1
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Liu J, Sun K, Wang H. Mechanism of multistability in chaotic maps. CHAOS (WOODBURY, N.Y.) 2024; 34:083102. [PMID: 39088346 DOI: 10.1063/5.0219361] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2024] [Accepted: 07/12/2024] [Indexed: 08/03/2024]
Abstract
This research aims to investigate the mechanisms of multistability in chaotic maps. The study commences by examining the fundamental principles governing the development of homogeneous multistability using a basic one-dimensional chain-climbing map. Findings suggest that the phase space can be segmented into distinct uniform mediums where particles exhibit consistent movement. As critical parameter values are reached, channels emerge between these mediums, resulting in deterministic chaotic diffusion. Additionally, the study delves into the topic of introducing heterogeneous factors on the formation of heterogeneous multistability in the one-dimensional map. A thorough examination of phenomena such as multistate intermittency highlights the intimate connection between specific phase transition occurrences and channel formation. Finally, by analyzing two instances-a memristive chaotic map and a hyperchaotic map-the underlying factors contributing to the emergence of multistability are scrutinized. This study offers an alternative perspective for verifying the fundamental principles of homogenous and heterogeneous multistability in complex high-dimensional chaotic maps.
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Affiliation(s)
- Jin Liu
- School of Physics, Central South University, Changsha 410083, China
| | - Kehui Sun
- School of Physics, Central South University, Changsha 410083, China
| | - Huihai Wang
- School of Electronic Information, Central South University, Changsha 410083, China
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2
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Bloxham B, Lee H, Gore J. Biodiversity is enhanced by sequential resource utilization and environmental fluctuations via emergent temporal niches. PLoS Comput Biol 2024; 20:e1012049. [PMID: 38739654 PMCID: PMC11135710 DOI: 10.1371/journal.pcbi.1012049] [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: 10/18/2023] [Revised: 05/29/2024] [Accepted: 04/02/2024] [Indexed: 05/16/2024] Open
Abstract
How natural communities maintain their remarkable biodiversity and which species survive in complex communities are central questions in ecology. Resource competition models successfully explain many phenomena but typically predict only as many species as resources can coexist. Here, we demonstrate that sequential resource utilization, or diauxie, with periodic growth cycles can support many more species than resources. We explore how communities modify their own environments by sequentially depleting resources to form sequences of temporal niches, or intermediately depleted environments. Biodiversity is enhanced when community-driven or environmental fluctuations modulate the resource depletion order and produce different temporal niches on each growth cycle. Community-driven fluctuations under constant environmental conditions are rare, but exploring them illuminates the temporal niche structure that emerges from sequential resource utilization. With environmental fluctuations, we find most communities have more stably coexisting species than resources with survivors accurately predicted by the same temporal niche structure and each following a distinct optimal strategy. Our results thus present a new niche-based approach to understanding highly diverse fluctuating communities.
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Affiliation(s)
- Blox Bloxham
- Physics of Living Systems, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America
| | - Hyunseok Lee
- Physics of Living Systems, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America
| | - Jeff Gore
- Physics of Living Systems, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America
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3
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Bi MX, Fan H, Yan XH, Lai YC. Folding State within a Hysteresis Loop: Hidden Multistability in Nonlinear Physical Systems. PHYSICAL REVIEW LETTERS 2024; 132:137201. [PMID: 38613259 DOI: 10.1103/physrevlett.132.137201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2023] [Revised: 11/28/2023] [Accepted: 02/12/2024] [Indexed: 04/14/2024]
Abstract
Identifying hidden states in nonlinear physical systems that evade direct experimental detection is important as disturbances and noises can place the system in a hidden state with detrimental consequences. We study a cavity magnonic system whose main physics is photon and magnon Kerr effects. Sweeping a bifurcation parameter in numerical experiments (as would be done in actual experiments) leads to a hysteresis loop with two distinct stable steady states, but analytic calculation gives a third folded steady state "hidden" in the loop, which gives rise to the phenomenon of hidden multistability. We propose an experimentally feasible control method to drive the system into the folded hidden state. We demonstrate, through a ternary cavity magnonic system and a gene regulatory network, that such hidden multistability is in fact quite common. Our findings shed light on hidden dynamical states in nonlinear physical systems which are not directly observable but can present challenges and opportunities in applications.
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Affiliation(s)
- Meng-Xia Bi
- School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, China
| | - Huawei Fan
- School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, China
| | - Xiao-Hong Yan
- School of Material Science and Engineering, Jiangsu University, Zhenjiang 212013, China
| | - Ying-Cheng Lai
- School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA
- Department of Physics, Arizona State University, Tempe, Arizona 85287, USA
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4
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van Nes EH, Pujoni DGF, Shetty SA, Straatsma G, de Vos WM, Scheffer M. A tiny fraction of all species forms most of nature: Rarity as a sticky state. Proc Natl Acad Sci U S A 2024; 121:e2221791120. [PMID: 38165929 PMCID: PMC10786311 DOI: 10.1073/pnas.2221791120] [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: 12/23/2022] [Accepted: 11/11/2023] [Indexed: 01/04/2024] Open
Abstract
Using data from a wide range of natural communities including the human microbiome, plants, fish, mushrooms, rodents, beetles, and trees, we show that universally just a few percent of the species account for most of the biomass. This is in line with the classical observation that the vast bulk of biodiversity is very rare. Attempts to find traits allowing the tiny fraction of abundant species to escape rarity have remained unsuccessful. Here, we argue that this might be explained by the fact that hyper-dominance can emerge through stochastic processes. We demonstrate that in neutrally competing groups of species, rarity tends to become a trap if environmental fluctuations result in gains and losses proportional to abundances. This counter-intuitive phenomenon arises because absolute change tends to zero for very small abundances, causing rarity to become a "sticky state", a pseudoattractor that can be revealed numerically in classical ball-in-cup landscapes. As a result, the vast majority of species spend most of their time in rarity leaving space for just a few others to dominate the neutral community. However, fates remain stochastic. Provided that there is some response diversity, roles occasionally shift as stochastic events or natural enemies bring an abundant species down allowing a rare species to rise to dominance. Microbial time series spanning thousands of generations support this prediction. Our results suggest that near-neutrality within niches may allow numerous rare species to persist in the wings of the dominant ones. Stand-ins may serve as insurance when former key species collapse.
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Affiliation(s)
- Egbert H. van Nes
- Aquatic Ecology and Water Quality Management Group, Environmental Science Department, Wageningen University, WageningenNL-6700 AA, The Netherlands
| | - Diego G. F. Pujoni
- Federal University of Minas Gerais, Departamento de Biologia Geral, Instituto de Ciências Biológicas, Laboratório de Limnologia, Ecotoxicologia e Ecologia Aquática, Belo HorizonteMG CEP31270-901, Brazil
| | - Sudarshan A. Shetty
- Laboratory of Microbiology, Wageningen University, WageningenNL-6700 EH, The Netherlands
| | - Gerben Straatsma
- Aquatic Ecology and Water Quality Management Group, Environmental Science Department, Wageningen University, WageningenNL-6700 AA, The Netherlands
| | - Willem M. de Vos
- Laboratory of Microbiology, Wageningen University, WageningenNL-6700 EH, The Netherlands
- Human Microbiome Research Program, Faculty of Medicine, University of Helsinki, Helsinki00014, Finland
| | - Marten Scheffer
- Aquatic Ecology and Water Quality Management Group, Environmental Science Department, Wageningen University, WageningenNL-6700 AA, The Netherlands
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5
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Rubio VE, Swenson NG. On functional groups and forest dynamics. Trends Ecol Evol 2024; 39:23-30. [PMID: 37673714 DOI: 10.1016/j.tree.2023.08.008] [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: 04/13/2023] [Revised: 08/09/2023] [Accepted: 08/10/2023] [Indexed: 09/08/2023]
Abstract
Functional trait variation measured on continuous scales has helped ecologists to unravel important ecological processes. However, forest ecologists have recently moved back toward using functional groups. There are pragmatic and biological rationales for focusing on functional groups. Both of these approaches have inherent limitations including binning clearly continuous distributions, poor trait-group matching, and narrow conceptual frameworks for why groups exist and how they evolved. We believe the pragmatic use of functional groups due to data deficiencies will eventually erode. Conversely, we argue that existing conceptual frameworks for why a limited number of tree functional groups may exist is a useful, but flawed, starting point for modeling forests that can be improved through the consideration of unmeasured axes of functional variation.
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Affiliation(s)
- Vanessa E Rubio
- Department of Biological Sciences, University of Notre Dame, Notre Dame, IN, USA.
| | - Nathan G Swenson
- Department of Biological Sciences, University of Notre Dame, Notre Dame, IN, USA.
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6
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Haraldsson M, Thébault E. Emerging niche clustering results from both competition and predation. Ecol Lett 2023. [PMID: 37157944 DOI: 10.1111/ele.14230] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2022] [Revised: 03/17/2023] [Accepted: 04/14/2023] [Indexed: 05/10/2023]
Abstract
Understanding species coexistence has been a central question in ecology for decades, and the notion that competing species need to differ in their ecological niche for stable coexistence has dominated. Recent theoretical and empirical work suggests differently. Species can also escape competitive exclusion by being similar, leading to clusters of species with similar traits. This theory has so far only been explored under competition. By combining mathematical and numerical analyses, we reveal that competition and predation are equally capable to promote clusters of similar species in prey-predator communities, their relative importance being modulated by resource availability. We further show that predation has a stabilizing effect on clustering patterns, making the clusters more diverse. Our results merge different ecological theories and bring new light to the emergent neutrality theory by adding the perspective of trophic interactions. These results open new perspectives to the study of trait distributions in ecological interaction networks.
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Affiliation(s)
- Matilda Haraldsson
- Institute of Ecology and Environmental Sciences (iEES-Paris), Sorbonne Université, CNRS, IRD, INRAE, Université Paris Est Créteil, Université Paris Cité, Paris, France
- Department of Marine Sciences, Gothenburg University, Gothenburg, Sweden
| | - Elisa Thébault
- Institute of Ecology and Environmental Sciences (iEES-Paris), Sorbonne Université, CNRS, IRD, INRAE, Université Paris Est Créteil, Université Paris Cité, Paris, France
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7
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Dequenne I, Philippart de Foy JM, Cani PD. Developing Strategies to Help Bee Colony Resilience in Changing Environments. Animals (Basel) 2022; 12:ani12233396. [PMID: 36496917 PMCID: PMC9737243 DOI: 10.3390/ani12233396] [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: 10/03/2022] [Revised: 11/16/2022] [Accepted: 11/30/2022] [Indexed: 12/10/2022] Open
Abstract
Climate change, loss of plant biodiversity, burdens caused by new pathogens, predators, and toxins due to human disturbance and activity are significant causes of the loss of bee colonies and wild bees. The aim of this review is to highlight some possible strategies that could help develop bee resilience in facing their changing environments. Scientists underline the importance of the links between nutrition, microbiota, and immune and neuroendocrine stress resistance of bees. Nutrition with special care for plant-derived molecules may play a major role in bee colony health. Studies have highlighted the importance of pollen, essential oils, plant resins, and leaves or fungi as sources of fundamental nutrients for the development and longevity of a honeybee colony. The microbiota is also considered as a key factor in bee physiology and a cornerstone between nutrition, metabolism, growth, health, and pathogen resistance. Another stressor is the varroa mite parasite. This parasite is a major concern for beekeepers and needs specific strategies to reduce its severe impact on honeybees. Here we discuss how helping bees to thrive, especially through changing environments, is of great concern for beekeepers and scientists.
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Affiliation(s)
- Isabelle Dequenne
- J-M Philippart de Foy & I Dequenne Consultation, Avenue Orban, 127, 1150 Brussels, Belgium
| | | | - Patrice D. Cani
- Metabolism and Nutrition Research Group, Louvain Drug Research Institute, UCLouvain, Université Catholique de Louvain, 1200 Brussels, Belgium
- WELBIO Department, WEL Research Institute, Walloon Excellence in Life Sciences and BIOtechnology (WELBIO), Avenue Pasteur, 6, 1300 Wavre, Belgium
- Correspondence:
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8
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Exploiting deterministic features in apparently stochastic data. Sci Rep 2022; 12:19843. [PMID: 36400910 PMCID: PMC9674651 DOI: 10.1038/s41598-022-23212-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: 07/06/2022] [Accepted: 10/26/2022] [Indexed: 11/19/2022] Open
Abstract
Many processes in nature are the result of many coupled individual subsystems (like population dynamics or neurosystems). Not always such systems exhibit simple stable behaviors that in the past science has mostly focused on. Often, these systems are characterized by bursts of seemingly stochastic activity, interrupted by quieter periods. The hypothesis is that the presence of a strong deterministic ingredient is often obscured by the stochastic features. We test this by modeling classically stochastic considered real-world data from both, the stochastic as well as the deterministic approaches to find that the deterministic approach's results level with those from the stochastic side. Moreover, the deterministic approach is shown to reveal the full dynamical systems landscape, which can be exploited for steering the dynamics into a desired regime.
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9
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Meng Y, Lai YC, Grebogi C. The fundamental benefits of multiplexity in ecological networks. J R Soc Interface 2022; 19:20220438. [PMID: 36167085 PMCID: PMC9514891 DOI: 10.1098/rsif.2022.0438] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2022] [Accepted: 09/01/2022] [Indexed: 11/12/2022] Open
Abstract
A tipping point presents perhaps the single most significant threat to an ecological system as it can lead to abrupt species extinction on a massive scale. Climate changes leading to the species decay parameter drifts can drive various ecological systems towards a tipping point. We investigate the tipping-point dynamics in multi-layer ecological networks supported by mutualism. We unveil a natural mechanism by which the occurrence of tipping points can be delayed by multiplexity that broadly describes the diversity of the species abundances, the complexity of the interspecific relationships, and the topology of linkages in ecological networks. For a double-layer system of pollinators and plants, coupling between the network layers occurs when there is dispersal of pollinator species. Multiplexity emerges as the dispersing species establish their presence in the destination layer and have a simultaneous presence in both. We demonstrate that the new mutualistic links induced by the dispersing species with the residence species have fundamental benefits to the well-being of the ecosystem in delaying the tipping point and facilitating species recovery. Articulating and implementing control mechanisms to induce multiplexity can thus help sustain certain types of ecosystems that are in danger of extinction as the result of environmental changes.
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Affiliation(s)
- Yu Meng
- Institute for Complex Systems and Mathematical Biology, School of Natural and Computing Sciences, King’s College, University of Aberdeen, AB24 3UE, UK
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, Dresden 01187, Germany
- Center for Systems Biology Dresden, Pfotenhauerstraße 108, Dresden 01307, Germany
| | - Ying-Cheng Lai
- School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA
- Department of Physics, Arizona State University, Tempe, AZ 85287, USA
| | - Celso Grebogi
- Institute for Complex Systems and Mathematical Biology, School of Natural and Computing Sciences, King’s College, University of Aberdeen, AB24 3UE, UK
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10
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Fragata I, Costa-Pereira R, Kozak M, Majer A, Godoy O, Magalhães S. Specific sequence of arrival promotes coexistence via spatial niche pre-emption by the weak competitor. Ecol Lett 2022; 25:1629-1639. [PMID: 35596732 DOI: 10.1111/ele.14021] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2022] [Revised: 03/17/2022] [Accepted: 03/29/2022] [Indexed: 11/26/2022]
Abstract
Historical contingency, such as the order of species arrival, can modify competitive outcomes via niche modification or pre-emption. However, how these mechanisms ultimately modify stabilising niche and average fitness differences remains largely unknown. By experimentally assembling two congeneric spider mite species feeding on tomato plants during two generations, we show that order of arrival affects species' competitive ability and changes the outcome of competition. Contrary to expectations, order of arrival did not cause positive frequency dependent priority effects. Instead, coexistence was predicted when the inferior competitor (Tetranychus urticae) arrived first. In that case, T. urticae colonised the preferred feeding stratum (leaves) of T. evansi leading to spatial niche pre-emption, which equalised fitness and reduced niche differences, driving community assembly to a close-to-neutrality scenario. Our study demonstrates how the order of species arrival and the spatial context of competitive interactions may jointly determine whether species can coexist.
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Affiliation(s)
- Inês Fragata
- Centre for Ecology, Evolution and Environmental Changes, Department of Animal Biology, Faculty of Sciences University of Lisbon, Lisbon, Portugal
| | - Raul Costa-Pereira
- Department of Animal Biology, Institute of Biology, Universidade Estadual de Campinas, Campinas, Brazil
| | - Mariya Kozak
- Centre for Ecology, Evolution and Environmental Changes, Department of Animal Biology, Faculty of Sciences University of Lisbon, Lisbon, Portugal
| | - Agnieszka Majer
- Population Ecology Lab, Faculty of Biology, Adam Mickiewicz University, Poznań, Poland
| | - Oscar Godoy
- Department of Biology, Instituto Universitario de Investigación Marina (INMAR), Universidad de Cádiz, Puerto Real, Spain
| | - Sara Magalhães
- Centre for Ecology, Evolution and Environmental Changes, Department of Animal Biology, Faculty of Sciences University of Lisbon, Lisbon, Portugal
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11
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García-Callejas D, Bartomeus I, Godoy O. The spatial configuration of biotic interactions shapes coexistence-area relationships in an annual plant community. Nat Commun 2021; 12:6192. [PMID: 34702825 PMCID: PMC8548393 DOI: 10.1038/s41467-021-26487-2] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2021] [Accepted: 09/24/2021] [Indexed: 11/18/2022] Open
Abstract
The increase of species richness with area is a universal phenomenon on Earth. However, this observation contrasts with our poor understanding of how these species-area relationships (SARs) emerge from the collective effects of area, spatial heterogeneity, and local interactions. By combining a structuralist approach with five years of empirical observations in a highly-diverse Mediterranean grassland, we show that spatial heterogeneity plays a little role in the accumulation of species richness with area in our system. Instead, as we increase the sampled area more species combinations are realized, and they coexist mainly due to direct pairwise interactions rather than by changes in single-species dominance or by indirect interactions. We also identify a small set of transient species with small population sizes that are consistently found across spatial scales. These findings empirically support the importance of the architecture of species interactions together with stochastic events for driving coexistence- and species-area relationships.
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Affiliation(s)
- David García-Callejas
- Estación Biológica de Doñana, C/Américo Vespucio 26, 41092, Seville, Spain.
- Departamento de Biología, Instituto Universitario de Investigación Marina (INMAR), Universidad de Cádiz, E-11510, Puerto Real, Spain.
| | - Ignasi Bartomeus
- Estación Biológica de Doñana, C/Américo Vespucio 26, 41092, Seville, Spain
| | - Oscar Godoy
- Departamento de Biología, Instituto Universitario de Investigación Marina (INMAR), Universidad de Cádiz, E-11510, Puerto Real, Spain
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12
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Graco‐Roza C, Segura AM, Kruk C, Domingos P, Soininen J, Marinho MM. Clumpy coexistence in phytoplankton: the role of functional similarity in community assembly. OIKOS 2021. [DOI: 10.1111/oik.08677] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Caio Graco‐Roza
- Laboratory of Phytoplankton of Ecology and Physiology, Dept of Plant Biology, Univ. of Rio de Janeiro State Rio de Janeiro Brazil
- Univ. of Helsinki, Dept of Geosciences and Geography Helsinki Finland
| | - Angel M. Segura
- Modelización Estadística de Datos e Inteligencia Artificial (MEDIA) CURE-Rocha, Univ. de la República Uruguay
| | - Carla Kruk
- Sección Limnología, IECA, Facultad de Ciencias, Univ. de la República Uruguay
| | - Patrícia Domingos
- Laboratory of Phytoplankton of Ecology and Physiology, Dept of Plant Biology, Univ. of Rio de Janeiro State Rio de Janeiro Brazil
| | - Janne Soininen
- Univ. of Helsinki, Dept of Geosciences and Geography Helsinki Finland
| | - Marcelo Manzi Marinho
- Laboratory of Phytoplankton of Ecology and Physiology, Dept of Plant Biology, Univ. of Rio de Janeiro State Rio de Janeiro Brazil
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13
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van Eldijk TJB, Bisschop K, Etienne RS. Uniting Community Ecology and Evolutionary Rescue Theory: Community-Wide Rescue Leads to a Rapid Loss of Rare Species. Front Ecol Evol 2020. [DOI: 10.3389/fevo.2020.552268] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
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14
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Kim D, Ohr S. Coexistence of plant species under harsh environmental conditions: an evaluation of niche differentiation and stochasticity along salt marsh creeks. ACTA ACUST UNITED AC 2020. [DOI: 10.1186/s41610-020-00161-y] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
Abstract
Background
Ecologists have achieved much progress in the study of mechanisms that maintain species coexistence and diversity. In this paper, we reviewed a wide range of past research related to these topics, focusing on five theoretical bodies: (1) coexistence by niche differentiation, (2) coexistence without niche differentiation, (3) coexistence along environmental stress gradients, (4) coexistence under non-equilibrium versus equilibrium conditions, and (5) modern perspectives.
Results
From the review, we identified that there are few models that can be generally and confidently applicable to different ecological systems. This problem arises mainly because most theories have not been substantiated by enough empirical research based on field data to test various coexistence hypotheses at different spatial scales. We also found that little is still known about the mechanisms of species coexistence under harsh environmental conditions. This is because most previous models treat disturbance as a key factor shaping community structure, but they do not explicitly deal with stressful systems with non-lethal conditions. We evaluated the mainstream ideas of niche differentiation and stochasticity for the coexistence of plant species across salt marsh creeks in southwestern Denmark. The results showed that diversity indices, such as Shannon–Wiener diversity, richness, and evenness, decreased with increasing surface elevation and increased with increasing niche overlap and niche breadth. The two niche parameters linearly decreased with increasing elevation. These findings imply a substantial influence of an equalizing mechanism that reduces differences in relative fitness among species in the highly stressful environments of the marsh. We propose that species evenness increases under very harsh conditions if the associated stress is not lethal. Finally, we present a conceptual model of patterns related to the level of environmental stress and niche characteristics along a microhabitat gradient (i.e., surface elevation).
Conclusions
The ecology of stressful systems with non-lethal conditions will be increasingly important as ongoing global-scale climate change extends the period of chronic stresses that are not necessarily fatal to inhabiting plants. We recommend that more ecologists continue this line of research.
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15
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Wiedermann M, Smith EK, Heitzig J, Donges JF. A network-based microfoundation of Granovetter's threshold model for social tipping. Sci Rep 2020; 10:11202. [PMID: 32641784 PMCID: PMC7343878 DOI: 10.1038/s41598-020-67102-6] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2020] [Accepted: 06/02/2020] [Indexed: 11/11/2022] Open
Abstract
Social tipping, where minorities trigger larger populations to engage in collective action, has been suggested as one key aspect in addressing contemporary global challenges. Here, we refine Granovetter’s widely acknowledged theoretical threshold model of collective behavior as a numerical modelling tool for understanding social tipping processes and resolve issues that so far have hindered such applications. Based on real-world observations and social movement theory, we group the population into certain or potential actors, such that – in contrast to its original formulation – the model predicts non-trivial final shares of acting individuals. Then, we use a network cascade model to explain and analytically derive that previously hypothesized broad threshold distributions emerge if individuals become active via social interaction. Thus, through intuitive parameters and low dimensionality our refined model is adaptable to explain the likelihood of engaging in collective behavior where social-tipping-like processes emerge as saddle-node bifurcations and hysteresis.
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Affiliation(s)
- Marc Wiedermann
- FutureLab on Game Theory & Networks of Interacting Agents, Complexity Science, Potsdam Institute for Climate Impact Research, Member of the Leibniz Association, P.O. Box 60 12 03, 14412, Potsdam, Germany.
| | - E Keith Smith
- GESIS - Leibniz Institute for the Social Sciences, Member of the Leibniz Association, Unter Sachsenhausen 6-8, 50667, Cologne, Germany.,Institute of Science, Technology and Policy, ETH Zurich, Zurich, Switzerland
| | - Jobst Heitzig
- FutureLab on Game Theory & Networks of Interacting Agents, Complexity Science, Potsdam Institute for Climate Impact Research, Member of the Leibniz Association, P.O. Box 60 12 03, 14412, Potsdam, Germany
| | - Jonathan F Donges
- FutureLab Earth Resilience in the Anthropocene, Earth System Analysis, Potsdam Institute for Climate Impact Research, Member of the Leibniz Association, P.O. Box 60 12 03, 14412, Potsdam, Germany.,Stockholm Resilience Centre, Stockholm University, Kräftriket 2B, 114 19, Stockholm, Sweden
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16
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Rodríguez-Sánchez P, van Nes EH, Scheffer M. Neutral competition boosts cycles and chaos in simulated food webs. ROYAL SOCIETY OPEN SCIENCE 2020; 7:191532. [PMID: 32742676 PMCID: PMC7353966 DOI: 10.1098/rsos.191532] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/03/2019] [Accepted: 05/18/2020] [Indexed: 06/11/2023]
Abstract
Similarity of competitors has been proposed to facilitate coexistence of species because it slows down competitive exclusion, thus making it easier for equalizing mechanisms to maintain diverse communities. On the other hand, previous studies suggest that chaotic ecosystems can have a higher biodiversity. Here, we link these two previously unrelated findings, by analysing the dynamics of food web models. We show that near-neutrality of competition of prey, in the presence of predators, increases the chance of developing chaotic dynamics. Moreover, we confirm that chaotic dynamics correlate with a higher biodiversity.
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Thakur MP, Phillips HRP, Brose U, De Vries FT, Lavelle P, Loreau M, Mathieu J, Mulder C, Van der Putten WH, Rillig MC, Wardle DA, Bach EM, Bartz MLC, Bennett JM, Briones MJI, Brown G, Decaëns T, Eisenhauer N, Ferlian O, Guerra CA, König‐Ries B, Orgiazzi A, Ramirez KS, Russell DJ, Rutgers M, Wall DH, Cameron EK. Towards an integrative understanding of soil biodiversity. Biol Rev Camb Philos Soc 2020; 95:350-364. [PMID: 31729831 PMCID: PMC7078968 DOI: 10.1111/brv.12567] [Citation(s) in RCA: 55] [Impact Index Per Article: 13.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2019] [Revised: 10/07/2019] [Accepted: 10/11/2019] [Indexed: 12/25/2022]
Abstract
Soil is one of the most biodiverse terrestrial habitats. Yet, we lack an integrative conceptual framework for understanding the patterns and mechanisms driving soil biodiversity. One of the underlying reasons for our poor understanding of soil biodiversity patterns relates to whether key biodiversity theories (historically developed for aboveground and aquatic organisms) are applicable to patterns of soil biodiversity. Here, we present a systematic literature review to investigate whether and how key biodiversity theories (species-energy relationship, theory of island biogeography, metacommunity theory, niche theory and neutral theory) can explain observed patterns of soil biodiversity. We then discuss two spatial compartments nested within soil at which biodiversity theories can be applied to acknowledge the scale-dependent nature of soil biodiversity.
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Affiliation(s)
- Madhav P. Thakur
- Department of Terrestrial EcologyNetherlands Institute of Ecology (NIOO‐KNAW)WageningenGelderland, The Netherlands
- German Centre for Integrative Biodiversity Research (iDiv), Halle‐Jena‐LeipzigLeipzigSaxony, Germany
- Institute of Biology, Leipzig UniversityLeipzigSaxony, Germany
| | - Helen R. P. Phillips
- German Centre for Integrative Biodiversity Research (iDiv), Halle‐Jena‐LeipzigLeipzigSaxony, Germany
| | - Ulrich Brose
- German Centre for Integrative Biodiversity Research (iDiv), Halle‐Jena‐LeipzigLeipzigSaxony, Germany
- Institute of Biodiversity, Friedrich Schiller University JenaJenaThuringia, Germany
| | - Franciska T. De Vries
- School of Earth and Environmental Sciences, The University of ManchesterManchesterNorth West England, UK
| | | | - Michel Loreau
- Centre for Biodiversity Theory and Modelling, Theoretical and Experimental Ecology Station, CNRS and Paul Sabatier UniversityMoulisOccitanie, France
| | - Jerome Mathieu
- Sorbonne Université, CNRS, UPECParisÎle-de-France, France
| | - Christian Mulder
- Department BiologicalGeological and Environmental Sciences, University of CataniaCataniaSicily, Italy
| | - Wim H. Van der Putten
- Department of Terrestrial EcologyNetherlands Institute of Ecology (NIOO‐KNAW)WageningenGelderland, The Netherlands
- Laboratory of NematologyWageningen UniversityWageningenGelderland, The Netherlands
| | - Matthias C. Rillig
- Freie Universität Berlin, Institute of BiologyBerlinGermany
- Berlin‐Brandenburg Institute of Advanced Biodiversity Research (BBIB)BerlinGermany
| | - David A. Wardle
- Asian School for the Environment, Nanyang Technological UniversitySingaporeSingapore
| | - Elizabeth M. Bach
- Department of Biology and School of Global Environmental SustainabilityColorado State UniversityFort CollinsCOUSA
| | - Marie L. C. Bartz
- Center of Functional Ecology, Department of Life SciencesUniversity of CoimbraCoimbraCentro, Portugal
- Universidade Positivo, Rua Professor Pedro Viriato Parigot de SouzaCuritiba Paraná, Brazil
| | - Joanne M. Bennett
- German Centre for Integrative Biodiversity Research (iDiv), Halle‐Jena‐LeipzigLeipzigSaxony, Germany
- Institute of Biology, Martin Luther University Halle‐WittenbergHalle (Saale)Saxony-Anhalt, Germany
| | - Maria J. I. Briones
- Departamento de Ecología y Biología AnimalUniversidad de VigoVigoGalicien, Spain
| | | | - Thibaud Decaëns
- Centre d'Ecologie Fonctionnelle et Evolutive (CEFE UMR 5175, CNRS–Université de Montpellier–Université Paul‐Valéry Montpellier–EPHE)MontpellierOccitanie, France
| | - Nico Eisenhauer
- German Centre for Integrative Biodiversity Research (iDiv), Halle‐Jena‐LeipzigLeipzigSaxony, Germany
- Institute of Biology, Leipzig UniversityLeipzigSaxony, Germany
| | - Olga Ferlian
- German Centre for Integrative Biodiversity Research (iDiv), Halle‐Jena‐LeipzigLeipzigSaxony, Germany
- Institute of Biology, Leipzig UniversityLeipzigSaxony, Germany
| | - Carlos António Guerra
- German Centre for Integrative Biodiversity Research (iDiv), Halle‐Jena‐LeipzigLeipzigSaxony, Germany
- Institute of Biology, Martin Luther University Halle‐WittenbergHalle (Saale)Saxony-Anhalt, Germany
| | - Birgitta König‐Ries
- German Centre for Integrative Biodiversity Research (iDiv), Halle‐Jena‐LeipzigLeipzigSaxony, Germany
- Institute of Computer Science, Friedrich Schiller University JenaJenaThuringia, Germany
| | - Alberto Orgiazzi
- European Commission, Joint Research Centre (JRC), Sustainable Resources DirectorateIspraVareseItaly
| | - Kelly S. Ramirez
- Department of Terrestrial EcologyNetherlands Institute of Ecology (NIOO‐KNAW)WageningenGelderland, The Netherlands
| | - David J. Russell
- Senckenberg Museum of Natural History GörlitzGoerlitzSaxony, Germany
| | - Michiel Rutgers
- National Institute for Public Health and the EnvironmentBilthovenUtrecht, The Netherlands
| | - Diana H. Wall
- Department of Biology and School of Global Environmental SustainabilityColorado State UniversityFort CollinsCOUSA
| | - Erin K. Cameron
- Faculty of Biological and Environmental SciencesUniversity of HelsinkiHelsinki, Uusimaa, Finland
- Department of Environmental ScienceSaint Mary's UniversityHalifaxNova ScotiaCanada
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Zhang E, Thibaut LM, Terauds A, Raven M, Tanaka MM, van Dorst J, Wong SY, Crane S, Ferrari BC. Lifting the veil on arid-to-hyperarid Antarctic soil microbiomes: a tale of two oases. MICROBIOME 2020; 8:37. [PMID: 32178729 PMCID: PMC7076931 DOI: 10.1186/s40168-020-00809-w] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/25/2019] [Accepted: 02/20/2020] [Indexed: 06/10/2023]
Abstract
BACKGROUND Resident soil microbiota play key roles in sustaining the core ecosystem processes of terrestrial Antarctica, often involving unique taxa with novel functional traits. However, the full scope of biodiversity and the niche-neutral processes underlying these communities remain unclear. In this study, we combine multivariate analyses, co-occurrence networks and fitted species abundance distributions on an extensive set of bacterial, micro-eukaryote and archaeal amplicon sequencing data to unravel soil microbiome patterns of nine sites across two east Antarctic regions, the Vestfold Hills and Windmill Islands. To our knowledge, this is the first microbial biodiversity report on the hyperarid Vestfold Hills soil environment. RESULTS Our findings reveal distinct regional differences in phylogenetic composition, abundance and richness amongst microbial taxa. Actinobacteria dominated soils in both regions, yet Bacteroidetes were more abundant in the Vestfold Hills compared to the Windmill Islands, which contained a high abundance of novel phyla. However, intra-region comparisons demonstrate greater homogeneity of soil microbial communities and measured environmental parameters between sites at the Vestfold Hills. Community richness is largely driven by a variable suite of parameters but robust associations between co-existing members highlight potential interactions and sharing of niche space by diverse taxa from all three microbial domains of life examined. Overall, non-neutral processes appear to structure the polar soil microbiomes studied here, with niche partitioning being particularly strong for bacterial communities at the Windmill Islands. Eukaryotic and archaeal communities reveal weaker niche-driven signatures accompanied by multimodality, suggesting the emergence of neutrality. CONCLUSION We provide new information on assemblage patterns, environmental drivers and non-random occurrences for Antarctic soil microbiomes, particularly the Vestfold Hills, where basic diversity, ecology and life history strategies of resident microbiota are largely unknown. Greater understanding of these basic ecological concepts is a pivotal step towards effective conservation management.
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Affiliation(s)
- Eden Zhang
- School of Biotechnology and Biomolecular Sciences, University of New South Wales, Sydney, 2052, Australia
| | - Loïc M Thibaut
- School of Biotechnology and Biomolecular Sciences, University of New South Wales, Sydney, 2052, Australia
| | - Aleks Terauds
- Australian Antarctic Division, Department of Environment, Antarctic Conservation and Management, 203 Channel Highway, Kingston, TAS, 7050, Australia
| | - Mark Raven
- Commonwealth Scientific and Industrial Research Organisation, Mineralogical Services, Urrbrae, SA, 5064, Australia
| | - Mark M Tanaka
- School of Biotechnology and Biomolecular Sciences, University of New South Wales, Sydney, 2052, Australia
| | - Josie van Dorst
- School of Biotechnology and Biomolecular Sciences, University of New South Wales, Sydney, 2052, Australia
| | - Sin Yin Wong
- School of Biotechnology and Biomolecular Sciences, University of New South Wales, Sydney, 2052, Australia
| | - Sally Crane
- School of Biotechnology and Biomolecular Sciences, University of New South Wales, Sydney, 2052, Australia
| | - Belinda C Ferrari
- School of Biotechnology and Biomolecular Sciences, University of New South Wales, Sydney, 2052, Australia.
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20
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Rossberg AG, Gaedke U, Kratina P. Dome patterns in pelagic size spectra reveal strong trophic cascades. Nat Commun 2019; 10:4396. [PMID: 31562299 PMCID: PMC6764997 DOI: 10.1038/s41467-019-12289-0] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2018] [Accepted: 08/30/2019] [Indexed: 11/09/2022] Open
Abstract
In ecological communities, especially the pelagic zones of aquatic ecosystems, certain body-size ranges are often over-represented compared to others. Community size spectra, the distributions of community biomass over the logarithmic body-mass axis, tend to exhibit regularly spaced local maxima, called “domes”, separated by steep troughs. Contrasting established theory, we explain these dome patterns as manifestations of top-down trophic cascades along aquatic food chains. Compiling high quality size-spectrum data and comparing these with a size-spectrum model introduced in this study, we test this theory and develop a detailed picture of the mechanisms by which bottom-up and top-down effects interact to generate dome patterns. Results imply that strong top-down trophic cascades are common in freshwater communities, much more than hitherto demonstrated, and may arise in nutrient rich marine systems as well. Transferring insights from the general theory of non-linear pattern formation to domes patterns, we provide new interpretations of past lake-manipulation experiments. An important question in ecology is how much species at higher trophic levels affect lower levels through top-down cascades. Here the authors show through analyses of pelagic size spectra that such cascades are strong in freshwater systems and can also arise in nutrient rich marine systems.
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Affiliation(s)
- Axel G Rossberg
- School of Biological and Chemical Sciences, Queen Mary University of London, Mile End Rd, London, E1 4NS, UK. .,Centre for Environment, Fisheries and Aquaculture Science (Cefas), Pakefield Rd, Lowestoft, NR33 0HT, UK. .,International Initiative for Theoretical Ecology, Unit 10, 317 Essex Road, London, N1 2EE, UK.
| | - Ursula Gaedke
- Department of Ecology and Ecosystem Modeling, Institute for Biochemistry and Biology, University of Potsdam, Am Neuen Palais 10, 14469, Potsdam, Germany
| | - Pavel Kratina
- School of Biological and Chemical Sciences, Queen Mary University of London, Mile End Rd, London, E1 4NS, UK.
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Abstract
We propose four postulates as the minimum set of logical propositions necessary for a theory of pulse dynamics and disturbance in ecosystems: (1) resource dynamics characterizes the magnitude, rate, and duration of resource change caused by pulse events, including the continuing changes in resources that are the result of abiotic and biotic processes; (2) energy flux characterizes the energy flow that controls the variation in the rates of resource assimilation across ecosystems; (3) patch dynamics characterizes the distribution of resource patches over space and time, and the resulting patterns of biotic diversity, ecosystem structure, and cross-scale feedbacks of pulses processes; and (4) biotic trait diversity characterizes the evolutionary responses to pulse dynamics and, in turn, the way trait diversity affects ecosystem dynamics during and after pulse events. We apply the four postulates to an important class of pulse events, biomass-altering disturbances, and derive seven generalizations that predict disturbance magnitude, resource trajectory, rate of resource change, disturbance probability, biotic trait diversification at evolutionary scales, biotic diversity at ecological scales, and functional resilience. Ultimately, theory must define the variable combinations that result in dynamic stability, comprising resistance, recovery, and adaptation.
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Affiliation(s)
- Anke Jentsch
- Disturbance EcologyBayreuth Center of Ecology and Environmental Research BayCEER95440 Bayreuth UniversityBayreuthGermany
| | - Peter White
- BiologyUniversity of North Carolina at Chapel HillChapel HillNorth Carolina27561USA
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Reconstructing functional networks in the human intestinal tract using synthetic microbiomes. Curr Opin Biotechnol 2019; 58:146-154. [PMID: 30959425 DOI: 10.1016/j.copbio.2019.03.009] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2019] [Revised: 02/06/2019] [Accepted: 03/04/2019] [Indexed: 12/22/2022]
Abstract
The human intestinal tract harbors one of the most densely populated and open microbial ecosystems. The application of multi-omics approaches has provided insight into a wide array of complex interactions between the various groups of mainly anaerobic colonic microbes as well as the host-microbe dialogue. Integration of multi-omics techniques in cultivation based experiments that vary in complexity from monocultures to synthetic microbial communities identified key metabolic players in the trophic interactions as well as their ecological dynamics. A synergy between these approaches will be of utmost importance to reconstruct the functional interaction networks at the ecosystem level within the human intestinal microbiome. The improved understanding of microbiome functioning at ecosystem level will further aid in developing better predictive models and design of effective microbiome modulation strategies for health benefits.
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Niche Estimation Above and Below the Species Level. Trends Ecol Evol 2019; 34:260-273. [DOI: 10.1016/j.tree.2018.10.012] [Citation(s) in RCA: 91] [Impact Index Per Article: 18.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2018] [Revised: 10/26/2018] [Accepted: 10/29/2018] [Indexed: 11/19/2022]
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D’Andrea R, Riolo M, Ostling AM. Generalizing clusters of similar species as a signature of coexistence under competition. PLoS Comput Biol 2019; 15:e1006688. [PMID: 30668562 PMCID: PMC6358094 DOI: 10.1371/journal.pcbi.1006688] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2018] [Revised: 02/01/2019] [Accepted: 11/30/2018] [Indexed: 12/02/2022] Open
Abstract
Patterns of trait distribution among competing species can potentially reveal the processes that allow them to coexist. It has been recently proposed that competition may drive the spontaneous emergence of niches comprising clusters of similar species, in contrast with the dominant paradigm of greater-than-chance species differences. However, current clustering theory relies largely on heuristic rather than mechanistic models. Furthermore, studies of models incorporating demographic stochasticity and immigration, two key players in community assembly, did not observe clusters. Here we demonstrate clustering under partitioning of resources, partitioning of environmental gradients, and a competition-colonization tradeoff. We show that clusters are robust to demographic stochasticity, and can persist under immigration. While immigration may sustain clusters that are otherwise transient, too much dilutes the pattern. In order to detect and quantify clusters in nature, we introduce and validate metrics which have no free parameters nor require arbitrary trait binning, and weigh species by their abundances rather than relying on a presence-absence count. By generalizing beyond the circumstances where clusters have been observed, our study contributes to establishing them as an update to classical trait patterning theory.
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Affiliation(s)
- Rafael D’Andrea
- Ecology and Evolutionary Biology, University of Michigan, Ann Arbor, Michigan, United States of America
- Plant Biology, University of Illinois, Urbana-Champaign, Illinois, United States of America
| | - Maria Riolo
- Ecology and Evolutionary Biology, University of Michigan, Ann Arbor, Michigan, United States of America
| | - Annette M. Ostling
- Ecology and Evolutionary Biology, University of Michigan, Ann Arbor, Michigan, United States of America
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Klecka J, Hadrava J, Biella P, Akter A. Flower visitation by hoverflies (Diptera: Syrphidae) in a temperate plant-pollinator network. PeerJ 2018; 6:e6025. [PMID: 30533311 PMCID: PMC6282941 DOI: 10.7717/peerj.6025] [Citation(s) in RCA: 36] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2018] [Accepted: 10/25/2018] [Indexed: 11/20/2022] Open
Abstract
Hoverflies (Diptera: Syrphidae) are among the most important pollinators, although they attract less attention than bees. They are usually thought to be rather opportunistic flower visitors, although previous studied demonstrated that they show colour preferences and their nectar feeding is affected by morphological constraints related to flower morphology. Despite the growing appreciation of hoverflies and other non-bee insects as pollinators, there is a lack of community-wide studies of flower visitation by syrphids. The aim of this paper is to provide a detailed analysis of flower visitation patterns in a species rich community of syrphids in a Central European grassland and to evaluate how species traits shape the structure of the plant-hoverfly flower visitation network. We found that different species varied in the level of specialisation, and while some species visited a similar spectre of flowers, others partitioned resources more strongly. There was a consistent difference in both specialisation and flower preferences between three syrphid subfamilies. Eristalinae and Pipizinae were more specialised than Syrphinae. Trait-based analyses showed that relative flower visitation (i) increased with plant height, but most strongly in Eristalinae; (ii) increased with inflorescence size in small species from all three subfamilies, but was independent of inflorescence size in large species of Eristalinae and Syrphinae; and (iii) depended on flower colour, but in a subfamily-specific way. Eristalinae showed the strongest flower colour preferences for white flowers, Pipizinae visited mostly white and yellow flowers, while Syrphinae were less affected by flower colour. Exploration of the structure of the plant-hoverfly flower visitation network showed that the network was both modular and nested. We also found that there were almost no differences in specialisation and relative visitation frequency between males and females. Overall, we showed that flower visitation in syrphids was affected by phylogenetic relatedness, body size of syrphids and several plant traits.
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Affiliation(s)
- Jan Klecka
- Czech Academy of Sciences, Biology Centre, Institute of Entomology, České Budějovice, Czech Republic
| | - Jiří Hadrava
- Czech Academy of Sciences, Biology Centre, Institute of Entomology, České Budějovice, Czech Republic
- Department of Zoology, Faculty of Science, Charles University, Prague, Czech Republic
| | - Paolo Biella
- Czech Academy of Sciences, Biology Centre, Institute of Entomology, České Budějovice, Czech Republic
- Department of Zoology, Faculty of Science, University of South Bohemia, České Budějovice, Czech Republic
| | - Asma Akter
- Czech Academy of Sciences, Biology Centre, Institute of Entomology, České Budějovice, Czech Republic
- Department of Zoology, Faculty of Science, University of South Bohemia, České Budějovice, Czech Republic
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26
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Global dynamics of a mutualism–competition model with one resource and multiple consumers. J Math Biol 2018; 78:683-710. [DOI: 10.1007/s00285-018-1288-9] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2017] [Revised: 08/15/2018] [Indexed: 10/28/2022]
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