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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.
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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
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2
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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.
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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
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3
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Colombo EH, López C, Hernández-García E. Pulsed Interaction Signals as a Route to Biological Pattern Formation. PHYSICAL REVIEW LETTERS 2023; 130:058401. [PMID: 36800461 DOI: 10.1103/physrevlett.130.058401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2022] [Accepted: 01/04/2023] [Indexed: 06/18/2023]
Abstract
We identify a mechanism for biological spatial pattern formation arising when the signals that mediate interactions between individuals in a population have pulsed character. Our general population-signal framework shows that while for a slow signal-dynamics limit no pattern formation is observed for any values of the model parameters, for a fast limit, on the contrary, pattern formation can occur. Furthermore, at these limits, our framework reduces, respectively, to reaction-diffusion and spatially nonlocal models, thus bridging these approaches.
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Affiliation(s)
- Eduardo H Colombo
- Department of Ecology and Evolutionary Biology, Princeton University, Princeton, New Jersey 08544, USA
- Department of Ecology, Evolution, and Natural Resources, Rutgers University, New Brunswick, New Jersey 08901, USA
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC), CSIC-UIB, Campus Universitat Illes Balears, 07122 Palma de Mallorca, Spain
| | - Cristóbal López
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC), CSIC-UIB, Campus Universitat Illes Balears, 07122 Palma de Mallorca, Spain
| | - Emilio Hernández-García
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC), CSIC-UIB, Campus Universitat Illes Balears, 07122 Palma de Mallorca, Spain
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4
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Olivieri F, Prattichizzo F, Lattanzio F, Bonfigli AR, Spazzafumo L. Antifragility and antiinflammaging: Can they play a role for a healthy longevity? Ageing Res Rev 2023; 84:101836. [PMID: 36574863 DOI: 10.1016/j.arr.2022.101836] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2022] [Revised: 12/14/2022] [Accepted: 12/21/2022] [Indexed: 12/25/2022]
Abstract
One of the most exciting challenges of the research on aging is to explain how the environmental factors interact with the genetic background to modulate the chances to reach the extreme limit of human life in healthy conditions. The complex epigenetic mechanisms can explain both the interaction between DNA and environmental factors, and the long-distance persistence of lifestyle effects, due to the so called "epigenetic memory". One of the most extensively investigated theories on aging focuses on the inflammatory responses, suggesting that the age-related progression of low-grade and therefore for long time subclinical, chronic, systemic, inflammatory process, named "inflammaging", could be the most relevant risk factor for the development and progression of the most common age-related diseases and ultimately of death. The results of many studies on long-lived people, especially on centenarians, suggested that healthy old people can cope with inflammaging upregulating the antiinflammaging responses. Overall, a genetic make-up coding for a strong antiinflammaging response and an age-related ability to remodel key metabolic pathways to cope with a plethora of antigens and stressors seem to be the best ways for reach the extreme limit of human lifespan in health status. In this scenario, we wondered if the antifragility concept, recently developed in the framework of business and risk analysis, could add some information to disentangle the heterogeneous nature of the aging process in human. The antifragility is the property of the complex systems to increase their performances because of high stress. Based on this theory we were wondering if some subjects could be able to modulate faster than others their epigenome to cope with a plethora of stressors during life, probably modulating the inflammatory and anti-inflammatory responses. In this framework, antifragility could share some common mechanisms with anti-inflammaging, modulating the ability to restrain the inflammatory responses, so that antifragility and antiinflammaging could be viewed as different pieces of the same puzzle, both impinging upon the chances to travel along the healthy aging trajectory.
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Affiliation(s)
- Fabiola Olivieri
- Department of Clinical and Molecular Sciences, DISCLIMO, Università Politecnica Delle Marche, Ancona, Italy; Clinica di Medicina di Laboratorio e di Precisione, IRCCS INRCA, Ancona, Italy.
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5
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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.
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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
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6
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Inderjit, Callaway RM, Meron E. Vegetation patterning and biodiversity of plant communities. Phys Life Rev 2022; 42:29-32. [DOI: 10.1016/j.plrev.2022.05.008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2022] [Accepted: 05/23/2022] [Indexed: 11/30/2022]
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7
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Rietkerk M, Bastiaansen R, Banerjee S, van de Koppel J, Baudena M, Doelman A. Evasion of tipping in complex systems through spatial pattern formation. Science 2021; 374:eabj0359. [PMID: 34618584 DOI: 10.1126/science.abj0359] [Citation(s) in RCA: 50] [Impact Index Per Article: 16.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Abstract
[Figure: see text].
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Affiliation(s)
- Max Rietkerk
- Copernicus Institute of Sustainable Development, Utrecht University, 3508 TC, Utrecht, Netherlands
| | - Robbin Bastiaansen
- Department of Physics, Institute for Marine and Atmospheric Research Utrecht, Utrecht University, 3508 TA, Utrecht, Netherlands
| | - Swarnendu Banerjee
- Copernicus Institute of Sustainable Development, Utrecht University, 3508 TC, Utrecht, Netherlands.,The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India.,Indian Statistical Institute, Agricultural and Ecological Research Unit, Kolkata 700108, India
| | - Johan van de Koppel
- Department of Estuarine and Delta Systems, Royal Netherlands Institute for Sea Research, 4400 AC, Yerseke, Netherlands.,Groningen Institute for Evolutionary Life Sciences, Conservation Ecology Group, University of Groningen, 9700 CC, Groningen, Netherlands
| | - Mara Baudena
- Copernicus Institute of Sustainable Development, Utrecht University, 3508 TC, Utrecht, Netherlands.,National Research Council of Italy, Institute of Atmospheric Sciences and Climate (CNR-ISAC), 10133 Torino, Italy
| | - Arjen Doelman
- Mathematical Institute, Leiden University, 2300 RA, Leiden, Netherlands
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8
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Belowground feedbacks as drivers of spatial self-organization and community assembly. Phys Life Rev 2021; 38:1-24. [PMID: 34334324 DOI: 10.1016/j.plrev.2021.07.002] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2021] [Accepted: 07/12/2021] [Indexed: 02/03/2023]
Abstract
Vegetation patterning in water-limited and other resource-limited ecosystems highlights spatial self-organization processes as potentially key drivers of community assembly. These processes provide insight into predictable landscape-level relationships between organisms and their abiotic environment in the form of regular and irregular patterns of biota and resources. However, two aspects have largely been overlooked; the roles played by plant - soil-biota feedbacks and allelopathy in spatial self-organization, and their potential contribution, along with plant-resource feedbacks, to community assembly through spatial self-organization. Here, we expand the drivers of spatial self-organization from a focus on plant-resource feedbacks to include plant - soil-biota feedbacks and allelopathy, and integrate concepts of nonlinear physics and community ecology to generate a new hypothesis. According to this hypothesis, below-ground processes can affect community assemblages through two types of spatial self-organization, global and local. The former occurs simultaneously across whole ecosystems, leading to self-organized patterns of biota, allelochemicals and resources, and niche partitioning. The latter occurs locally in ecotones, and determines ecotone structure and motion, invasion dynamics, and species coexistence. Studies of the two forms of spatial self-organization are important for understanding the organization of plant communities in drier climates which are likely to involve spatial patterning or re-patterning. Such studies are also important for developing new practices of ecosystem management, based on local manipulations at ecotones, to slow invasion dynamics or induce transitions from transitive to intransitive networks of interspecific interactions which increase species diversity.
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9
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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.
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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
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10
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Equihua M, Espinosa Aldama M, Gershenson C, López-Corona O, Munguía M, Pérez-Maqueo O, Ramírez-Carrillo E. Ecosystem antifragility: beyond integrity and resilience. PeerJ 2020; 8:e8533. [PMID: 32095358 PMCID: PMC7020813 DOI: 10.7717/peerj.8533] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2019] [Accepted: 01/07/2020] [Indexed: 12/18/2022] Open
Abstract
We review the concept of ecosystem resilience in its relation to ecosystem integrity from an information theory approach. We summarize the literature on the subject identifying three main narratives: ecosystem properties that enable them to be more resilient; ecosystem response to perturbations; and complexity. We also include original ideas with theoretical and quantitative developments with application examples. The main contribution is a new way to rethink resilience, that is mathematically formal and easy to evaluate heuristically in real-world applications: ecosystem antifragility. An ecosystem is antifragile if it benefits from environmental variability. Antifragility therefore goes beyond robustness or resilience because while resilient/robust systems are merely perturbation-resistant, antifragile structures not only withstand stress but also benefit from it.
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Affiliation(s)
- Miguel Equihua
- Red Ambiente y Sustentabilidad, Instituto de Ecología A.C., Xalapa, Veracruz, México
| | | | - Carlos Gershenson
- IIMAS, Universidad Nacional Autónoma de México, CDMX, México.,Centro de Ciencias de la Complejidad (C3), Universidad Nacional Autónoma de México, CDMX, México.,ITMO University, St. Petersburg, Russia
| | - Oliver López-Corona
- Red Ambiente y Sustentabilidad, Instituto de Ecología A.C., Xalapa, Veracruz, México.,Centro de Ciencias de la Complejidad (C3), Universidad Nacional Autónoma de México, CDMX, México.,Cátedras CONACyT, Comisión Nacional para el Conocimiento y Uso de la Biodiversidad (CONABIO), CDMX, México
| | - Mariana Munguía
- Comisión Nacional para el Conocimiento y Uso de la Biodiversidad (CONABIO), CDMX, México
| | - Octavio Pérez-Maqueo
- Red Ambiente y Sustentabilidad, Instituto de Ecología A.C., Xalapa, Veracruz, México
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11
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Olmeda F, Ben Amar M. Clonal pattern dynamics in tumor: the concept of cancer stem cells. Sci Rep 2019; 9:15607. [PMID: 31666555 PMCID: PMC6821776 DOI: 10.1038/s41598-019-51575-1] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2019] [Accepted: 09/27/2019] [Indexed: 12/19/2022] Open
Abstract
We present a multiphase model for solid tumor initiation and progression focusing on the properties of cancer stem cells (CSC). CSCs are a small and singular cell sub-population having outstanding capacities: high proliferation rate, self-renewal and extreme therapy resistance. Our model takes all these factors into account under a recent perspective: the possibility of phenotype switching of differentiated cancer cells (DC) to the stem cell state, mediated by chemical activators. This plasticity of cancerous cells complicates the complete eradication of CSCs and the tumor suppression. The model in itself requires a sophisticated treatment of population dynamics driven by chemical factors. We analytically demonstrate that the rather important number of parameters, inherent to any biological complexity, is reduced to three pivotal quantities.Three fixed points guide the dynamics, and two of them may lead to an optimistic issue, predicting either a control of the cancerous cell population or a complete eradication. The space environment, critical for the tumor outcome, is introduced via a density formalism. Disordered patterns are obtained inside a stable growing contour driven by the CSC. Somewhat surprisingly, despite the patterning instability, the contour maintains its circular shape but ceases to grow for a typical size independently of segregation patterns or obstacles located inside.
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Affiliation(s)
- Fabrizio Olmeda
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, D-01187, Dresden, Germany
- Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005, Paris, France
| | - Martine Ben Amar
- Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005, Paris, France.
- Institut Universitaire de Cancérologie, Faculté de médecine, Sorbonne Université, 91 Bd de l'Hôpital, 75013, Paris, France.
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12
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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.
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13
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Dornelas V, Colombo EH, Anteneodo C. Single-species fragmentation: The role of density-dependent feedback. Phys Rev E 2019; 99:062225. [PMID: 31330753 DOI: 10.1103/physreve.99.062225] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2019] [Indexed: 11/07/2022]
Abstract
Internal feedback is commonly present in biological populations and can play a crucial role in the emergence of collective behavior. To describe the temporal evolution of the distribution of a single-species population, we consider a generalization of the Fisher-KPP equation. This equation includes the elementary processes of random motion, reproduction, and, importantly, nonlocal interspecific competition, which introduces a spatial scale of interaction. In addition, we take into account feedback mechanisms in diffusion and growth processes, mimicked by power-law density dependencies. This feedback includes, for instance, anomalous diffusion, reaction to overcrowding or to the rarefaction of the population, as well as Allee-like effects. We show that, depending on the kind of feedback that takes place, the population can self-organize splitting into disconnected subpopulations, in the absence of external constraints. Through extensive numerical simulations, we investigate the temporal evolution and the characteristics of the stationary population distribution in the one-dimensional case. We discuss the crucial role that density-dependence has on pattern formation, particularly on fragmentation, which can bring important consequences to processes such as epidemic spread and speciation.
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Affiliation(s)
- V Dornelas
- Department of Physics, PUC-Rio, Rua Marquês de São Vicente, 225, 22451-900, Rio de Janeiro, Brazil
| | - E H Colombo
- IFISC (CSIC-UIB), Campus Universitat Illes Balears, 07122, Palma de Mallorca, Spain
| | - C Anteneodo
- Department of Physics, PUC-Rio, Rua Marquês de São Vicente, 225, 22451-900, Rio de Janeiro, Brazil.,Institute of Science and Technology for Complex Systems, Rio de Janeiro, Brazil
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