of Technology Haifa Israel
| | - Moshe Shachak
- The Jacob Blaustein Institutes for Desert Research Ben‐Gurion University of the Negev Beer‐Sheva Israel
| |
Collapse
|
33
|
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
|
34
|
Eigentler L, Sherratt JA. Metastability as a Coexistence Mechanism in a Model for Dryland Vegetation Patterns. Bull Math Biol 2019; 81:2290-2322. [PMID: 31012031 DOI: 10.1007/s11538-019-00606-z] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2018] [Accepted: 04/11/2019] [Indexed: 11/25/2022]
Abstract
Vegetation patterns are a ubiquitous feature of water-deprived ecosystems. Despite the competition for the same limiting resource, coexistence of several plant species is commonly observed. We propose a two-species reaction-diffusion model based on the single-species Klausmeier model, to analytically investigate the existence of states in which both species coexist. Ecologically, the study finds that coexistence is supported if there is a small difference in the plant species' average fitness, measured by the ratio of a species' capabilities to convert water into new biomass to its mortality rate. Mathematically, coexistence is not a stable solution of the system, but both spatially uniform and patterned coexistence states occur as metastable states. In this context, a metastable solution in which both species coexist corresponds to a long transient (exceeding [Formula: see text] years in dimensional parameters) to a stable one-species state. This behaviour is characterised by the small size of a positive eigenvalue which has the same order of magnitude as the average fitness difference between the two species. Two mechanisms causing the occurrence of metastable solutions are established: a spatially uniform unstable equilibrium and a stable one-species pattern which is unstable to the introduction of a competitor. We further discuss effects of asymmetric interspecific competition (e.g. shading) on the metastability property.
Collapse
Affiliation(s)
- Lukas Eigentler
- Department of Mathematics, Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK.
| | - Jonathan A Sherratt
- Department of Mathematics, Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK
| |
Collapse
|
35
|
Fernandez-Oto C, Tzuk O, Meron E. Front Instabilities Can Reverse Desertification. PHYSICAL REVIEW LETTERS 2019; 122:048101. [PMID: 30768298 DOI: 10.1103/physrevlett.122.048101] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2018] [Revised: 11/26/2018] [Indexed: 06/09/2023]
Abstract
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.
Collapse
Affiliation(s)
- Cristian Fernandez-Oto
- Department of Solar Energy and Environmental Physics, BIDR, Ben-Gurion University of the Negev, Sede Boqer Campus, 84990 Israel
- Complex Systems Group, Facultad de Ingenieria y Ciencias Aplicadas, Universidad de los Andes, Av. Mon. Alvaro del Portillo 12.455 Santiago, Chile
| | - Omer Tzuk
- Physics Department, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
| | - Ehud Meron
- Department of Solar Energy and Environmental Physics, BIDR, Ben-Gurion University of the Negev, Sede Boqer Campus, 84990 Israel
- Physics Department, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
| |
Collapse
|
36
|
Tzuk O, Ujjwal SR, Fernandez-Oto C, Seifan M, Meron E. Interplay between exogenous and endogenous factors in seasonal vegetation oscillations. Sci Rep 2019; 9:354. [PMID: 30674956 PMCID: PMC6344492 DOI: 10.1038/s41598-018-36898-9] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2018] [Accepted: 11/26/2018] [Indexed: 11/09/2022] Open
Abstract
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.
Collapse
Affiliation(s)
- Omer Tzuk
- Department of Physics, Ben-Gurion University of the Negev, Beer Sheva, 84105, Israel.
| | - Sangeeta R Ujjwal
- Department of Solar Energy and Environmental Physics, SIDEER, BIDR, Ben-Gurion University of the Negev, Sede Boqer Campus, Beer Sheva, 84990, Israel
| | - Cristian Fernandez-Oto
- Department of Solar Energy and Environmental Physics, SIDEER, BIDR, Ben-Gurion University of the Negev, Sede Boqer Campus, Beer Sheva, 84990, Israel.,Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Av. Mon. Alvaro del Portillo, 12.455, Santiago, Chile
| | - Merav Seifan
- Mitrani Department of Desert Ecology, SIDEER, BIDR, Ben-Gurion University of the Negev, Sede Boqer Campus, Beer Sheva, 84990, Israel
| | - Ehud Meron
- Department of Physics, Ben-Gurion University of the Negev, Beer Sheva, 84105, Israel.,Department of Solar Energy and Environmental Physics, SIDEER, BIDR, Ben-Gurion University of the Negev, Sede Boqer Campus, Beer Sheva, 84990, Israel
| |
Collapse
|
37
|
Siero E, Siteur K, Doelman A, Koppel JVD, Rietkerk M, Eppinga MB. Grazing Away the Resilience of Patterned Ecosystems. Am Nat 2019; 193:472-480. [PMID: 30794443 DOI: 10.1086/701669] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Abstract
Ecosystems' responses to changing environmental conditions can be modulated by spatial self-organization. A prominent example of this can be found in drylands, where formation of vegetation patterns attenuates the magnitude of degradation events in response to decreasing rainfall. In model studies, the pattern wavelength responds to changing conditions, which is reflected by a rather gradual decline in biomass in response to decreasing rainfall. Although these models are spatially explicit, they have adopted a mean-field approach to grazing. By taking into account spatial variability when modeling grazing, we find that (over)grazing can lead to a dramatic shift in biomass, so that degradation occurs at rainfall rates that would otherwise still maintain a relatively productive ecosystem. Moreover, grazing increases the resilience of degraded ecosystem states. Consequently, restoration of degraded ecosystems could benefit from the introduction of temporary small-scale exclosures to escape from the basin of attraction of degraded states.
Collapse
|
38
|
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]
|
39
|
Tlidi M, Clerc MG, Escaff D, Couteron P, Messaoudi M, Khaffou M, Makhoute A. Observation and modelling of vegetation spirals and arcs in isotropic environmental conditions: dissipative structures in arid landscapes. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2018; 376:rsta.2018.0026. [PMID: 30420548 PMCID: PMC6232604 DOI: 10.1098/rsta.2018.0026] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 06/09/2018] [Indexed: 06/09/2023]
Abstract
We report for the first time on the formation of spirals like vegetation patterns in isotropic and uniform environmental conditions. The vegetation spirals are not waves and they do not rotate. They belong to the class of dissipative structures found out of equilibrium. Isolated or interacting spirals and arcs observed in South America (Bolivia) and North Africa (Morocco) are interpreted as a result of curvature instability that affects the circular shape of localized patches. The biomass exhibits a dynamical behaviour with arcs that transform into spirals. Interpretation of observations and of the predictions provided by the theory is illustrated by recent measurements of peculiar plant morphology (the alfa plant, or Stipa tenacissima L.) originated from northwestern Africa and the southern part of the Iberian Peninsula.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)
- M Tlidi
- Département de Physique, Faculté des Sciences, Université Libre de Bruxelles (U.L.B.), CP. 231, Campus Plaine, Bruxelles, 1050 Belgium
| | - M G Clerc
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile
| | - D Escaff
- Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Monseñor Alvaro del Portillo 12455, Las Condes, Santiago, Chile
| | - P Couteron
- AMAP, IRD, CIRADm CNRS INRA, University Montpellier, Montpellier, France
| | - M Messaoudi
- Faculté des Sciences, Université Moulay Ismail, Dynamique des Systemes Complexes et Simulation Numérique, B.P. 11201, Zitoune, Meknès, Morocco
| | - M Khaffou
- Faculté des Sciences, Université Moulay Ismail, Dynamique des Systemes Complexes et Simulation Numérique, B.P. 11201, Zitoune, Meknès, Morocco
| | - A Makhoute
- Faculté des Sciences, Université Moulay Ismail, Dynamique des Systemes Complexes et Simulation Numérique, B.P. 11201, Zitoune, Meknès, Morocco
| |
Collapse
|
40
|
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
|
41
|
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
|
42
|
Gandhi P, Werner L, Iams S, Gowda K, Silber M. A topographic mechanism for arcing of dryland vegetation bands. J R Soc Interface 2018; 15:rsif.2018.0508. [PMID: 30305423 DOI: 10.1098/rsif.2018.0508] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2018] [Accepted: 09/12/2018] [Indexed: 11/12/2022] Open
Abstract
Banded patterns consisting of alternating bare soil and dense vegetation have been observed in water-limited ecosystems across the globe, often appearing along gently sloped terrain with the stripes aligned transverse to the elevation gradient. In many cases, these vegetation bands are arced, with field observations suggesting a link between the orientation of arcing relative to the grade and the curvature of the underlying terrain. We modify the water transport in the Klausmeier model of water-biomass interactions, originally posed on a uniform hillslope, to qualitatively capture the influence of terrain curvature on the vegetation patterns. Numerical simulations of this modified model indicate that the vegetation bands arc convex-downslope when growing on top of a ridge, and convex-upslope when growing in a valley. This behaviour is consistent with observations from remote sensing data that we present here. Model simulations show further that whether bands grow on ridges, valleys or both depends on the precipitation level. A survey of three banded vegetation sites, each with a different aridity level, indicates qualitatively similar behaviour.
Collapse
Affiliation(s)
- Punit Gandhi
- Mathematical Biosciences Institute, Ohio State University, Columbus, OH 43210, USA
| | - Lucien Werner
- Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA 91125, USA
| | - Sarah Iams
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
| | - Karna Gowda
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| | - Mary Silber
- Committee on Computational and Applied Mathematics and Department of Statistics,University of Chicago, Chicago, IL 60637, USA
| |
Collapse
|
43
|
Foundation species enhance food web complexity through non-trophic facilitation. PLoS One 2018; 13:e0199152. [PMID: 30169517 PMCID: PMC6118353 DOI: 10.1371/journal.pone.0199152] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2018] [Accepted: 06/03/2018] [Indexed: 11/24/2022] Open
Abstract
Food webs are an integral part of every ecosystem on the planet, yet understanding the mechanisms shaping these complex networks remains a major challenge. Recently, several studies suggested that non-trophic species interactions such as habitat modification and mutualisms can be important determinants of food web structure. However, it remains unclear whether these findings generalize across ecosystems, and whether non-trophic interactions affect food webs randomly, or affect specific trophic levels or functional groups. Here, we combine analyses of 58 food webs from seven terrestrial, freshwater and coastal systems to test (1) the general hypothesis that non-trophic facilitation by habitat-forming foundation species enhances food web complexity, and (2) whether these enhancements have either random or targeted effects on particular trophic levels, functional groups, and linkages throughout the food web. Our empirical results demonstrate that foundation species consistently enhance food web complexity in all seven ecosystems. Further analyses reveal that 15 out of 19 food web properties can be well-approximated by assuming that foundation species randomly facilitate species throughout the trophic network. However, basal species are less strongly, and carnivores are more strongly facilitated in foundation species' food webs than predicted based on random facilitation, resulting in a higher mean trophic level and a longer average chain length. Overall, we conclude that foundation species strongly enhance food web complexity through non-trophic facilitation of species across the entire trophic network. We therefore suggest that the structure and stability of food webs often depends critically on non-trophic facilitation by foundation species.
Collapse
|
44
|
Parametric transitions between bare and vegetated states in water-driven patterns. Proc Natl Acad Sci U S A 2018; 115:8125-8130. [PMID: 30038019 DOI: 10.1073/pnas.1721765115] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Conditions for vegetation spreading and pattern formation are mathematically framed through an analysis encompassing three fundamental processes: flow stochasticity, vegetation dynamics, and sediment transport. Flow unsteadiness is included through Poisson stochastic processes whereby vegetation dynamics appears as a secondary instability, which is addressed by Floquet theory. Results show that the model captures the physical conditions heralding the transition between bare and vegetated fluvial states where the nonlinear formation and growth of finite alternate bars are accounted for by Center Manifold Projection. This paves the way to understand changes in biogeomorphological styles induced by man in the Anthropocene and of natural origin since the Paleozoic (Devonian plant hypothesis).
Collapse
|
45
|
Solé RV, Montañez R, Duran-Nebreda S, Rodriguez-Amor D, Vidiella B, Sardanyés J. Population dynamics of synthetic terraformation motifs. ROYAL SOCIETY OPEN SCIENCE 2018; 5:180121. [PMID: 30109068 PMCID: PMC6083676 DOI: 10.1098/rsos.180121] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2018] [Accepted: 05/22/2018] [Indexed: 05/23/2023]
Abstract
Ecosystems are complex systems, currently experiencing several threats associated with global warming, intensive exploitation and human-driven habitat degradation. Because of a general presence of multiple stable states, including states involving population extinction, and due to the intrinsic nonlinearities associated with feedback loops, collapse in ecosystems could occur in a catastrophic manner. It has been recently suggested that a potential path to prevent or modify the outcome of these transitions would involve designing synthetic organisms and synthetic ecological interactions that could push these endangered systems out of the critical boundaries. In this paper, we investigate the dynamics of the simplest mathematical models associated with four classes of ecological engineering designs, named Terraformation motifs (TMs). These TMs put in a nutshell different ecological strategies. In this context, some fundamental types of bifurcations pervade the systems' dynamics. Mutualistic interactions can enhance persistence of the systems by means of saddle-node bifurcations. The models without cooperative interactions show that ecosystems achieve restoration through transcritical bifurcations. Thus, our analysis of the models allows us to define the stability conditions and parameter domains where these TMs must work.
Collapse
Affiliation(s)
- Ricard V. Solé
- ICREA-Complex Systems Lab, Universitat Pompeu Fabra, Dr Aiguader 88, 08003 Barcelona, Spain
- Institut de Biologia Evolitiva, CSIC-Universitat Pompeu Fabra, Passeig Marítim 37, 08003 Barcelona, Spain
- Santa Fe Institute 1399 Hyde Park Road, Santa Fe, NM 87501, USA
| | - Raúl Montañez
- ICREA-Complex Systems Lab, Universitat Pompeu Fabra, Dr Aiguader 88, 08003 Barcelona, Spain
- Institut de Biologia Evolitiva, CSIC-Universitat Pompeu Fabra, Passeig Marítim 37, 08003 Barcelona, Spain
| | - Salva Duran-Nebreda
- ICREA-Complex Systems Lab, Universitat Pompeu Fabra, Dr Aiguader 88, 08003 Barcelona, Spain
- Institut de Biologia Evolitiva, CSIC-Universitat Pompeu Fabra, Passeig Marítim 37, 08003 Barcelona, Spain
| | - Daniel Rodriguez-Amor
- ICREA-Complex Systems Lab, Universitat Pompeu Fabra, Dr Aiguader 88, 08003 Barcelona, Spain
- Institut de Biologia Evolitiva, CSIC-Universitat Pompeu Fabra, Passeig Marítim 37, 08003 Barcelona, Spain
- Physics of Living Systems, Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Blai Vidiella
- ICREA-Complex Systems Lab, Universitat Pompeu Fabra, Dr Aiguader 88, 08003 Barcelona, Spain
- Institut de Biologia Evolitiva, CSIC-Universitat Pompeu Fabra, Passeig Marítim 37, 08003 Barcelona, Spain
| | - Josep Sardanyés
- ICREA-Complex Systems Lab, Universitat Pompeu Fabra, Dr Aiguader 88, 08003 Barcelona, Spain
- Institut de Biologia Evolitiva, CSIC-Universitat Pompeu Fabra, Passeig Marítim 37, 08003 Barcelona, Spain
- Centre de Recerca Matemàtica, Edifici C, Campus de Bellaterra, 08193, Bellaterra, Barcelona, Spain
- Barcelona Graduate School of Mathematics (BGSMath), Edifici C, Campus de Bellaterra, 08193, Bellaterra, Barcelona, Spain
| |
Collapse
|
46
|
Analysis of a model for banded vegetation patterns in semi-arid environments with nonlocal dispersal. J Math Biol 2018; 77:739-763. [PMID: 29666921 DOI: 10.1007/s00285-018-1233-y] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2017] [Revised: 01/14/2018] [Indexed: 10/17/2022]
Abstract
Vegetation patterns are a characteristic feature of semi-arid regions. On hillsides these patterns occur as stripes running parallel to the contours. The Klausmeier model, a coupled reaction-advection-diffusion system, is a deliberately simple model describing the phenomenon. In this paper, we replace the diffusion term describing plant dispersal by a more realistic nonlocal convolution integral to account for the possibility of long-range dispersal of seeds. Our analysis focuses on the rainfall level at which there is a transition between uniform vegetation and pattern formation. We obtain results, valid to leading order in the large parameter comparing the rate of water flow downhill to the rate of plant dispersal, for a negative exponential dispersal kernel. Our results indicate that both a wider dispersal of seeds and an increase in dispersal rate inhibit the formation of patterns. Assuming an evolutionary trade-off between these two quantities, mathematically motivated by the limiting behaviour of the convolution term, allows us to make comparisons to existing results for the original reaction-advection-diffusion system. These comparisons show that the nonlocal model always predicts a larger parameter region supporting pattern formation. We then numerically extend the results to other dispersal kernels, showing that the tendency to form patterns depends on the type of decay of the kernel.
Collapse
|
47
|
Cornacchia L, van de Koppel J, van der Wal D, Wharton G, Puijalon S, Bouma TJ. Landscapes of facilitation: how self-organized patchiness of aquatic macrophytes promotes diversity in streams. Ecology 2018; 99:832-847. [DOI: 10.1002/ecy.2177] [Citation(s) in RCA: 45] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 06/13/2017] [Revised: 12/27/2017] [Accepted: 01/16/2018] [Indexed: 11/06/2022]
Affiliation(s)
- Loreta Cornacchia
- NIOZ Royal Netherlands Institute for Sea Research; Department of Estuarine and Delta Systems; Utrecht University; P.O. Box 140 Yerseke 4400 AC The Netherlands
- Groningen Institute for Evolutionary Life Sciences; University of Groningen; PO Box 11103 Groningen 9700 CC The Netherlands
| | - Johan van de Koppel
- NIOZ Royal Netherlands Institute for Sea Research; Department of Estuarine and Delta Systems; Utrecht University; P.O. Box 140 Yerseke 4400 AC The Netherlands
- Groningen Institute for Evolutionary Life Sciences; University of Groningen; PO Box 11103 Groningen 9700 CC The Netherlands
| | - Daphne van der Wal
- NIOZ Royal Netherlands Institute for Sea Research; Department of Estuarine and Delta Systems; Utrecht University; P.O. Box 140 Yerseke 4400 AC The Netherlands
- Faculty of Geo-Information Science and Earth Observation (ITC); University of Twente; P.O. Box 217 Enschede 7500 AE The Netherlands
| | | | - Sara Puijalon
- UMR 5023 LEHNA; CNRS; Université Lyon 1; ENTPE; Villeurbanne France
| | - Tjeerd J. Bouma
- NIOZ Royal Netherlands Institute for Sea Research; Department of Estuarine and Delta Systems; Utrecht University; P.O. Box 140 Yerseke 4400 AC The Netherlands
- Groningen Institute for Evolutionary Life Sciences; University of Groningen; PO Box 11103 Groningen 9700 CC The Netherlands
| |
Collapse
|
48
|
Huang T, Zhang H, Dai L, Cong X, Ma S. Formation of banded vegetation patterns resulted from interactions between sediment deposition and vegetation growth. C R Biol 2018; 341:167-181. [PMID: 29503122 DOI: 10.1016/j.crvi.2018.01.008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2017] [Revised: 01/24/2018] [Accepted: 01/25/2018] [Indexed: 11/15/2022]
Abstract
This research investigates the formation of banded vegetation patterns on hillslopes affected by interactions between sediment deposition and vegetation growth. The following two perspectives in the formation of these patterns are taken into consideration: (a) increased sediment deposition from plant interception, and (b) reduced plant biomass caused by sediment accumulation. A spatial model is proposed to describe how the interactions between sediment deposition and vegetation growth promote self-organization of banded vegetation patterns. Based on theoretical and numerical analyses of the proposed spatial model, vegetation bands can result from a Turing instability mechanism. The banded vegetation patterns obtained in this research resemble patterns reported in the literature. Moreover, measured by sediment dynamics, the variation of hillslope landform can be described. The model predicts how treads on hillslopes evolve with the banded patterns. Thus, we provide a quantitative interpretation for coevolution of vegetation patterns and landforms under effects of sediment redistribution.
Collapse
Affiliation(s)
- Tousheng Huang
- Research Center for Engineering Ecology and Nonlinear Science, North China Electric Power University, Beijing 102206, PR China; Industrial Systems Engineering, University of Regina, Regina, SK S4S 0A2, Canada
| | - Huayong Zhang
- Research Center for Engineering Ecology and Nonlinear Science, North China Electric Power University, Beijing 102206, PR China.
| | - Liming Dai
- Industrial Systems Engineering, University of Regina, Regina, SK S4S 0A2, Canada
| | - Xuebing Cong
- Research Center for Engineering Ecology and Nonlinear Science, North China Electric Power University, Beijing 102206, PR China
| | - Shengnan Ma
- Research Center for Engineering Ecology and Nonlinear Science, North China Electric Power University, Beijing 102206, PR China
| |
Collapse
|
49
|
Feudel U, Pisarchik AN, Showalter K. Multistability and tipping: From mathematics and physics to climate and brain-Minireview and preface to the focus issue. CHAOS (WOODBURY, N.Y.) 2018; 28:033501. [PMID: 29604626 DOI: 10.1063/1.5027718] [Citation(s) in RCA: 36] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Multistability refers to the coexistence of different stable states in nonlinear dynamical systems. This phenomenon has been observed in laboratory experiments and in nature. In this introduction, we briefly introduce the classes of dynamical systems in which this phenomenon has been found and discuss the extension to new system classes. Furthermore, we introduce the concept of critical transitions and discuss approaches to distinguish them according to their characteristics. Finally, we present some specific applications in physics, neuroscience, biology, ecology, and climate science.
Collapse
Affiliation(s)
- Ulrike Feudel
- Theoretical Physics/Complex Systems, ICBM, University of Oldenburg, 26129 Oldenburg, Germany
| | - Alexander N Pisarchik
- Center for Biomedical Technology, Technical University of Madrid, Campus Montegancedo, 28223 Pozuelo de Alarcon, Madrid, Spain
| | - Kenneth Showalter
- C. Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, West Virginia 26506-6045, USA
| |
Collapse
|
50
|
Zelnik YR, Gandhi P, Knobloch E, Meron E. Implications of tristability in pattern-forming ecosystems. CHAOS (WOODBURY, N.Y.) 2018; 28:033609. [PMID: 29604648 DOI: 10.1063/1.5018925] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
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.
Collapse
Affiliation(s)
- Yuval R Zelnik
- Centre for Biodiversity Theory and Modelling, Theoretical and Experimental Ecology Station, CNRS and Paul Sabatier University, 09200 Moulis, France
| | - Punit Gandhi
- Mathematical Biosciences Institute, Ohio State University, Columbus, Ohio 43210, USA
| | - Edgar Knobloch
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Ehud Meron
- Department of Solar Energy and Environmental Physics, Ben-Gurion University of the Negev, Sede Boqer Campus, Midreshet Ben-Gurion 8499000, Israel
| |
Collapse
|