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Terry JCD, O'Sullivan JD, Rossberg AG. Schrödinger's Range-Shifting Cat: How Skewed Temperature Dependence Impacts Persistence with Climate Change. Am Nat 2024; 203:161-173. [PMID: 38306288 DOI: 10.1086/728002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2024]
Abstract
AbstractThe majority of species display strongly asymmetric responses to climatic variables, yet most analytic models used to investigate how species will respond to climate change assume symmetric responses, with largely unknown consequences. Applying a known mapping of population dynamical equations onto corresponding well-studied problems from quantum mechanics, we extend analytical results to incorporate this asymmetry. We derive expressions in terms of parameters representing climate velocity, dispersal rate, maximum growth rate, niche width, high-frequency climate variability, and environmental performance curve skew for three key responses: (1) population persistence, (2) lag between range displacement and climate displacement, and (3) location of maximum population sensitivity. We find that asymmetry impacts these climate change responses, but surprisingly, under our model assumptions, the direction (i.e., warm skewed or cool skewed) of performance curve asymmetry does not strongly contribute to either persistence or lags. Conservation measures to support range-shifting populations may have most benefit near their environmental optimum or where the environmental dependence is shallow, irrespective of whether this is the leading or trailing edge. A metapopulation simulation corroborates our results. Our results shed fresh light on how key features of a species' environmental performance curve can impact its response to climate change.
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2
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Atkinson A, Rossberg AG, Gaedke U, Sprules G, Heneghan RF, Batziakas S, Grigoratou M, Fileman E, Schmidt K, Frangoulis C. Steeper size spectra with decreasing phytoplankton biomass indicate strong trophic amplification and future fish declines. Nat Commun 2024; 15:381. [PMID: 38195697 PMCID: PMC10776571 DOI: 10.1038/s41467-023-44406-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2023] [Accepted: 12/12/2023] [Indexed: 01/11/2024] Open
Abstract
Under climate change, model ensembles suggest that declines in phytoplankton biomass amplify into greater reductions at higher trophic levels, with serious implications for fisheries and carbon storage. However, the extent and mechanisms of this trophic amplification vary greatly among models, and validation is problematic. In situ size spectra offer a novel alternative, comparing biomass of small and larger organisms to quantify the net efficiency of energy transfer through natural food webs that are already challenged with multiple climate change stressors. Our global compilation of pelagic size spectrum slopes supports trophic amplification empirically, independently from model simulations. Thus, even a modest (16%) decline in phytoplankton this century would magnify into a 38% decline in supportable biomass of fish within the intensively-fished mid-latitude ocean. We also show that this amplification stems not from thermal controls on consumers, but mainly from temperature or nutrient controls that structure the phytoplankton baseline of the food web. The lack of evidence for direct thermal effects on size structure contrasts with most current thinking, based often on more acute stress experiments or shorter-timescale responses. Our synthesis of size spectra integrates these short-term dynamics, revealing the net efficiency of food webs acclimating and adapting to climatic stressors.
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Affiliation(s)
- Angus Atkinson
- Plymouth Marine Laboratory, Prospect Place, The Hoe, Plymouth, PL13DH, UK.
| | - Axel G Rossberg
- School of Biological and Behavioural Sciences, Queen Mary University of London, Mile End Road, London, E1 4NS, UK
| | - Ursula Gaedke
- Institute of Biochemistry and Biology, University of Potsdam, 14469, Potsdam, Germany
| | - Gary Sprules
- Department of Biology, University of Toronto Mississauga, 3359 Mississauga Rd. N., Mississauga, ON, L5L 1C6, Canada
| | - Ryan F Heneghan
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD, Australia
| | - Stratos Batziakas
- Hellenic Centre for Marine Research, Former U.S. Base at Gournes, P.O. Box 2214, Heraklion GR-71003, Crete, Greece
| | | | - Elaine Fileman
- Plymouth Marine Laboratory, Prospect Place, The Hoe, Plymouth, PL13DH, UK
| | - Katrin Schmidt
- University of Plymouth, School of Geography, Earth and Environmental Sciences, Plymouth, PL4 8AA, UK
| | - Constantin Frangoulis
- Hellenic Centre for Marine Research, Former U.S. Base at Gournes, P.O. Box 2214, Heraklion GR-71003, Crete, Greece
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3
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O’Sullivan JD, Terry JCD, Wilson R, Rossberg AG. Community composition exceeds area as a predictor of long-term conservation value. PLoS Comput Biol 2023; 19:e1010804. [PMID: 36716317 PMCID: PMC9946215 DOI: 10.1371/journal.pcbi.1010804] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2022] [Revised: 02/22/2023] [Accepted: 12/09/2022] [Indexed: 02/01/2023] Open
Abstract
Conserving biodiversity often requires deciding which sites to prioritise for protection. Predicting the impact of habitat loss is a major challenge, however, since impacts can be distant from the perturbation in both space and time. Here we study the long-term impacts of habitat loss in a mechanistic metacommunity model. We find that site area is a poor predictor of long-term, regional-scale extinctions following localised perturbation. Knowledge of the compositional distinctness (average between-site Bray-Curtis dissimilarity) of the removed community can markedly improve the prediction of impacts on regional assemblages, even when biotic responses play out at substantial spatial or temporal distance from the initial perturbation. Fitting the model to two empirical datasets, we show that this conclusions holds in the empirically relevant parameter range. Our results robustly demonstrate that site area alone is not sufficient to gauge conservation priorities; analysis of compositional distinctness permits improved prioritisation at low cost.
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Affiliation(s)
- Jacob D. O’Sullivan
- School of Biological and Behavioural Sciences, Queen Mary University of London, London, United Kingdom
- * E-mail:
| | - J. Christopher D. Terry
- School of Biological and Behavioural Sciences, Queen Mary University of London, London, United Kingdom
| | - Ramesh Wilson
- School of Biological and Behavioural Sciences, Queen Mary University of London, London, United Kingdom
| | - Axel G. Rossberg
- School of Biological and Behavioural Sciences, Queen Mary University of London, London, United Kingdom
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4
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Gutiérrez Al‐Khudhairy OU, Rossberg AG. Evolution of prudent predation in complex food webs. Ecol Lett 2022; 25:1055-1074. [PMID: 35229972 PMCID: PMC9540554 DOI: 10.1111/ele.13979] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2021] [Revised: 11/03/2021] [Accepted: 12/17/2021] [Indexed: 01/09/2023]
Abstract
Prudent predators catch sufficient prey to sustain their populations but not as much as to undermine their populations' survival. The idea that predators evolve to be prudent has been dismissed in the 1970s, but the arguments invoked then are untenable in the light of modern evolution theory. The evolution of prudent predation has repeatedly been demonstrated in two-species predator-prey metacommunity models. However, the vigorous population fluctuations that these models predict are not widely observed. Here we show that in complex model food webs prudent predation evolves as a result of consumer-mediated ('apparent') competitive exclusion of resources, which disadvantages aggressive consumers and does not generate such fluctuations. We make testable predictions for empirical signatures of this mechanism and its outcomes. Then we discuss how these predictions are borne out across freshwater, marine and terrestrial ecosystems. Demonstrating explanatory power of evolved prudent predation well beyond the question of predator-prey coexistence, the predicted signatures explain unexpected declines of invasive alien species, the shape of stock-recruitment relations of fish, and the clearance rates of pelagic consumers across the latitudinal gradient and 15 orders of magnitude in body mass. Specific research to further test this theory is proposed.
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Affiliation(s)
| | - Axel G. Rossberg
- School of Biological and Behavioural SciencesQueen Mary University of LondonLondonUK
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5
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Abstract
Turnover of species composition through time is frequently observed in ecosystems. It is often interpreted as indicating the impact of changes in the environment. Continuous turnover due solely to ecological dynamics-species interactions and dispersal-is also known to be theoretically possible; however the prevalence of such autonomous turnover in natural communities remains unclear. Here we demonstrate that observed patterns of compositional turnover and other important macroecological phenomena can be reproduced in large spatially explicit model ecosystems, without external forcing such as environmental change or the invasion of new species into the model. We find that autonomous turnover is triggered by the onset of ecological structural instability-the mechanism that also limits local biodiversity. These results imply that the potential role of autonomous turnover as a widespread and important natural process is underappreciated, challenging assumptions implicit in many observation and management tools. Quantifying the baseline level of compositional change would greatly improve ecological status assessments.
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Affiliation(s)
- Jacob D O'Sullivan
- School of Biological and Chemical Sciences, Queen Mary University of London, London, UK.
| | - J Christopher D Terry
- School of Biological and Chemical Sciences, Queen Mary University of London, London, UK
| | - Axel G Rossberg
- School of Biological and Chemical Sciences, Queen Mary University of London, London, UK
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6
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Rossberg AG. What Are the Fundamental Questions Regarding Evolution in Ecological Networks? Trends Ecol Evol 2020; 35:863-865. [PMID: 32674868 DOI: 10.1016/j.tree.2020.06.004] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2020] [Revised: 06/09/2020] [Accepted: 06/12/2020] [Indexed: 10/23/2022]
Affiliation(s)
- Axel G Rossberg
- School of Biological and Chemical Sciences, Queen Mary University of London, London, UK.
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7
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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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8
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O’Sullivan JD, Knell RJ, Rossberg AG. Metacommunity‐scale biodiversity regulation and the self‐organised emergence of macroecological patterns. Ecol Lett 2019; 22:1428-1438. [DOI: 10.1111/ele.13294] [Citation(s) in RCA: 34] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2018] [Revised: 01/21/2019] [Accepted: 05/05/2019] [Indexed: 01/07/2023]
Affiliation(s)
- Jacob D. O’Sullivan
- School of Biological and Chemical Sciences Queen Mary University of London Mile End Road LondonE1 4NS UK
| | - Robert J. Knell
- School of Biological and Chemical Sciences Queen Mary University of London Mile End Road LondonE1 4NS UK
| | - Axel G. Rossberg
- School of Biological and Chemical Sciences Queen Mary University of London Mile End Road LondonE1 4NS UK
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9
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Rossberg AG, Uusitalo L, Berg T, Zaiko A, Chenuil A, Uyarra MC, Borja A, Lynam CP. Quantitative criteria for choosing targets and indicators for sustainable use of ecosystems. Ecol Indic 2017; 72:215-224. [PMID: 28149199 PMCID: PMC5268354 DOI: 10.1016/j.ecolind.2016.08.005] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/12/2015] [Revised: 08/04/2016] [Accepted: 08/06/2016] [Indexed: 06/06/2023]
Abstract
Wide-ranging, indicator-based assessments of large, complex ecosystems are playing an increasing role in guiding environmental policy and management. An example is the EU's Marine Strategy Framework Directive, which requires Member States to take measures to reach "good environmental status" (GES) in European marine waters. However, formulation of indicator targets consistent with the Directive's high-level policy goal of sustainable use has proven challenging. We develop a specific, quantitative interpretation of the concepts of GES and sustainable use in terms of indicators and associated targets, by sharply distinguishing between current uses to satisfy current societal needs and preferences, and unknown future uses. We argue that consistent targets to safeguard future uses derive from a requirement that any environmental state indicator should recover within a defined time (e.g. 30 years) to its pressure-free range of variation when all pressures are hypothetically removed. Within these constraints, specific targets for current uses should be set. Routes to implementation of this proposal for indicators of fish-community size structure, population size of selected species, eutrophication, impacts of non-indigenous species, and genetic diversity are discussed. Important policy implications are that (a) indicator target ranges, which may be wider than natural ranges, systematically and rationally derive from our proposal; (b) because relevant state indicators tend to respond slowly, corresponding pressures should also be monitored and assessed;
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Affiliation(s)
- Axel G. Rossberg
- Centre for Environment, Fisheries and Aquaculture Science (Cefas), Pakefield Road, Lowestoft NR33 0HT, UK and School of Biological and Chemical Sciences, Queen Mary University of London, 327 Mile End Rd, London E1, UK
| | - Laura Uusitalo
- Marine Research Centre, Finnish Environment Institute (SYKE). Mechelininkatu 34a, P.O. Box 140, FI-00251 Helsinki, Finland
| | - Torsten Berg
- MariLim Aquatic Research GmbH, Heinrich-Wöhlk-Straße 14, 24232 Schönkirchen, Germany
| | - Anastasija Zaiko
- Marine Science and Technology Center, Klaipeda University, H. Manto 84, LT 92294, Klaipeda, Lithuania
| | - Anne Chenuil
- Aix-Marseille Univ, Univ Avignon, CNRS, IRD, IMBE, Marseille, France
| | - María C. Uyarra
- AZTI-Tecnalia, Herrera Kaia, Portualdea s/n, 20100 Pasaia, Spain
| | - Angel Borja
- AZTI-Tecnalia, Herrera Kaia, Portualdea s/n, 20100 Pasaia, Spain
| | - Christopher P. Lynam
- Centre for Environment, Fisheries and Aquaculture Science (Cefas), Pakefield Road, Lowestoft NR33 0HT, UK
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10
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Schipper AM, Belmaker J, de Miranda MD, Navarro LM, Böhning-Gaese K, Costello MJ, Dornelas M, Foppen R, Hortal J, Huijbregts MAJ, Martín-López B, Pettorelli N, Queiroz C, Rossberg AG, Santini L, Schiffers K, Steinmann ZJN, Visconti P, Rondinini C, Pereira HM. Contrasting changes in the abundance and diversity of North American bird assemblages from 1971 to 2010. Glob Chang Biol 2016; 22:3948-3959. [PMID: 27002684 DOI: 10.1111/gcb.13292] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2015] [Accepted: 03/05/2016] [Indexed: 05/04/2023]
Abstract
Although it is generally recognized that global biodiversity is declining, few studies have examined long-term changes in multiple biodiversity dimensions simultaneously. In this study, we quantified and compared temporal changes in the abundance, taxonomic diversity, functional diversity, and phylogenetic diversity of bird assemblages, using roadside monitoring data of the North American Breeding Bird Survey from 1971 to 2010. We calculated 12 abundance and diversity metrics based on 5-year average abundances of 519 species for each of 768 monitoring routes. We did this for all bird species together as well as for four subgroups based on breeding habitat affinity (grassland, woodland, wetland, and shrubland breeders). The majority of the biodiversity metrics increased or remained constant over the study period, whereas the overall abundance of birds showed a pronounced decrease, primarily driven by declines of the most abundant species. These results highlight how stable or even increasing metrics of taxonomic, functional, or phylogenetic diversity may occur in parallel with substantial losses of individuals. We further found that patterns of change differed among the species subgroups, with both abundance and diversity increasing for woodland birds and decreasing for grassland breeders. The contrasting changes between abundance and diversity and among the breeding habitat groups underscore the relevance of a multifaceted approach to measuring biodiversity change. Our findings further stress the importance of monitoring the overall abundance of individuals in addition to metrics of taxonomic, functional, or phylogenetic diversity, thus confirming the importance of population abundance as an essential biodiversity variable.
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Affiliation(s)
- Aafke M Schipper
- Institute for Water and Wetland Research, Department of Environmental Science, Radboud University, PO Box 9010, 6500 GL, Nijmegen, The Netherlands
- Netherlands Environmental Assessment Agency (PBL), PO Box 303, 3720 AH, Bilthoven, The Netherlands
| | - Jonathan Belmaker
- Department of Zoology and the Steinhardt Museum of Natural History, George S. Wise Faculty of Life Sciences, Tel Aviv University, Tel Aviv, 69978, Israel
| | - Murilo Dantas de Miranda
- German Centre for Integrative Biodiversity Research (iDiv), Deutscher Platz 5e, 04103, Leipzig, Germany
- Institute of Biology, Martin Luther University Halle Wittenberg, Am Kirchtor 1, 06108, Halle (Saale), Germany
| | - Laetitia M Navarro
- German Centre for Integrative Biodiversity Research (iDiv), Deutscher Platz 5e, 04103, Leipzig, Germany
- Institute of Biology, Martin Luther University Halle Wittenberg, Am Kirchtor 1, 06108, Halle (Saale), Germany
| | - Katrin Böhning-Gaese
- Senckenberg Biodiversity and Climate Research Centre (BiK-F), Senckenberganlage 25, 60325, Frankfurt (Main), Germany
- Institute for Ecology, Evolution & Diversity, Goethe University Frankfurt, Max von Laue Str. 13, 60439, Frankfurt (Main), Germany
| | - Mark J Costello
- Institute of Marine Science, University of Auckland, Auckland, 1142, New Zealand
| | - Maria Dornelas
- Centre for Biological Diversity, University of St Andrews, St Andrews, KY16 9TH, Scotland
| | - Ruud Foppen
- SOVON Dutch Centre for Field Ornithology, PO Box 6521, 6503 GA, Nijmegen, The Netherlands
- Institute for Water and Wetland Research, Department of Animal Ecology and Physiology, Radboud University, PO Box 9010, 6500 GL, Nijmegen, The Netherlands
| | - Joaquín Hortal
- Department of Biogeography and Global Change, Museo Nacional de Ciencias Naturales (MNCN-CSIC), C/José Gutiérrez Abascal 2, 28006 , Madrid, Spain
| | - Mark A J Huijbregts
- Institute for Water and Wetland Research, Department of Environmental Science, Radboud University, PO Box 9010, 6500 GL, Nijmegen, The Netherlands
- Netherlands Environmental Assessment Agency (PBL), PO Box 303, 3720 AH, Bilthoven, The Netherlands
| | - Berta Martín-López
- Institute of Ethics and Transdisciplinary Sustainability Research, Faculty of Sustainability, Leuphana University of Lüneburg, Scharnhorststrasse 1, 21335, Lüneburg, Germany
| | - Nathalie Pettorelli
- Institute of Zoology, Zoological Society of London, Regent's Park, NW1 4RY, London, UK
| | - Cibele Queiroz
- Stockholm Resilience Centre, Stockholm University, Kräftriket 2B, 10691, Stockholm, Sweden
| | - Axel G Rossberg
- School of Biological and Chemical Sciences, Queen Mary University of London, Mile End Road, London, E1 4NS, UK
| | - Luca Santini
- Global Mammal Assessment Program, Department of Biology and Biotechnologies, Sapienza Università di Roma, Viale dell'Università 32, 00185, Rome, Italy
| | - Katja Schiffers
- Senckenberg Biodiversity and Climate Research Centre (BiK-F), Senckenberganlage 25, 60325, Frankfurt (Main), Germany
| | - Zoran J N Steinmann
- Institute for Water and Wetland Research, Department of Environmental Science, Radboud University, PO Box 9010, 6500 GL, Nijmegen, The Netherlands
| | - Piero Visconti
- UNEP World Conservation Monitoring Centre, 219 Huntingdon Road, Cambridge, CB3 0DL, UK
| | - Carlo Rondinini
- Global Mammal Assessment Program, Department of Biology and Biotechnologies, Sapienza Università di Roma, Viale dell'Università 32, 00185, Rome, Italy
| | - Henrique M Pereira
- German Centre for Integrative Biodiversity Research (iDiv), Deutscher Platz 5e, 04103, Leipzig, Germany
- Institute of Biology, Martin Luther University Halle Wittenberg, Am Kirchtor 1, 06108, Halle (Saale), Germany
- Infraestruturas de Portugal Biodiversity Chair, CIBIO/InBIO, Universidado do Porto, Campus Agrário de Vairão, Rua Padre Armando Quintas 7, 4485-661, Vairão, Portugal
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11
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James A, Plank MJ, Rossberg AG, Beecham J, Emmerson M, Pitchford JW. Constructing Random Matrices to Represent Real Ecosystems. Am Nat 2015; 185:680-92. [DOI: 10.1086/680496] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
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12
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Fung T, Farnsworth KD, Reid DG, Rossberg AG. Impact of biodiversity loss on production in complex marine food webs mitigated by prey-release. Nat Commun 2015; 6:6657. [PMID: 25799523 PMCID: PMC4382996 DOI: 10.1038/ncomms7657] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2014] [Accepted: 02/17/2015] [Indexed: 11/09/2022] Open
Abstract
Public concern over biodiversity loss is often rationalized as a threat to ecosystem functioning, but biodiversity-ecosystem functioning (BEF) relations are hard to empirically quantify at large scales. We use a realistic marine food-web model, resolving species over five trophic levels, to study how total fish production changes with species richness. This complex model predicts that BEF relations, on average, follow simple Michaelis-Menten curves when species are randomly deleted. These are shaped mainly by release of fish from predation, rather than the release from competition expected from simpler communities. Ordering species deletions by decreasing body mass or trophic level, representing 'fishing down the food web', accentuates prey-release effects and results in unimodal relationships. In contrast, simultaneous unselective harvesting diminishes these effects and produces an almost linear BEF relation, with maximum multispecies fisheries yield at ≈40% of initial species richness. These findings have important implications for the valuation of marine biodiversity.
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Affiliation(s)
- Tak Fung
- National University of Singapore, Department of Biological Sciences, 14 Science Drive 4, Singapore 117543, Singapore
| | - Keith D Farnsworth
- Queen's University Belfast, School of Biological Sciences, Belfast BT9 7BL, UK
| | - David G Reid
- Fisheries Science Services, Marine Institute, Rinville, Oranmore, County Galway, Ireland
| | - Axel G Rossberg
- 1] Queen's University Belfast, School of Biological Sciences, Belfast BT9 7BL, UK [2] Centre for Environment, Fisheries and Aquaculture Science (Cefas), Suffolk NR33 0HT, UK
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13
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Affiliation(s)
- Axel G Rossberg
- Centre for Environment, Fisheries and Aquaculture Science (Cefas), , Pakefield Road, Lowestoft NR33 0HT, UK, Department of Mathematical Sciences, University of Bath, , Claverton Down, Bath BA2 7AY, UK, Theoretical Physics Division, School of Physics and Astronomy, University of Manchester, , Manchester M13 9PL, UK
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14
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Abstract
The rapid advance in genetic sequencing technologies has provided an unprecedented amount of data on the biodiversity of meiofauna. It was hoped that these data would allow the identification and counting of species, distinguished as tight clusters of similar genomes. Surprisingly, this appears not to be the case. Here, we begin a theoretical discussion of this phenomenon, drawing on an individual-based ecological model to inform our arguments. The determining factor in the emergence (or not) of distinguishable genetic clusters in the model is the product of population size with mutation rate—a measure of the adaptability of the population as a whole. This result suggests that indeed one should not expect to observe clearly distinguishable species groupings in data gathered from ultrasequencing of meiofauna.
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Affiliation(s)
- Axel G Rossberg
- Centre for Environment, Fisheries and Aquaculture Science, Pakefield Road, Lowestoft NR33 0HT, UK.
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15
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van Leeuwen E, Brännström Å, Jansen VAA, Dieckmann U, Rossberg AG. A generalized functional response for predators that switch between multiple prey species. J Theor Biol 2013; 328:89-98. [PMID: 23422235 DOI: 10.1016/j.jtbi.2013.02.003] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2012] [Revised: 12/21/2012] [Accepted: 02/08/2013] [Indexed: 11/26/2022]
Abstract
We develop a theory for the food intake of a predator that can switch between multiple prey species. The theory addresses empirical observations of prey switching and is based on the behavioural assumption that a predator tends to continue feeding on prey that are similar to the prey it has consumed last, in terms of, e.g., their morphology, defences, location, habitat choice, or behaviour. From a predator's dietary history and the assumed similarity relationship among prey species, we derive a general closed-form multi-species functional response for describing predators switching between multiple prey species. Our theory includes the Holling type II functional response as a special case and makes consistent predictions when populations of equivalent prey are aggregated or split. An analysis of the derived functional response enables us to highlight the following five main findings. (1) Prey switching leads to an approximate power-law relationship between ratios of prey abundance and prey intake, consistent with experimental data. (2) In agreement with empirical observations, the theory predicts an upper limit of 2 for the exponent of such power laws. (3) Our theory predicts deviations from power-law switching at very low and very high prey-abundance ratios. (4) The theory can predict the diet composition of a predator feeding on multiple prey species from diet observations for predators feeding only on pairs of prey species. (5) Predators foraging on more prey species will show less pronounced prey switching than predators foraging on fewer prey species, thus providing a natural explanation for the known difficulties of observing prey switching in the field.
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Affiliation(s)
- E van Leeuwen
- School of Biological Sciences, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK.
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16
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Abstract
We introduce and analyse an individual-based evolutionary model, in which a population of genetically diverse organisms compete with each other for limited resources. Through theoretical analysis and stochastic simulations, we show that the model exhibits a pattern-forming instability which is highly amplified by the effects of demographic noise, leading to the spontaneous formation of genotypic clusters. This mechanism supports the thesis that stochasticity has a central role in the formation and coherence of species.
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Affiliation(s)
- Tim Rogers
- Theoretical Physics Division, School of Physics and Astronomy, The University of Manchester, M13 9PL, UK
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17
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Abstract
Food webs are the complex networks of trophic interactions that stoke the metabolic fires of life. To understand what structures these interactions in natural communities, ecologists have developed simple models to capture their main architectural features. However, apparently realistic food webs can be generated by models invoking either predator-prey body-size hierarchies or evolutionary constraints as structuring mechanisms. As a result, this approach has not conclusively revealed which factors are the most important. Here we cut to the heart of this debate by directly comparing the influence of phylogeny and body size on food web architecture. Using data from 13 food webs compiled by direct observation, we confirm the importance of both factors. Nevertheless, phylogeny dominates in most networks. Moreover, path analysis reveals that the size-independent direct effect of phylogeny on trophic structure typically outweighs the indirect effect that could be captured by considering body size alone. Furthermore, the phylogenetic signal is asymmetric: closely related species overlap in their set of consumers far more than in their set of resources. This is at odds with several food web models, which take only the view-point of consumers when assigning interactions. The echo of evolutionary history clearly resonates through current food webs, with implications for our theoretical models and conservation priorities.
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Affiliation(s)
- Russell E Naisbit
- Unit of Ecology and Evolution, Department of Biology, University of Fribourg, Chemin du Musée 10, 1700 Fribourg, Switzerland
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Mulder C, Boit A, Mori S, Vonk JA, Dyer SD, Faggiano L, Geisen S, González AL, Kaspari M, Lavorel S, Marquet PA, Rossberg AG, Sterner RW, Voigt W, Wall DH. Distributional (In)Congruence of Biodiversity–Ecosystem Functioning. ADV ECOL RES 2012. [DOI: 10.1016/b978-0-12-396992-7.00001-0] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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Rossberg AG, Farnsworth KD, Satoh K, Pinnegar JK. Universal power-law diet partitioning by marine fish and squid with surprising stability-diversity implications. Proc Biol Sci 2010; 278:1617-25. [PMID: 21068048 DOI: 10.1098/rspb.2010.1483] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
A central question in community ecology is how the number of trophic links relates to community species richness. For simple dynamical food-web models, link density (the ratio of links to species) is bounded from above as the number of species increases; but empirical data suggest that it increases without bounds. We found a new empirical upper bound on link density in large marine communities with emphasis on fish and squid, using novel methods that avoid known sources of bias in traditional approaches. Bounds are expressed in terms of the diet-partitioning function (DPF): the average number of resources contributing more than a fraction f to a consumer's diet, as a function of f. All observed DPF follow a functional form closely related to a power law, with power-law exponents independent of species richness at the measurement accuracy. Results imply universal upper bounds on link density across the oceans. However, the inherently scale-free nature of power-law diet partitioning suggests that the DPF itself is a better defined characterization of network structure than link density.
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Abstract
A question central to modelling and, ultimately, managing food webs concerns the dimensionality of trophic niche space, that is, the number of independent traits relevant for determining consumer-resource links. Food-web topologies can often be interpreted by assuming resource traits to be specified by points along a line and each consumer's diet to be given by resources contained in an interval on this line. This phenomenon, called intervality, has been known for 30 years and is widely acknowledged to indicate that trophic niche space is close to one-dimensional. We show that the degrees of intervality observed in nature can be reproduced in arbitrary-dimensional trophic niche spaces, provided that the processes of evolutionary diversification and adaptation are taken into account. Contrary to expectations, intervality is least pronounced at intermediate dimensions and steadily improves towards lower- and higher-dimensional trophic niche spaces.
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Mulder C, Den Hollander HA, Vonk JA, Rossberg AG, op Akkerhuis GAJMJ, Yeates GW. Soil resource supply influences faunal size-specific distributions in natural food webs. Naturwissenschaften 2009; 96:813-26. [PMID: 19440684 PMCID: PMC2705724 DOI: 10.1007/s00114-009-0539-4] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/06/2009] [Revised: 04/06/2009] [Accepted: 04/06/2009] [Indexed: 11/27/2022]
Abstract
The large range of body-mass values of soil organisms provides a tool to assess the ecological organization of soil communities. The goal of this paper is to identify graphical and quantitative indicators of soil community composition and ecosystem functioning, and to illustrate their application to real soil food webs. The relationships between log-transformed mass and abundance of soil organisms in 20 Dutch meadows and heathlands were investigated. Using principles of allometry, maximal use can be made of ecological theory to build and explain food webs. The aggregate contribution of small invertebrates such as nematodes to the entire community is high under low soil phosphorus content and causes shifts in the mass-abundance relationships and in the trophic structures. We show for the first time that the average of the trophic link lengths is a reliable predictor for assessing soil fertility responses. Ordered trophic link pairs suggest a self-organizing structure of food webs according to resource availability and can predict environmental shifts in ecologically meaningful ways.
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Affiliation(s)
- Christian Mulder
- Department of Ecology, National Institute for Public Health and the Environment, Box 1, Bilthoven, 3720 BA, The Netherlands.
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Kumar P, Hiremath US, Yelamaggad CV, Rossberg AG, Krishnamurthy KS. Electroconvection in a Homeotropic Bent-Rod Nematic Liquid Crystal Beyond the Dielectric Inversion Frequency. J Phys Chem B 2008; 112:9753-60. [DOI: 10.1021/jp803798g] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Pramoda Kumar
- Centre for Liquid Crystal Research, P.O. Box 1329, Jalahalli, Bangalore 560 013, India, and EEP, International Institute for Applied Systems Analysis, 2361 Laxenburg, Austria
| | - Uma S. Hiremath
- Centre for Liquid Crystal Research, P.O. Box 1329, Jalahalli, Bangalore 560 013, India, and EEP, International Institute for Applied Systems Analysis, 2361 Laxenburg, Austria
| | - C. V. Yelamaggad
- Centre for Liquid Crystal Research, P.O. Box 1329, Jalahalli, Bangalore 560 013, India, and EEP, International Institute for Applied Systems Analysis, 2361 Laxenburg, Austria
| | - Axel G. Rossberg
- Centre for Liquid Crystal Research, P.O. Box 1329, Jalahalli, Bangalore 560 013, India, and EEP, International Institute for Applied Systems Analysis, 2361 Laxenburg, Austria
| | - K. S. Krishnamurthy
- Centre for Liquid Crystal Research, P.O. Box 1329, Jalahalli, Bangalore 560 013, India, and EEP, International Institute for Applied Systems Analysis, 2361 Laxenburg, Austria
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Kumar P, Hiremath US, Yelamaggad CV, Rossberg AG, Krishnamurthy KS. Drifting Periodic Structures in a Degenerate-Planar Bent-Rod Nematic Liquid Crystal Beyond the Dielectric Inversion Frequency. J Phys Chem B 2008; 112:9270-4. [DOI: 10.1021/jp804264m] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Pramoda Kumar
- Centre for Liquid Crystal Research, P.O. Box 1329, Jalahalli, Bangalore 560 013, India, and EEP, International Institute for Applied Systems Analysis, 2361 Laxenburg, Austria
| | - Uma S. Hiremath
- Centre for Liquid Crystal Research, P.O. Box 1329, Jalahalli, Bangalore 560 013, India, and EEP, International Institute for Applied Systems Analysis, 2361 Laxenburg, Austria
| | - C. V. Yelamaggad
- Centre for Liquid Crystal Research, P.O. Box 1329, Jalahalli, Bangalore 560 013, India, and EEP, International Institute for Applied Systems Analysis, 2361 Laxenburg, Austria
| | - Axel G. Rossberg
- Centre for Liquid Crystal Research, P.O. Box 1329, Jalahalli, Bangalore 560 013, India, and EEP, International Institute for Applied Systems Analysis, 2361 Laxenburg, Austria
| | - K. S. Krishnamurthy
- Centre for Liquid Crystal Research, P.O. Box 1329, Jalahalli, Bangalore 560 013, India, and EEP, International Institute for Applied Systems Analysis, 2361 Laxenburg, Austria
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Serizawa H, Amemiya T, Enomoto T, Rossberg AG, Itoh K. Mathematical modeling of colony formation in algal blooms: phenotypic plasticity in cyanobacteria. Ecol Res 2007. [DOI: 10.1007/s11284-007-0447-z] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Amemiya T, Enomoto T, Rossberg AG, Yamamoto T, Inamori Y, Itoh K. Stability and dynamical behavior in a lake-model and implications for regime shifts in real lakes. Ecol Modell 2007. [DOI: 10.1016/j.ecolmodel.2007.03.019] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Rossberg AG, Matsuda H, Amemiya T, Itoh K. Food webs: Experts consuming families of experts. J Theor Biol 2006; 241:552-63. [PMID: 16466654 DOI: 10.1016/j.jtbi.2005.12.021] [Citation(s) in RCA: 74] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2005] [Revised: 12/21/2005] [Accepted: 12/24/2005] [Indexed: 10/25/2022]
Abstract
Food webs of habitats as diverse as lakes or desert valleys are known to exhibit common "food-web patterns", but the detailed mechanisms generating these structures have remained unclear. By employing a stochastic, dynamical model, we show that many aspects of the structure of predatory food webs can be understood as the traces of an evolutionary history where newly evolving species avoid direct competition with their relatives. The tendency to avoid sharing natural enemies (apparent competition) with related species is considerably weaker. Thus, "experts consuming families of experts" can be identified as the main underlying food-web pattern. We report the results of a systematic, quantitative model validation showing that the model is surprisingly accurate.
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Affiliation(s)
- A G Rossberg
- Yokohama National University, Graduate School of Environment and Information Sciences, Yokohama 240-8501, Japan.
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Rossberg AG, Yanagi K, Amemiya T, Itoh K. Estimating trophic link density from quantitative but incomplete diet data. J Theor Biol 2006; 243:261-72. [PMID: 16890962 DOI: 10.1016/j.jtbi.2006.06.019] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2006] [Revised: 06/14/2006] [Accepted: 06/15/2006] [Indexed: 11/25/2022]
Abstract
The trophic link density and the stability of food webs are thought to be related, but the nature of this relation is controversial. This article introduces a method for estimating the link density from diet tables which do not cover the complete food web and do not resolve all diet items to species level. A simple formula for the error of this estimate is derived. Link density is determined as a function of a threshold diet fraction below which diet items are ignored ("diet partitioning function"). Furthermore, analytic relationships between this threshold-dependent link density and the generality distribution of food webs are established. A preliminary application of the method to field data suggests that empirical results relating link density to diversity might need to be revisited.
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Affiliation(s)
- A G Rossberg
- Yokohama National University, Graduate School of Environment and Information Sciences, Yokohama 240-8501, Japan.
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Tatsumi S, Sano M, Rossberg AG. Observation of stable phase jump lines in convection of a twisted nematic liquid crystal. Phys Rev E Stat Nonlin Soft Matter Phys 2006; 73:011704. [PMID: 16486166 DOI: 10.1103/physreve.73.011704] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2005] [Indexed: 05/06/2023]
Abstract
We report observations of stable, localized, linelike structures in the spatially periodic pattern formed by nematic electroconvection, along which the phase of the pattern jumps by pi. With increasing electric voltage, these lines form a gridlike structure that goes over into a structure indistinguishable from the well-known grid pattern. We present theoretical arguments that suggest that the twisted cell geometry we are using is indirectly stabilizing the phase jump lines, and that the phase jump lines lattice is caused by an interaction of phase jump lines and a zig-zag instability of the surrounding pattern.
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Affiliation(s)
- Soichi Tatsumi
- Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku Tokyo 113-0033, Japan.
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Rossberg AG, Matsuda H, Koike F, Amemiya T, Makino M, Morino M, Kubo T, Shimode S, Nakai S, Katoh M, Shigeoka T, Urano K. A guideline for ecological risk management procedures. Landscape Ecol Eng 2005. [DOI: 10.1007/s11355-005-0018-9] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Rossberg AG, Matsuda H, Amemiya T, Itoh K. Some properties of the speciation model for food-web structure-mechanisms for degree distributions and intervality. J Theor Biol 2005; 238:401-15. [PMID: 16045940 DOI: 10.1016/j.jtbi.2005.05.025] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2005] [Revised: 05/26/2005] [Accepted: 05/31/2005] [Indexed: 10/25/2022]
Abstract
We present a mathematical analysis of the speciation model for food-web structure, which had in previous work been shown to yield a good description of empirical data of food-web topology. The degree distributions of the network are derived. Properties of the speciation model are compared to those of other models that successfully describe empirical data. It is argued that the speciation model unifies the underlying ideas of previous theories. In particular, it offers a mechanistic explanation for the success of the niche model of Williams and Martinez and the frequent observation of intervality in empirical food webs.
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Affiliation(s)
- A G Rossberg
- Yokohama National University, Graduate School of Environment and Information Sciences, Yokohama, Kanagawa 240-8501, Japan.
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Abstract
We present methods for detecting phase synchronization of two unidirectionally coupled, self-sustained noisy oscillators from a signal of the driven oscillator alone. One method detects soft phase locking; another hard phase locking. Both are applied to the problem of detecting phase synchronization in von Kármán vortex flow meters.
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Affiliation(s)
- A G Rossberg
- Center for Data Analysis and Modeling, Albert-Ludwigs-Universität Freiburg, Eckerstr. 1, 79104 Freiburg, Germany
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Rossberg AG, Bartholomé K, Timmer J. Data-driven optimal filtering for phase and frequency of noisy oscillations: Application to vortex flow metering. Phys Rev E Stat Nonlin Soft Matter Phys 2004; 69:016216. [PMID: 14995702 DOI: 10.1103/physreve.69.016216] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2003] [Indexed: 05/24/2023]
Abstract
A method for measuring the phase of oscillations from noisy time series is proposed. To obtain the phase, the signal is filtered in such a way that the filter output has minimal relative variation in the amplitude over all filters with complex-valued impulse response. The argument of the filter output yields the phase. Implementation of the algorithm and interpretation of the result are discussed. We argue that the phase obtained by the proposed method has a low susceptibility to measurement noise and a low rate of artificial phase slips. The method is applied for the detection and classification of mode locking in vortex flow meters. A measure for the strength of mode locking is proposed.
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Affiliation(s)
- A G Rossberg
- Zentrum für Datenanalyse und Modellbildung, Universität Freiburg, Eckerstrasse 1, 79104 Freiburg, Germany.
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Eber N, Németh S, Rossberg AG, Kramer L, Buka A. Magnetic field effect on the thresholds of a sequence of transitions in the electroconvection of a homeotropic nematic liquid crystal. Phys Rev E Stat Nonlin Soft Matter Phys 2002; 66:036213. [PMID: 12366230 DOI: 10.1103/physreve.66.036213] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2002] [Indexed: 05/23/2023]
Abstract
We present a detailed analysis of the characteristics of electroconvection patterns in a homeotropic nematic liquid crystal under the influence of a variable magnetic field. An unambiguous observation of low frequency "reentrant" normal rolls and a nonmonotonic magnetic field dependence of the threshold voltages is reported. The effect of the magnetic field on the normal roll-abnormal roll transition is determined, which is in good agreement with theoretical predictions of the weakly nonlinear analysis.
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Affiliation(s)
- Nándor Eber
- Research Institute for Solid State Physics and Optics, Hungarian Academy of Sciences, Budapest, P.O.B. 49, H-1525 Hungary
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Rossberg AG. Three-dimensional pattern formation, multiple homogeneous soft modes, and nonlinear dielectric electroconvection. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 2000; 62:8114-32. [PMID: 11138097 DOI: 10.1103/physreve.62.8114] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2000] [Indexed: 11/07/2022]
Abstract
Patterns forming spontaneously in extended, three-dimensional, dissipative systems are likely to excite several homogeneous soft modes ( approximately hydrodynamic modes) of the underlying physical system, much more than quasi-one- (1D) and two-dimensional (2D) patterns are. The reason is the lack of damping boundaries. This paper compares two analytic techniques to derive the pattern dynamics from hydrodynamics, which are usually equivalent but lead to different results when applied to multiple homogeneous soft modes. Dielectric electroconvection in nematic liquid crystals is introduced as a model for 3D pattern formation. The 3D pattern dynamics including soft modes are derived. For slabs of large but finite thickness the description is reduced further to a 2D one. It is argued that the range of validity of 2D descriptions is limited to a very small region above threshold. The transition from 2D to 3D pattern dynamics is discussed. Experimentally testable predictions for the stable range of ideal patterns and the electric Nusselt numbers are made. For most results analytic approximations in terms of material parameters are given.
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Affiliation(s)
- AG Rossberg
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
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Rossberg AG. Twist localizes three-dimensional patterns. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 2000; 62:4682-7. [PMID: 11089007 DOI: 10.1103/physreve.62.4682] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2000] [Indexed: 11/07/2022]
Abstract
A mechanism for the localization of spatially periodic, self-organized patterns in anisotropic media which requires systems extended in all three spatial dimensions is presented: When the anisotropy axis is twisted, the pattern becomes localized in planes parallel to the anisotropy axis. An analytical description of the effect is developed, and used to interpret recent experiments in the high-frequency regime of electroconvection by Bohatsch and Stannarius [Phys. Rev. E 60, 5591 (1999)]. The localization width is found to be of the order of magnitude of the geometrical average of the pattern wavelength and the inverse twist.
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Affiliation(s)
- AG Rossberg
- Department of Physics, Kyoto University, 606-8502 Kyoto, Japan
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Rossberg AG, Eber N, Buka A, Kramer L. Abnormal rolls and regular arrays of disclinations in homeotropic electroconvection. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 2000; 61:R25-R28. [PMID: 11046364 DOI: 10.1103/physreve.61.r25] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/1999] [Indexed: 05/23/2023]
Abstract
We present the first quantitative verification of an amplitude description for systems with (nearly) spontaneously broken isotropy, in particular for the recently discovered abnormal-roll states. We also obtain a conclusive picture of the three-dimensional director configuration in a spatial period doubling phenomenon involving disclination loops. The first observation of two Lifshitz frequencies in electroconvection is reported.
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Affiliation(s)
- AG Rossberg
- Department of Physics, Kyoto University, 606-8502 Kyoto, Japan
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Rossberg AG, Hertrich A, Kramer L, Pesch W. Weakly nonlinear theory of pattern-forming systems with spontaneously broken isotropy. Phys Rev Lett 1996; 76:4729-4732. [PMID: 10061366 DOI: 10.1103/physrevlett.76.4729] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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