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Ros V, Roy F, Biroli G, Bunin G, Turner AM. Generalized Lotka-Volterra Equations with Random, Nonreciprocal Interactions: The Typical Number of Equilibria. PHYSICAL REVIEW LETTERS 2023; 130:257401. [PMID: 37418712 DOI: 10.1103/physrevlett.130.257401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2023] [Accepted: 05/31/2023] [Indexed: 07/09/2023]
Abstract
We compute the typical number of equilibria of the generalized Lotka-Volterra equations describing species-rich ecosystems with random, nonreciprocal interactions using the replicated Kac-Rice method. We characterize the multiple-equilibria phase by determining the average abundance and similarity between equilibria as a function of their diversity (i.e., of the number of coexisting species) and of the variability of the interactions. We show that linearly unstable equilibria are dominant, and that the typical number of equilibria differs with respect to the average number.
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Affiliation(s)
- Valentina Ros
- Université Paris-Saclay, CNRS, LPTMS, 91405 Orsay, France
| | - Felix Roy
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Giulio Biroli
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Guy Bunin
- Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Ari M Turner
- Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel
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2
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Bach L, Ram A, Ijaz UZ, Evans TJ, Haydon DT, Lindström J. The Effects of Smoking on Human Pharynx Microbiota Composition and Stability. Microbiol Spectr 2023; 11:e0216621. [PMID: 36786634 PMCID: PMC10101099 DOI: 10.1128/spectrum.02166-21] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2021] [Accepted: 01/16/2023] [Indexed: 02/15/2023] Open
Abstract
The oral microbiota is essential to the health of the host, yet little is known about how it responds to disturbances. We examined the oropharyngeal microbiota of 30 individuals over 40 weeks. As the oropharynx is an important gateway to pathogens, and as smoking is associated with increased incidence and severity of respiratory infections, we compared the microbiota of smokers and nonsmokers to shed light on its potential for facilitating infections. We hypothesized that decreased species diversity, decreased community stability, or increased differences in community structure could facilitate invading pathogens. We found that smoking is associated with reduced alpha diversity, greater differences in community structure, and increased environmental filtering. The effects of short-term perturbations (antibiotic use and participants exhibiting cold symptoms) were also investigated. Antibiotic use had a negative effect on alpha diversity, irrespective of smoking status, and both antibiotic use and cold symptoms were associated with highly unique bacterial communities. A stability analysis of models built from the data indicated that there were no differences in local or global stability in the microbial communities of smokers, compared to nonsmokers, and that their microbiota are equally resistant to species invasions. Results from these models suggest that smoker microbiota are perturbed but characterized by alternative stable states that are as stable and invasion-resistant as are the microbiota of nonsmokers. Smoking is unlikely to increase the risk of infectious disease through the altered composition and ecological function of the microbiota; this is more likely due to the effects of smoking on the local and systemic immune system. IMPORTANCE Smoking is associated with an increased risk of respiratory infections. Hypothetically, the altered community diversity of smokers' pharyngeal microbiota, together with changes in their ecological stability properties, could facilitate their invasion by pathogens. To address this question, we analyzed longitudinal microbiota data of baseline healthy individuals who were either smokers or nonsmokers. While the results indicate reduced biodiversity and increased species turnover in the smokers' pharyngeal microbiota, their ecological stability properties were not different from those of the microbiota of nonsmokers, implying, in ecological terms, that the smokers' microbial communities are not less resistant to invasions. Therefore, the study suggests that the increased propensity of respiratory infections that is seen in smokers is more likely associated with changes in the local and systemic immune system than with ecological changes in the microbial communities.
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Affiliation(s)
- Lydia Bach
- School of Biodiversity, One Health and Veterinary Medicine, University of Glasgow, United Kingdom
| | - Asha Ram
- School of Biodiversity, One Health and Veterinary Medicine, University of Glasgow, United Kingdom
| | - Umer Z. Ijaz
- School of Science and Engineering, University of Glasgow, United Kingdom
| | - Thomas J. Evans
- School of Infection and Immunity, Glasgow Biomedical Research Centre, University of Glasgow, United Kingdom
| | - Daniel T. Haydon
- School of Biodiversity, One Health and Veterinary Medicine, University of Glasgow, United Kingdom
| | - Jan Lindström
- School of Biodiversity, One Health and Veterinary Medicine, University of Glasgow, United Kingdom
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3
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Saeedian M, Pigani E, Maritan A, Suweis S, Azaele S. Effect of delay on the emergent stability patterns in generalized Lotka-Volterra ecological dynamics. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210245. [PMID: 35599557 DOI: 10.1098/rsta.2021.0245] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
Understanding the conditions of feasibility and stability in ecological systems is a major challenge in theoretical ecology. The seminal work of May in 1972 and recent developments based on the theory of random matrices have shown the existence of emergent universal patterns of both stability and feasibility in ecological dynamics. However, only a few studies have investigated the role of delay coupled with population dynamics in the emergence of feasible and stable states. In this work, we study the effects of delay on generalized Loka-Volterra population dynamics of several interacting species in closed ecological environments. First, we investigate the relation between feasibility and stability of the modelled ecological community in the absence of delay and find a simple analytical relation when intra-species interactions are dominant. We then show how, by increasing the time delay, there is a transition in the stability phases of the population dynamics: from an equilibrium state to a stable non-point attractor phase. We calculate analytically the critical delay of that transition and show that it is in excellent agreement with numerical simulations. Finally, following a similar approach to characterizing stability in empirical studies, we investigate the coefficient of variation, which quantifies the magnitude of population fluctuations. We show that in the oscillatory regime induced by the delay, the variability at community level decreases for increasing diversity. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.
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Affiliation(s)
- Meghdad Saeedian
- Dipartimento di Fisica 'G. Galilei', Università di Padova, Via Marzolo 8, 35131 Padova, Italy
- School of Biological Sciences, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
| | - Emanuele Pigani
- Dipartimento di Fisica 'G. Galilei', Università di Padova, Via Marzolo 8, 35131 Padova, Italy
- Stazione Zoologica Anton Dohrn, Villa Comunale, 80121 Naples, Italy
| | - Amos Maritan
- Dipartimento di Fisica 'G. Galilei', Università di Padova, Via Marzolo 8, 35131 Padova, Italy
| | - Samir Suweis
- Dipartimento di Fisica 'G. Galilei', Università di Padova, Via Marzolo 8, 35131 Padova, Italy
- Padova Neuroscience Center, University of Padova, Padova, Italy
| | - Sandro Azaele
- Dipartimento di Fisica 'G. Galilei', Università di Padova, Via Marzolo 8, 35131 Padova, Italy
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4
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Dunn TL, Jones DM, Heaney JH. Cold Entropy: Assessing Individual Differences in Cognitive Adaptability during Cold Stress. ECOLOGICAL PSYCHOLOGY 2022. [DOI: 10.1080/10407413.2022.2055473] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Timothy L. Dunn
- Warfighter Performance Department, Naval Health Research Center
| | - Douglas M. Jones
- Warfighter Performance Department, Naval Health Research Center
- Leidos Inc
| | - Jay H. Heaney
- Warfighter Performance Department, Naval Health Research Center
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5
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Adams MP, Sisson SA, Helmstedt KJ, Baker CM, Holden MH, Plein M, Holloway J, Mengersen KL, McDonald-Madden E. Informing management decisions for ecological networks, using dynamic models calibrated to noisy time-series data. Ecol Lett 2020; 23:607-619. [PMID: 31989772 DOI: 10.1111/ele.13465] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2019] [Revised: 06/13/2019] [Accepted: 12/27/2019] [Indexed: 12/25/2022]
Abstract
Well-intentioned environmental management can backfire, causing unforeseen damage. To avoid this, managers and ecologists seek accurate predictions of the ecosystem-wide impacts of interventions, given small and imprecise datasets, which is an incredibly difficult task. We generated and analysed thousands of ecosystem population time series to investigate whether fitted models can aid decision-makers to select interventions. Using these time-series data (sparse and noisy datasets drawn from deterministic Lotka-Volterra systems with two to nine species, of known network structure), dynamic model forecasts of whether a species' future population will be positively or negatively affected by rapid eradication of another species were correct > 70% of the time. Although 70% correct classifications is only slightly better than an uninformative prediction (50%), this classification accuracy can be feasibly improved by increasing monitoring accuracy and frequency. Our findings suggest that models may not need to produce well-constrained predictions before they can inform decisions that improve environmental outcomes.
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Affiliation(s)
- Matthew P Adams
- School of Earth and Environmental Sciences, The University of Queensland, St Lucia, Qld, 4072, Australia.,Centre for Biodiversity and Conservation Science, The University of Queensland, St Lucia, Qld, 4072, Australia.,ARC Centre of Excellence for Mathematical and Statistical Frontiers, The University of Queensland, St Lucia, Qld, 4072, Australia
| | - Scott A Sisson
- School of Mathematics and Statistics, The University of New South Wales, Sydney, NSW, 2052, Australia
| | - Kate J Helmstedt
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Qld, 4001, Australia.,ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, Qld, 4001, Australia
| | - Christopher M Baker
- Centre for Biodiversity and Conservation Science, The University of Queensland, St Lucia, Qld, 4072, Australia.,School of Mathematical Sciences, Queensland University of Technology, Brisbane, Qld, 4001, Australia.,School of Biological Sciences, The University of Queensland, St Lucia, Qld, 4072, Australia.,CSIRO Ecosystem Sciences, Ecosciences Precinct, Dutton Park, Qld, 4102, Australia.,Centre of Excellence for Environmental Decisions, The University of Queensland, St Lucia, Qld, 4072, Australia
| | - Matthew H Holden
- Centre for Biodiversity and Conservation Science, The University of Queensland, St Lucia, Qld, 4072, Australia.,School of Biological Sciences, The University of Queensland, St Lucia, Qld, 4072, Australia.,Centre of Excellence for Environmental Decisions, The University of Queensland, St Lucia, Qld, 4072, Australia.,Centre for Applications in Natural Resource Mathematics, School of Mathematics and Physics, The University of Queensland, St Lucia, Qld, 4072, Australia
| | - Michaela Plein
- School of Earth and Environmental Sciences, The University of Queensland, St Lucia, Qld, 4072, Australia.,Centre for Biodiversity and Conservation Science, The University of Queensland, St Lucia, Qld, 4072, Australia.,Administration de la Nature et des Forêts, 6, rue de la Gare, 6731, Grevenmacher, Luxembourg
| | - Jacinta Holloway
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Qld, 4001, Australia.,ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, Qld, 4001, Australia
| | - Kerrie L Mengersen
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Qld, 4001, Australia.,ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, Qld, 4001, Australia
| | - Eve McDonald-Madden
- School of Earth and Environmental Sciences, The University of Queensland, St Lucia, Qld, 4072, Australia.,Centre for Biodiversity and Conservation Science, The University of Queensland, St Lucia, Qld, 4072, Australia.,Centre of Excellence for Environmental Decisions, The University of Queensland, St Lucia, Qld, 4072, Australia
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6
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Brechtel A, Gross T, Drossel B. Far-ranging generalist top predators enhance the stability of meta-foodwebs. Sci Rep 2019; 9:12268. [PMID: 31439912 PMCID: PMC6706381 DOI: 10.1038/s41598-019-48731-y] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2019] [Accepted: 08/12/2019] [Indexed: 11/08/2022] Open
Abstract
Identifying stabilizing factors in foodwebs is a long standing challenge with wide implications for community ecology and conservation. Here, we investigate the stability of spatially resolved meta-foodwebs with far-ranging super-predators for whom the whole meta-foodwebs appears to be a single habitat. By using a combination of generalized modeling with a master stability function approach, we are able to efficiently explore the asymptotic stability of large classes of realistic many-patch meta-foodwebs. We show that meta-foodwebs with far-ranging top predators are more stable than those with localized top predators. Moreover, adding far-ranging generalist top predators to a system can have a net stabilizing effect. These results highlight the importance of top predator conservation.
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Affiliation(s)
- Andreas Brechtel
- Technische Universität Darmstadt, Institute for condensed matter physics, Hochschulstr. 6, Darmstadt, 64289, Germany.
| | - Thilo Gross
- UC Davis, Department of Computer Science, 1 Shields Av, Davis, Ca, 95616, USA
| | - Barbara Drossel
- Technische Universität Darmstadt, Institute for condensed matter physics, Hochschulstr. 6, Darmstadt, 64289, Germany
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7
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Wang S, Brose U, Gravel D. Intraguild predation enhances biodiversity and functioning in complex food webs. Ecology 2019; 100:e02616. [PMID: 30636279 DOI: 10.1002/ecy.2616] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 06/08/2018] [Revised: 10/18/2018] [Accepted: 12/20/2018] [Indexed: 11/09/2022]
Abstract
Intraguild predation (IGP), that is, feeding interaction between two consumers that share the same resource species, is commonly observed in natural food webs. IGP expands vertical niche space and slows down energy flows from lower to higher trophic levels, which potentially affects the diversity and dynamics of food webs. Here, we use food-web models to investigate the effects of IGP on species diversity and ecosystem functioning. We first simulate a five-species food-web module with different strengths of IGP at the herbivore and/or carnivore level. Results show that as the strength of IGP within a trophic level increases, the biomass of its resource level increases because of predation release; this increased biomass in turn alters the energy fluxes and biomass of other trophic levels. These results are then extended by subsequent simulations of more diverse food webs. As the strength of IGP increases, simulated food webs maintain (1) higher species diversity at different trophic levels, (2) higher total biomasses at different trophic levels, and (3) larger energy fluxes across trophic levels. Our results challenge the intuitive hypothesis that food-web structure should maximize the efficiency of energy transfer across trophic levels; instead, they suggest that the assembly of food webs should be governed by a balance between efficiency (of energy transfer) and persistence (i.e., the maintenance of species and biomasses). Our simulations also show that the relationship between biodiversity and ecosystem functioning (e.g., total biomass or primary production) is much stronger in the presence of IGP, reconciling the contrast from recent studies based on food-chain and food-web models. Our findings shed new light on the functional role of IGP and contribute to resolving the debate on structure, diversity and functioning in complex food webs.
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Affiliation(s)
- Shaopeng Wang
- Institute of Ecology, College of Urban and Environmental Sciences, and Key Laboratory for Earth Surface Processes of the Ministry of Education, Peking University, Bejing, 100871, China
| | - Ulrich Brose
- EcoNetLab, German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig, 04103, Germany.,Institute of Biodiversity, Friedrich Schiller University Jena, 07743, Germany
| | - Dominique Gravel
- Département de Biologie, Universite de Sherbrooke, Sherbrooke, Québec, J1K 2R1, Canada
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8
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Yang Q, Fowler MS, Jackson AL, Donohue I. The predictability of ecological stability in a noisy world. Nat Ecol Evol 2019; 3:251-259. [DOI: 10.1038/s41559-018-0794-x] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2018] [Accepted: 12/20/2018] [Indexed: 02/01/2023]
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9
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Galla T. Dynamically evolved community size and stability of random Lotka-Volterra ecosystems
(a). ACTA ACUST UNITED AC 2018. [DOI: 10.1209/0295-5075/123/48004] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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10
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Zholtkevych GN, Nosov KV, Bespalov YG, Rak LI, Abhishek M, Vysotskaya EV. Descriptive Modeling of the Dynamical Systems and Determination of Feedback Homeostasis at Different Levels of Life Organization. Acta Biotheor 2018; 66:177-199. [PMID: 29797159 DOI: 10.1007/s10441-018-9321-3] [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: 11/01/2016] [Accepted: 04/03/2018] [Indexed: 11/29/2022]
Abstract
The state-of-art research in the field of life's organization confronts the need to investigate a number of interacting components, their properties and conditions of sustainable behaviour within a natural system. In biology, ecology and life sciences, the performance of such stable system is usually related to homeostasis, a property of the system to actively regulate its state within a certain allowable limits. In our previous work, we proposed a deterministic model for systems' homeostasis. The model was based on dynamical system's theory and pairwise relationships of competition, amensalism and antagonism taken from theoretical biology and ecology. However, the present paper proposes a different dimension to our previous results based on the same model. In this paper, we introduce the influence of inter-component relationships in a system, wherein the impact is characterized by direction (neutral, positive, or negative) as well as its (absolute) value, or strength. This makes the model stochastic which, in our opinion, is more consistent with real-world elements affected by various random factors. The case study includes two examples from areas of hydrobiology and medicine. The models acquired for these cases enabled us to propose a convincing explanation for corresponding phenomena identified by different types of natural systems.
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Affiliation(s)
- G N Zholtkevych
- V. N. Karazin Kharkiv National University, Svobody sqr., 4, Kharkiv, 61077, Ukraine
| | - K V Nosov
- V. N. Karazin Kharkiv National University, Svobody sqr., 4, Kharkiv, 61077, Ukraine.
| | - Yu G Bespalov
- V. N. Karazin Kharkiv National University, Svobody sqr., 4, Kharkiv, 61077, Ukraine
| | - L I Rak
- V. N. Karazin Kharkiv National University, Svobody sqr., 4, Kharkiv, 61077, Ukraine
| | - M Abhishek
- Robert Gordon University, Aberdeen, AB115AP, UK
| | - E V Vysotskaya
- Kharkiv National University of Radio Electronics, Nauky ave., 14, Kharkiv, 61166, Ukraine
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11
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Douda J, Doudová J, Hulík J, Havrdová A, Boublík K. Reduced competition enhances community temporal stability under conditions of increasing environmental stress. Ecology 2018; 99:2207-2216. [DOI: 10.1002/ecy.2466] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 02/12/2018] [Revised: 06/03/2018] [Accepted: 06/21/2018] [Indexed: 11/11/2022]
Affiliation(s)
- Jan Douda
- Faculty of Environmental Sciences; Czech University of Life Sciences Prague; Kamýcká 129, Praha 6-Suchdol 165 00 Czech Republic
| | - Jana Doudová
- Faculty of Environmental Sciences; Czech University of Life Sciences Prague; Kamýcká 129, Praha 6-Suchdol 165 00 Czech Republic
| | - Josef Hulík
- Faculty of Environmental Sciences; Czech University of Life Sciences Prague; Kamýcká 129, Praha 6-Suchdol 165 00 Czech Republic
| | - Alena Havrdová
- Faculty of Environmental Sciences; Czech University of Life Sciences Prague; Kamýcká 129, Praha 6-Suchdol 165 00 Czech Republic
| | - Karel Boublík
- Faculty of Environmental Sciences; Czech University of Life Sciences Prague; Kamýcká 129, Praha 6-Suchdol 165 00 Czech Republic
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12
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Stone L. The feasibility and stability of large complex biological networks: a random matrix approach. Sci Rep 2018; 8:8246. [PMID: 29844420 PMCID: PMC5974107 DOI: 10.1038/s41598-018-26486-2] [Citation(s) in RCA: 37] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2017] [Accepted: 05/09/2018] [Indexed: 11/24/2022] Open
Abstract
In the 70's, Robert May demonstrated that complexity creates instability in generic models of ecological networks having random interaction matrices A. Similar random matrix models have since been applied in many disciplines. Central to assessing stability is the "circular law" since it describes the eigenvalue distribution for an important class of random matrices A. However, despite widespread adoption, the "circular law" does not apply for ecological systems in which density-dependence operates (i.e., where a species growth is determined by its density). Instead one needs to study the far more complicated eigenvalue distribution of the community matrix S = DA, where D is a diagonal matrix of population equilibrium values. Here we obtain this eigenvalue distribution. We show that if the random matrix A is locally stable, the community matrix S = DA will also be locally stable, providing the system is feasible (i.e., all species have positive equilibria D > 0). This helps explain why, unusually, nearly all feasible systems studied here are locally stable. Large complex systems may thus be even more fragile than May predicted, given the difficulty of assembling a feasible system. It was also found that the degree of stability, or resilience of a system, depended on the minimum equilibrium population.
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Affiliation(s)
- Lewi Stone
- Biomathematics Unit, Faculty of Life Sciences, Tel Aviv University, Ramat Aviv, Israel.
- Mathematical Sciences, Faculty of Science, RMIT University, Melbourne, Australia.
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13
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The Google matrix controls the stability of structured ecological and biological networks. Nat Commun 2016; 7:12857. [PMID: 27687986 PMCID: PMC5056432 DOI: 10.1038/ncomms12857] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/02/2016] [Accepted: 08/09/2016] [Indexed: 11/08/2022] Open
Abstract
May's celebrated theoretical work of the 70's contradicted the established paradigm by demonstrating that complexity leads to instability in biological systems. Here May's random-matrix modelling approach is generalized to realistic large-scale webs of species interactions, be they structured by networks of competition, mutualism or both. Simple relationships are found to govern these otherwise intractable models, and control the parameter ranges for which biological systems are stable and feasible. Our analysis of model and real empirical networks is only achievable on introducing a simplifying Google-matrix reduction scheme, which in the process, yields a practical ecological eigenvalue stability index. These results provide an insight into how network topology, especially connectance, influences species stable coexistence. Constraints controlling feasibility (positive equilibrium populations) in these systems are found more restrictive than those controlling stability, helping explain the enigma of why many classes of feasible ecological models are nearly always stable.
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14
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Gravel D, Massol F, Leibold MA. Stability and complexity in model meta-ecosystems. Nat Commun 2016; 7:12457. [PMID: 27555100 PMCID: PMC4999499 DOI: 10.1038/ncomms12457] [Citation(s) in RCA: 97] [Impact Index Per Article: 12.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2015] [Accepted: 07/05/2016] [Indexed: 11/26/2022] Open
Abstract
The diversity of life and its organization in networks of interacting species has been a long-standing theoretical puzzle for ecologists. Ever since May's provocative paper challenging whether 'large complex systems [are] stable' various hypotheses have been proposed to explain when stability should be the rule, not the exception. Spatial dynamics may be stabilizing and thus explain high community diversity, yet existing theory on spatial stabilization is limited, preventing comparisons of the role of dispersal relative to species interactions. Here we incorporate dispersal of organisms and material into stability-complexity theory. We find that stability criteria from classic theory are relaxed in direct proportion to the number of ecologically distinct patches in the meta-ecosystem. Further, we find the stabilizing effect of dispersal is maximal at intermediate intensity. Our results highlight how biodiversity can be vulnerable to factors, such as landscape fragmentation and habitat loss, that isolate local communities.
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Affiliation(s)
- Dominique Gravel
- Département de biologie, Université de Sherbrooke, 2500 Boul. De l'Université, Sherbrooke, Quebec, Canada J1K 2R1
| | - François Massol
- CNRS, Université de Lille - Sciences et Technologies, UMR 8198 Evo-Eco-Paleo (EEP), SPICI group, F-59655 Villeneuve d'Ascq, France
- UMR 5175 CEFE—Centre d'Ecologie Fonctionnelle et Evolutive (CNRS), 1919 Route de Mende, F-34293 Montpellier, France
| | - Mathew A. Leibold
- Department of Integrative Biology, University of Texas at Austin, Austin, Texas 78712, USA
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15
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Many weak interactions and few strong; food-web feasibility depends on the combination of the strength of species’ interactions and their correct arrangement. THEOR ECOL-NETH 2015. [DOI: 10.1007/s12080-015-0279-3] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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16
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de Mazancourt C, Isbell F, Larocque A, Berendse F, De Luca E, Grace JB, Haegeman B, Wayne Polley H, Roscher C, Schmid B, Tilman D, van Ruijven J, Weigelt A, Wilsey BJ, Loreau M. Predicting ecosystem stability from community composition and biodiversity. Ecol Lett 2013; 16:617-25. [PMID: 23438189 DOI: 10.1111/ele.12088] [Citation(s) in RCA: 213] [Impact Index Per Article: 19.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2012] [Revised: 11/08/2012] [Accepted: 01/15/2013] [Indexed: 11/30/2022]
Abstract
As biodiversity is declining at an unprecedented rate, an important current scientific challenge is to understand and predict the consequences of biodiversity loss. Here, we develop a theory that predicts the temporal variability of community biomass from the properties of individual component species in monoculture. Our theory shows that biodiversity stabilises ecosystems through three main mechanisms: (1) asynchrony in species' responses to environmental fluctuations, (2) reduced demographic stochasticity due to overyielding in species mixtures and (3) reduced observation error (including spatial and sampling variability). Parameterised with empirical data from four long-term grassland biodiversity experiments, our prediction explained 22-75% of the observed variability, and captured much of the effect of species richness. Richness stabilised communities mainly by increasing community biomass and reducing the strength of demographic stochasticity. Our approach calls for a re-evaluation of the mechanisms explaining the effects of biodiversity on ecosystem stability.
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Affiliation(s)
- Claire de Mazancourt
- Redpath Museum, McGill University, 859 Sherbrooke Street West, Montreal, Quebec, H3A 2K6, Canada.
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17
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Loreau M, de Mazancourt C. Biodiversity and ecosystem stability: a synthesis of underlying mechanisms. Ecol Lett 2013; 16 Suppl 1:106-15. [DOI: 10.1111/ele.12073] [Citation(s) in RCA: 611] [Impact Index Per Article: 55.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2012] [Revised: 10/27/2012] [Accepted: 12/13/2012] [Indexed: 11/30/2022]
Affiliation(s)
- Michel Loreau
- Centre for Biodiversity Theory and Modelling; Experimental Ecology Station; Centre National de la Recherche Scientifique; Moulis; 09200; France
| | - Claire de Mazancourt
- Centre for Biodiversity Theory and Modelling; Experimental Ecology Station; Centre National de la Recherche Scientifique; Moulis; 09200; France
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Yeakel JD, Guimarães PR, Novak M, Fox-Dobbs K, Koch PL. Probabilistic patterns of interaction: the effects of link-strength variability on food web structure. J R Soc Interface 2012; 9:3219-28. [PMID: 22832361 DOI: 10.1098/rsif.2012.0481] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Patterns of species interactions affect the dynamics of food webs. An important component of species interactions that is rarely considered with respect to food webs is the strengths of interactions, which may affect both structure and dynamics. In natural systems, these strengths are variable, and can be quantified as probability distributions. We examined how variation in strengths of interactions can be described hierarchically, and how this variation impacts the structure of species interactions in predator-prey networks, both of which are important components of ecological food webs. The stable isotope ratios of predator and prey species may be particularly useful for quantifying this variability, and we show how these data can be used to build probabilistic predator-prey networks. Moreover, the distribution of variation in strengths among interactions can be estimated from a limited number of observations. This distribution informs network structure, especially the key role of dietary specialization, which may be useful for predicting structural properties in systems that are difficult to observe. Finally, using three mammalian predator-prey networks (two African and one Canadian) quantified from stable isotope data, we show that exclusion of link-strength variability results in biased estimates of nestedness and modularity within food webs, whereas the inclusion of body size constraints only marginally increases the predictive accuracy of the isotope-based network. We find that modularity is the consequence of strong link-strengths in both African systems, while nestedness is not significantly present in any of the three predator-prey networks.
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Affiliation(s)
- Justin D Yeakel
- Department of Ecology and Evolutionary Biology, University of California, Santa Cruz, 1156 High Street, Santa Cruz, CA 95064, USA.
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Ruokolainen L, Ripa J. The strength of species interactions modifies population responses to environmental variation in competitive communities. J Theor Biol 2012; 310:199-205. [PMID: 22781554 DOI: 10.1016/j.jtbi.2012.06.035] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2012] [Revised: 06/26/2012] [Accepted: 06/27/2012] [Indexed: 11/17/2022]
Abstract
The life-history parameters of most living organisms are modified by fluctuations in environmental conditions. The impact of environmental autocorrelation on population persistence is well understood in single species systems. However, in multi-species communities the impact of stochasticity is complicated by the possibility of different species having differing intrinsic responses to the environment (environmental correlation). Previous work has shown that whether increasing between-species environmental correlation stabilises population fluctuations or not, depends on an interaction between density-dependence and environmental autocorrelation. Here we derive analytical conditions for how this interaction in turn depends on the strength of interspecific competition. Under relatively weak between-species interactions, increasing environmental autocorrelation always dampens population fluctuations, while increasing autocorrelation destabilises strongly interacting populations. In contrast, under intermediate interaction strengths, increasing autocorrelation destabilises (stabilises) population dynamics when populations respond independently (similarly) to environmental fluctuations. These results apply to a wide range of competitive communities and also have some relevance to consumer-resource systems. The results presented here help us better understand population responses to environmental fluctuations under different conditions.
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Affiliation(s)
- Lasse Ruokolainen
- Department of Biosciences, University of Helsinki, Viikinkaari 1, P. O. Box 65, FI-00014 Helsingin yliopisto, Finland.
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Gravel D, Canard E, Guichard F, Mouquet N. Persistence increases with diversity and connectance in trophic metacommunities. PLoS One 2011; 6:e19374. [PMID: 21637749 PMCID: PMC3103501 DOI: 10.1371/journal.pone.0019374] [Citation(s) in RCA: 69] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2010] [Accepted: 04/04/2011] [Indexed: 11/19/2022] Open
Abstract
BACKGROUND We are interested in understanding if metacommunity dynamics contribute to the persistence of complex spatial food webs subject to colonization-extinction dynamics. We study persistence as a measure of stability of communities within discrete patches, and ask how do species diversity, connectance, and topology influence it in spatially structured food webs. METHODOLOGY/PRINCIPAL FINDINGS We answer this question first by identifying two general mechanisms linking topology of simple food web modules and persistence at the regional scale. We then assess the robustness of these mechanisms to more complex food webs with simulations based on randomly created and empirical webs found in the literature. We find that linkage proximity to primary producers and food web diversity generate a positive relationship between complexity and persistence in spatial food webs. The comparison between empirical and randomly created food webs reveal that the most important element for food web persistence under spatial colonization-extinction dynamics is the degree distribution: the number of prey species per consumer is more important than their identity. CONCLUSIONS/SIGNIFICANCE With a simple set of rules governing patch colonization and extinction, we have predicted that diversity and connectance promote persistence at the regional scale. The strength of our approach is that it reconciles the effect of complexity on stability at the local and the regional scale. Even if complex food webs are locally prone to extinction, we have shown their complexity could also promote their persistence through regional dynamics. The framework we presented here offers a novel and simple approach to understand the complexity of spatial food webs.
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Affiliation(s)
- Dominique Gravel
- Department of Biology, McGill University, Montréal, Quebec, Canada.
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21
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García-López JM, Allué C. Modelling phytoclimatic versatility as a large scale indicator of adaptive capacity to climate change in forest ecosystems. Ecol Modell 2011. [DOI: 10.1016/j.ecolmodel.2011.02.001] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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22
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Vallina SM, Le Quéré C. Stability of complex food webs: Resilience, resistance and the average interaction strength. J Theor Biol 2011; 272:160-73. [DOI: 10.1016/j.jtbi.2010.11.043] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2010] [Revised: 11/25/2010] [Accepted: 11/29/2010] [Indexed: 10/18/2022]
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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] [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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Townsend SE, Haydon DT, Matthews L. On the generality of stability–complexity relationships in Lotka–Volterra ecosystems. J Theor Biol 2010; 267:243-51. [DOI: 10.1016/j.jtbi.2010.08.018] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2009] [Revised: 07/22/2010] [Accepted: 08/06/2010] [Indexed: 11/29/2022]
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Effects of evolutionary changes in prey use on the relationship between food web complexity and stability. POPUL ECOL 2010. [DOI: 10.1007/s10144-010-0212-y] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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27
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Gross T, Rudolf L, Levin SA, Dieckmann U. Generalized Models Reveal Stabilizing Factors in Food Webs. Science 2009; 325:747-50. [PMID: 19661430 DOI: 10.1126/science.1173536] [Citation(s) in RCA: 170] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- Thilo Gross
- Max Planck Institute for Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany.
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Hernandez MJ. Disentangling nature, strength and stability issues in the characterization of population interactions. J Theor Biol 2009; 261:107-19. [PMID: 19589344 DOI: 10.1016/j.jtbi.2009.07.001] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2008] [Revised: 06/30/2009] [Accepted: 07/01/2009] [Indexed: 10/20/2022]
Abstract
Many recent reviews discuss the adequacy of definitions and metrics for the strength of population interactions. However, the discussion on the beneficial or detrimental nature of interactions is clearly absent, or at the most, inadvertently merged into the strength debate. This deficiency is emerging with the increasing interest in theoretical studies of interactions that shift in their nature; e.g. associations that present a mixture of mutualistic and antagonistic aspects, such as pollination; or species with changes in role, such as mutualistic ants that predate on aphid partners. By exploring these models, major controversies are revealed underlying some traditional perspectives: the original Levins'community matrix reformulated into interaction and jacobian matrices, that is, interaction coefficients reinterpreted as partial derivatives, fail to recognize the ecological context of interactions. The 'effect of one species on the other' is not necessarily quantified by 'the effect of varying species densities'; and shifts in the signs of jacobian elements do not correspond to shifts in types of interaction but to stability properties. Thus, the generalised use of these approaches must be revised. On the other hand, the comparison of ultimate performances of populations when growing alone or in association, here referred to as the relative performance approach, conceptually represents the original meaning of the community matrix. This conception, although measured at population levels, is a reflection of properties at the individual level. This article inspects and discusses the formalities and ecological contexts of these approaches to characterization by means of known population interaction models: linear and non-linear, variable and non-variable; aiming to disentangle crucial conceptions that are usually mingled in the literature: the strength (magnitude) and the nature (detrimental or beneficial) of the interaction, which are sometimes used interchangeably, and the stability properties of the system, which have been misleadingly associated with the latter.
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Affiliation(s)
- Maria-Josefina Hernandez
- Laboratorio de Biología Teórica, Instituto de Zoología y Ecología Tropical, Facultad de Ciencias, Universidad Central de Venezuela, Apartado Postal 47058, Los Chaguaramos, Caracas 1041-A, Venezuela.
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Increasing community size and connectance can increase stability in competitive communities. J Theor Biol 2009; 258:179-88. [DOI: 10.1016/j.jtbi.2009.01.010] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2008] [Revised: 11/18/2008] [Accepted: 01/15/2009] [Indexed: 11/20/2022]
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Intrinsic properties of Boolean dynamics in complex networks. J Theor Biol 2009; 256:351-69. [PMID: 19014957 DOI: 10.1016/j.jtbi.2008.10.014] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2008] [Revised: 10/14/2008] [Accepted: 10/14/2008] [Indexed: 11/22/2022]
Abstract
We study intrinsic properties of attractor in Boolean dynamics of complex networks with scale-free topology, comparing with those of the so-called Kauffman's random Boolean networks. We numerically study both frozen and relevant nodes in each attractor in the dynamics of relatively small networks (20<or=N<or=200). We investigate numerically robustness of an attractor to a perturbation. An attractor with cycle length of l(c) in a network of size N consists of l(c) states in the state space of 2(N) states; each attractor has the arrangement of N nodes, where the cycle of attractor sweeps l(c) states. We define a perturbation as a flip of the state on a single node in the attractor state at a given time step. We show that the rate between unfrozen and relevant nodes in the dynamics of a complex network with scale-free topology is larger than that in Kauffman's random Boolean network model. Furthermore, we find that in a complex scale-free network with fluctuation of the in-degree number, attractors are more sensitive to a state flip for a highly connected node (i.e. input-hub node) than to that for a less connected node. By some numerical examples, we show that the number of relevant nodes increases, when an input-hub node is coincident with and/or connected with an output-hub node (i.e. a node with large output-degree) one another.
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Afraimovich V, Tristan I, Huerta R, Rabinovich MI. Winnerless competition principle and prediction of the transient dynamics in a Lotka-Volterra model. CHAOS (WOODBURY, N.Y.) 2008; 18:043103. [PMID: 19123613 DOI: 10.1063/1.2991108] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
Predicting the evolution of multispecies ecological systems is an intriguing problem. A sufficiently complex model with the necessary predicting power requires solutions that are structurally stable. Small variations of the system parameters should not qualitatively perturb its solutions. When one is interested in just asymptotic results of evolution (as time goes to infinity), then the problem has a straightforward mathematical image involving simple attractors (fixed points or limit cycles) of a dynamical system. However, for an accurate prediction of evolution, the analysis of transient solutions is critical. In this paper, in the framework of the traditional Lotka-Volterra model (generalized in some sense), we show that the transient solution representing multispecies sequential competition can be reproducible and predictable with high probability.
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Affiliation(s)
- Valentin Afraimovich
- Instituto de Investigacion en Comunicacion Optica, Universidad Autonoma de San Luis Potosi, Karakorum 1470, Lomas 4a, 78220 San Luis Potosi, S.L.P., Mexico
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Báez S, Collins SL. Shrub invasion decreases diversity and alters community stability in northern Chihuahuan Desert plant communities. PLoS One 2008; 3:e2332. [PMID: 18523686 PMCID: PMC2409219 DOI: 10.1371/journal.pone.0002332] [Citation(s) in RCA: 90] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2008] [Accepted: 04/25/2008] [Indexed: 12/04/2022] Open
Abstract
Background Global climate change is rapidly altering species range distributions and interactions within communities. As ranges expand, invading species change interactions in communities which may reduce stability, a mechanism known to affect biodiversity. In aridland ecosystems worldwide, the range of native shrubs is expanding as they invade and replace native grassland vegetation with significant consequences for biodiversity and ecosystem functioning. Methodology We used two long-term data sets to determine the effects of shrub encroachment by Larrea tridentata on subdominant community composition and stability in formerly native perennial grassland dominated by Bouteloua eriopoda in New Mexico, USA. Principal Findings Our results indicated that Larrea invasion decreased species richness during the last 100 years. We also found that over shorter temporal scales species-poor subdominant communities in areas invaded by Larrea were less stable (more variable in time) compared to species rich communities in grass-dominated vegetation. Compositional stability increased as cover of Bouteloua increased and decreased as cover of Larrea increased. Significance Changes in community stability due to altered interspecific interactions may be one mechanism by which biodiversity declines in grasslands following shrub invasion. As global warming increases, shrub encroachment into native grasslands worldwide will continue to alter species interactions and community stability both of which may lead to a decline in biodiversity.
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Affiliation(s)
- Selene Báez
- Department of Biology, University of New Mexico, Albuquerque, New Mexico, United States of America.
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33
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Christianou M, Kokkoris GD. Complexity does not affect stability in feasible model communities. J Theor Biol 2008; 253:162-9. [PMID: 18407292 DOI: 10.1016/j.jtbi.2008.03.001] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2007] [Revised: 02/19/2008] [Accepted: 03/02/2008] [Indexed: 11/30/2022]
Abstract
The complexity-stability relation is a central issue in ecology. In this paper, we show how the sampling method most often used to parameterize an ecological community, can affect the conclusions about whether or not complexity promotes stability and we suggest a sampling algorithm that overcomes the problem. We also illustrate the importance of treating feasibility separately from stability when constructing model communities. Using model Lotka-Volterra competition communities we found that probability of feasibility decreases with increasing interaction strength and number of species in the community. However, for feasible systems we found that local stability probability and resilience do not significantly differ between communities with few or many species, in contrast with earlier studies that, did not account for feasibility and concluded that species-poor communities had higher probability of being locally stable than species-rich communities.
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Affiliation(s)
- Maria Christianou
- Department of Marine Sciences, Faculty of Environment, University of the Aegean, University Hill, GR81100 Mytilene, Lesvos Island, Greece.
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34
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Calcagno V, Mouquet N, Jarne P, David P. Coexistence in a metacommunity: the competition-colonization trade-off is not dead. Ecol Lett 2006; 9:897-907. [PMID: 16913929 DOI: 10.1111/j.1461-0248.2006.00930.x] [Citation(s) in RCA: 125] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The competition-colonization trade-off model is often used to explain the coexistence of species. Yet its applicability has been severely criticized, mainly because the original model assumed a strict competitive hierarchy of species and did not allow for any preemptive effect. We considered the impact of relaxing both of these limitations on coexistence. Relaxing trade-off intensity makes coexistence less likely and introduces a minimum colonization rate below which any coexistence is impossible. Allowing for preemption introduces a limit to dissimilarity between species. Surprisingly, preemption does not impede coexistence as one could presume from previous studies, but can actually increase the likelihood of coexistence. Its effect on coexistence depends on whether or not species in the regional pool are strongly limited in their colonization ability. Preemption is predicted to favour coexistence when: (i) species are not strongly limited in their colonization ability; and (ii) the competitive trade-off is not infinitely intense.
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Affiliation(s)
- V Calcagno
- ISEM, University of Montpellier II, Montpellier, France.
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38
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Abstract
1. The loss of a species from an ecological community can trigger a cascade of secondary extinctions. Here we investigate how the complexity (connectance) of model communities affects their response to species loss. Using dynamic analysis based on a global criterion of persistence (permanence) and topological analysis we investigate the extent of secondary extinctions following the loss of different kinds of species. 2. We show that complex communities are, on average, more resistant to species loss than simple communities: the number of secondary extinctions decreases with increasing connectance. However, complex communities are more vulnerable to loss of top predators than simple communities. 3. The loss of highly connected species (species with many links to other species) and species at low trophic levels triggers, on average, the largest number of secondary extinctions. The effect of the connectivity of a species is strongest in webs with low connectance. 4. Most secondary extinctions are due to direct bottom-up effects: consumers go extinct when their resources are lost. Secondary extinctions due to trophic cascades and disruption of predator-mediated coexistence also occur. Secondary extinctions due to disruption of predator-mediated coexistence are more common in complex communities than in simple communities, while bottom-up and top-down extinction cascades are more common in simple communities. 5. Topological analysis of the response of communities to species loss always predicts a lower number of secondary extinctions than dynamic analysis, especially in food webs with high connectance.
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Affiliation(s)
- Anna Eklöf
- Department of Biology, IFM, Linköping University, Sweden
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Srivastava DS, Vellend M. Biodiversity-Ecosystem Function Research: Is It Relevant to Conservation? ANNUAL REVIEW OF ECOLOGY EVOLUTION AND SYSTEMATICS 2005. [DOI: 10.1146/annurev.ecolsys.36.102003.152636] [Citation(s) in RCA: 511] [Impact Index Per Article: 26.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Diane S. Srivastava
- Department of Zoology and Biodiversity Research Centre, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z4;
| | - Mark Vellend
- National Center for Ecological Analysis and Synthesis, Santa Barbara, California 93101-3351
- Current address: Departments of Botany and Zoology and Biodiversity Research Centre, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z4;
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Ebenman B, Jonsson T. Using community viability analysis to identify fragile systems and keystone species. Trends Ecol Evol 2005; 20:568-75. [PMID: 16701436 DOI: 10.1016/j.tree.2005.06.011] [Citation(s) in RCA: 92] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2005] [Revised: 06/08/2005] [Accepted: 06/29/2005] [Indexed: 10/25/2022]
Abstract
Owing to interdependences among species in ecological communities, the loss of one species can trigger a cascade of secondary extinctions with potentially dramatic effects on the functioning and stability of the community. It is, therefore, important to assess the risk and likely extent of secondary extinctions. Community viability analysis is a new technique that can be used to accomplish this goal. The analysis can also be used to identify fragile community structures and keystone species and, hence, to provide guidelines for conservation priorities. Here, we describe the principles underlying community viability analysis and review its contributions to our understanding of the response of ecological communities to species loss.
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Affiliation(s)
- Bo Ebenman
- Department of Biology, IFM, Linköping University, SE-58183 Linköping, Sweden.
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Christianou M, Ebenman B. Keystone species and vulnerable species in ecological communities: strong or weak interactors? J Theor Biol 2005; 235:95-103. [PMID: 15833316 DOI: 10.1016/j.jtbi.2004.12.022] [Citation(s) in RCA: 70] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2004] [Revised: 12/21/2004] [Accepted: 12/27/2004] [Indexed: 11/17/2022]
Abstract
The loss of a species from an ecological community can trigger a cascade of secondary extinctions. The probability of secondary extinction to take place and the number of secondary extinctions are likely to depend on the characteristics of the species that is lost--the strength of its interactions with other species--as well as on the distribution of interaction strengths in the whole community. Analysing the effects of species loss in model communities we found that removal of the following species categories triggered, on average, the largest number of secondary extinctions: (a) rare species interacting strongly with many consumers, (b) abundant basal species interacting weakly with their consumers and (c) abundant intermediate species interacting strongly with many resources. We also found that the keystone status of a species with given characteristics was context dependent, that is, dependent on the structure of the community where it was embedded. Species vulnerable to secondary extinctions were mainly species interacting weakly with their resources and species interacting strongly with their consumers.
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Affiliation(s)
- Maria Christianou
- Department of Biology, Theory and Modeling, IFM, Linköping University, Sweden.
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Wilson WG, Lundberg P. Biodiversity and the Lotka-Volterra theory of species interactions: open systems and the distribution of logarithmic densities. Proc Biol Sci 2004; 271:1977-84. [PMID: 15347523 PMCID: PMC1691812 DOI: 10.1098/rspb.2004.2809] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Theoretical interest in the distributions of species abundances observed in ecological communities has focused recently on the results of models that assume all species are identical in their interactions with one another, and rely upon immigration and speciation to promote coexistence. Here we examine a one-trophic level system with generalized species interactions, including species-specific intraspecific and interspecific interaction strengths, and density-independent immigration from a regional species pool. Comparisons between results from numerical integrations and an approximate analytic calculation for random communities demonstrate good agreement, and both approaches yield abundance distributions of nearly arbitrary shape, including bimodality for intermediate immigration rates.
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Ebenman B, Law R, Borrvall C. COMMUNITY VIABILITY ANALYSIS: THE RESPONSE OF ECOLOGICAL COMMUNITIES TO SPECIES LOSS. Ecology 2004. [DOI: 10.1890/03-8018] [Citation(s) in RCA: 98] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Teng J, McCann KS. Dynamics of Compartmented and Reticulate Food Webs in Relation to Energetic Flows. Am Nat 2004; 164:85-100. [PMID: 15266373 DOI: 10.1086/421723] [Citation(s) in RCA: 60] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2003] [Accepted: 03/16/2004] [Indexed: 11/03/2022]
Abstract
Using simple food webs, we address how the interactions of food web structure and energetic flows influence dynamics. We examine the effect of food web topologies with equivalent energetics (i.e., trophic interactions are equivalent at each trophic level), following which we vary energetic flows to include weak and strong interactions or nonequivalent energetics. In contrast to some work (Pimm 1979), we find that compartmented webs are more stable than reticulate webs. However, we find that nonequivalent energetics can stabilize previously unstable reticulate structures. It is not only weak flows that can be stabilizing but also the arrangement of the flows that emphasizes stabilizing mechanisms. We find that the main stabilizing mechanism is asynchrony, where structures and energetic arrangements that decrease synchrony such as internal segregation or competition will stabilize dynamics. Since compartments allow prey dynamics to behave somewhat independently, compartmentation readily promotes stability. In addition, these results can be scaled from simple food webs to more complex webs with many interacting subsystems so that linking weak subsystems to strong ones can stabilize dynamics. We show that food web dynamics are determined not only by topology but also the arrangement of weak and strong energetic flows.
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Affiliation(s)
- Jack Teng
- Department of Zoology, University of Toronto, 25 Harbord Street, Toronto, Ontario M5S 3G5, Canada.
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47
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Roberts A, Stone L. Advantageous indirect interactions in systems of competition. J Theor Biol 2004; 228:367-75. [PMID: 15135035 DOI: 10.1016/j.jtbi.2004.01.013] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2002] [Revised: 01/15/2004] [Accepted: 01/24/2004] [Indexed: 10/26/2022]
Abstract
Ecological foodwebs display complex networks of species interactions. Here we discuss how two species, whether directly interacting or not, can crucially affect each other 'indirectly' through their mutual associations with intermediary species. A technique is presented for quantifying these "indirect effects", so that a simple measure emerges for the degree of overall harm or advantage that a particular species encounters from another in the context of a given foodweb. If the system is one of pure competition, the "direct" interaction between any two species is of course harmful to both. But when the method is applied to such systems it predicts that, if all interactions are allowed for including the indirect, in a large proportion of pair interactions at least one species will be deriving benefit from the other. Computer-generated samples confirm that this proportion is accurately predicted. The many pathways for indirect interaction can thus often reverse the direct connection, so that competing species achieve an interaction here called 'Advantageous in A Community Context' (ACC).
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Affiliation(s)
- Alan Roberts
- Graduate School of Environmental Science, Monash University, Clayton, Vic. 3168, Australia
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Abstract
Empirical studies have shown that, in real ecosystems, species-interaction strengths are generally skewed in their distribution towards weak interactions. Some theoretical work also suggests that weak interactions, especially in omnivorous links, are important for the local stability of a community at equilibrium. However, the majority of theoretical studies use uniform distributions of interaction strengths to generate artificial communities for study. We investigate the effects of the underlying interaction-strength distribution upon the return time, permanence and feasibility of simple Lotka-Volterra equilibrium communities. We show that a skew towards weak interactions promotes local and global stability only when omnivory is present. It is found that skewed interaction strengths are an emergent property of stable omnivorous communities, and that this skew towards weak interactions creates a dynamic constraint maintaining omnivory. Omnivory is more likely to occur when omnivorous interactions are skewed towards weak interactions. However, a skew towards weak interactions increases the return time to equilibrium, delays the recovery of ecosystems and hence decreases the stability of a community. When no skew is imposed, the set of stable omnivorous communities shows an emergent distribution of skewed interaction strengths. Our results apply to both local and global concepts of stability and are robust to the definition of a feasible community. These results are discussed in the light of empirical data and other theoretical studies, in conjunction with their broader implications for community assembly.
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Affiliation(s)
- Mark Emmerson
- Department of Zoology, Ecology and Plant Sciences, University College Cork, Lee Maltings, Prospect Row, Cork, Ireland.
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Berlow EL, Neutel AM, Cohen JE, de Ruiter PC, Ebenman B, Emmerson M, Fox JW, Jansen VAA, Iwan Jones J, Kokkoris GD, Logofet DO, McKane AJ, Montoya JM, Petchey O. Interaction strengths in food webs: issues and opportunities. J Anim Ecol 2004. [DOI: 10.1111/j.0021-8790.2004.00833.x] [Citation(s) in RCA: 479] [Impact Index Per Article: 24.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Emmerson MC, Raffaelli D. Predator-prey body size, interaction strength and the stability of a real food web. J Anim Ecol 2004. [DOI: 10.1111/j.0021-8790.2004.00818.x] [Citation(s) in RCA: 289] [Impact Index Per Article: 14.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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