1
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Awender S, Wackerbauer R, Breed GA. How realistic features affect the stability of an Arctic marine food web model. CHAOS (WOODBURY, N.Y.) 2024; 34:013122. [PMID: 38242104 DOI: 10.1063/5.0176718] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2023] [Accepted: 12/14/2023] [Indexed: 01/21/2024]
Abstract
Rapid sea-ice decline and warmer waters are threatening the stability of Arctic ecosystems and potentially forcing their restructuring. Mathematical models that support observational evidence are becoming increasingly important. We develop a food web model for the Southern Beaufort Sea based on species with high ecological significance. Generalized modeling is applied to study the impact of realistic characteristics on food web stability; a powerful method that provides a linear stability analysis for systems with uncertainty in data and underlying physical processes. We find that including predator-specific foraging traits, weighted predator-prey interactions, and habitat constraints increase food-web stability. The absence of a fierce top predator (killer whale, polar bear, etc.) also significantly increases the portion of stable webs. Adding ecosystem background noise in terms of a collective impact of latent, minor ecosystem members shows a peak in stability at an optimum, relatively small background pressure. These results indicate that refining models with more realistic detail to account for the complexity of the ecological system may be key to bridge the gap between empirical observations and model predictions in ecosystem stability.
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Affiliation(s)
- Stefan Awender
- Department of Physics, University of Alaska Fairbanks, Fairbanks, Alaska 99775, USA
| | - Renate Wackerbauer
- Department of Physics, University of Alaska Fairbanks, Fairbanks, Alaska 99775, USA
| | - Greg A Breed
- Department of Biology & Wildlife, University of Alaska Fairbanks, Fairbanks, Alaska 99775, USA
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2
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Awender S, Wackerbauer R, Breed GA. Combining generalized modeling and specific modeling in the analysis of ecological networks. CHAOS (WOODBURY, N.Y.) 2023; 33:033130. [PMID: 37003835 DOI: 10.1063/5.0131352] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2022] [Accepted: 02/20/2023] [Indexed: 06/19/2023]
Abstract
The complexity of real food webs involves uncertainty in data and in underlying ecological processes, and modeling approaches deal with these challenges differently. Generalized modeling provides a linear stability analysis without narrow specification of all processes, and conventional dynamical systems models approximate functional forms to discuss trajectories in phase space. This study compares results and ecological interpretations from both methods in four-species ecological networks at steady state. We find that a specific (dynamical systems) model only provides a subset of stability data from the generalized model, which spans many plausible dynamic scenarios, allowing for conflicting results. Nevertheless, both approaches reveal that fixed points become stable when nutrient flows to predators are fettered and even more when the basal growth rate approaches a maximum. The specific model identifies a distinct ecosystem response to bottom-up forcing, the enrichment of lower trophic levels. Enrichment stabilizes a fixed point when basal species are in a resource-deprived environment but destabilizes it if resources become more abundant. The generalized model provides less specific information since infinitely many paths of enrichment are hypothetical. Nevertheless, generalized modeling of ecological systems is a powerful technique that enables a meta analysis of these uncertain complex systems.
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Affiliation(s)
- Stefan Awender
- Department of Physics, University of Alaska Fairbanks, Fairbanks, Alaska 99775, USA
| | - Renate Wackerbauer
- Department of Physics, University of Alaska Fairbanks, Fairbanks, Alaska 99775, USA
| | - Greg A Breed
- Department of Biology and Wildlife, University of Alaska Fairbanks, Fairbanks, Alaska 99775, USA
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3
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Giacomini HC. Metabolic responses of predators to prey density. Front Ecol Evol 2022. [DOI: 10.3389/fevo.2022.980812] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
The metabolic cost of foraging is the dark energy of ecological systems. It is much harder to observe and to measure than its beneficial counterpart, prey consumption, yet it is not inconsequential for the dynamics of prey and predator populations. Here I define the metabolic response as the change in energy expenditure of predators in response to changes in prey density. It is analogous and intrinsically linked to the functional response, which is the change in consumption rate with prey density, as they are both shaped by adjustments in foraging activity. These adjustments are adaptive, ubiquitous in nature, and are implicitly assumed by models of predator–prey dynamics that impose consumption saturation in functional responses. By ignoring the associated metabolic responses, these models violate the principle of energy conservation and likely underestimate the strength of predator–prey interactions. Using analytical and numerical approaches, I show that missing this component of interaction has broad consequences for dynamical stability and for the robustness of ecosystems to persistent environmental or anthropogenic stressors. Negative metabolic responses – those resulting from decreases in foraging activity when more prey is available, and arguably the most common – lead to lower local stability of food webs and a faster pace of change in population sizes, including higher excitability, higher frequency of oscillations, and quicker return times to equilibrium when stable. They can also buffer the effects of press perturbations, such as harvesting, on target populations and on their prey through top-down trophic cascades, but are expected to magnify bottom-up cascades, including the effects of nutrient enrichment or the effects of altering lower trophic levels that can be caused by environmental forcing and climate change. These results have implications for any resource management approach that relies on models of food web dynamics, which is the case of many applications of ecosystem-based fisheries management. Finally, besides having their own individual effects, metabolic responses have the potential to greatly alter, or even invert, functional response-stability relationships, and therefore can be critical to an integral understanding of predation and its influence on population dynamics and persistence.
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4
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Farahbakhsh I, Bauch CT, Anand M. Modelling coupled human-environment complexity for the future of the biosphere: strengths, gaps and promising directions. Philos Trans R Soc Lond B Biol Sci 2022; 377:20210382. [PMID: 35757879 PMCID: PMC9234813 DOI: 10.1098/rstb.2021.0382] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023] Open
Abstract
Humans and the environment form a single complex system where humans not only influence ecosystems but also react to them. Despite this, there are far fewer coupled human–environment system (CHES) mathematical models than models of uncoupled ecosystems. We argue that these coupled models are essential to understand the impacts of social interventions and their potential to avoid catastrophic environmental events and support sustainable trajectories on multi-decadal timescales. A brief history of CHES modelling is presented, followed by a review spanning recent CHES models of systems including forests and land use, coral reefs and fishing and climate change mitigation. The ability of CHES modelling to capture dynamic two-way feedback confers advantages, such as the ability to represent ecosystem dynamics more realistically at longer timescales, and allowing insights that cannot be generated using ecological models. We discuss examples of such key insights from recent research. However, this strength brings with it challenges of model complexity and tractability, and the need for appropriate data to parameterize and validate CHES models. Finally, we suggest opportunities for CHES models to improve human–environment sustainability in future research spanning topics such as natural disturbances, social structure, social media data, model discovery and early warning signals. This article is part of the theme issue ‘Ecological complexity and the biosphere: the next 30 years’.
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Affiliation(s)
| | - Chris T Bauch
- Department of Applied Mathematics, University of Waterloo, Waterloo, Canada
| | - Madhur Anand
- School of Environmental Sciences, University of Guelph, Guelph, Canada
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5
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Lyutov A, Uygun Y, Hütt MT. Local topological features of robust supply networks. APPLIED NETWORK SCIENCE 2022; 7:33. [PMID: 35615080 PMCID: PMC9122087 DOI: 10.1007/s41109-022-00470-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/17/2021] [Accepted: 05/06/2022] [Indexed: 06/15/2023]
Abstract
UNLABELLED The design of robust supply and distribution systems is one of the fundamental challenges at the interface of network science and logistics. Given the multitude of performance criteria, real-world constraints, and external influences acting upon such a system, even formulating an appropriate research question to address this topic is non-trivial. Here we present an abstraction of a supply and distribution system leading to a minimal model, which only retains stylized facts of the systemic function and, in this way, allows us to investigate the generic properties of robust supply networks. On this level of abstraction, a supply and distribution system is the strategic use of transportation to eliminate mismatches between production patterns (i.e., the amounts of goods produced at each production site of a company) and demand patterns (i.e., the amount of goods consumed at each location). When creating networks based on this paradigm and furthermore requiring the robustness of the system with respect to the loss of transportation routes (edge of the network) we see that robust networks are built from specific sets of subgraphs, while vulnerable networks display a markedly different subgraph composition. Our findings confirm a long-standing hypothesis in the field of network science, namely, that network motifs-statistically over-represented small subgraphs-are informative about the robust functioning of a network. Also, our findings offer a blueprint for enhancing the robustness of real-world supply and distribution systems. SUPPLEMENTARY INFORMATION The online version contains supplementary material available at 10.1007/s41109-022-00470-2.
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Affiliation(s)
- Alexey Lyutov
- Department of Mathematics and Logistics, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany
| | - Yilmaz Uygun
- Department of Mathematics and Logistics, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany
| | - Marc-Thorsten Hütt
- Department of Life Sciences and Chemistry, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany
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6
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Massing JC, Gross T. Generalized Structural Kinetic Modeling: A Survey and Guide. Front Mol Biosci 2022; 9:825052. [PMID: 35573734 PMCID: PMC9098827 DOI: 10.3389/fmolb.2022.825052] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2021] [Accepted: 03/29/2022] [Indexed: 11/13/2022] Open
Abstract
Many current challenges involve understanding the complex dynamical interplay between the constituents of systems. Typically, the number of such constituents is high, but only limited data sources on them are available. Conventional dynamical models of complex systems are rarely mathematically tractable and their numerical exploration suffers both from computational and data limitations. Here we review generalized modeling, an alternative approach for formulating dynamical models to gain insights into dynamics and bifurcations of uncertain systems. We argue that this approach deals elegantly with the uncertainties that exist in real world data and enables analytical insight or highly efficient numerical investigation. We provide a survey of recent successes of generalized modeling and a guide to the application of this modeling approach in future studies such as complex integrative ecological models.
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Affiliation(s)
- Jana C. Massing
- Helmholtz Institute for Functional Marine Biodiversity at the University of Oldenburg (HIFMB), Oldenburg, Germany
- Helmholtz Centre for Marine and Polar Research, Alfred-Wegener-Institute, Bremerhaven, Germany
- Institute for Chemistry and Biology of the Marine Environment (ICBM), Carl-von-Ossietzky University, Oldenburg, Germany
- *Correspondence: Jana C. Massing,
| | - Thilo Gross
- Helmholtz Institute for Functional Marine Biodiversity at the University of Oldenburg (HIFMB), Oldenburg, Germany
- Helmholtz Centre for Marine and Polar Research, Alfred-Wegener-Institute, Bremerhaven, Germany
- Institute for Chemistry and Biology of the Marine Environment (ICBM), Carl-von-Ossietzky University, Oldenburg, Germany
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7
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Krauß A, Gross T, Drossel B. Master stability functions for metacommunities with two types of habitats. Phys Rev E 2022; 105:044310. [PMID: 35590669 DOI: 10.1103/physreve.105.044310] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2021] [Accepted: 01/12/2022] [Indexed: 06/15/2023]
Abstract
Current questions in ecology revolve around instabilities in the dynamics on spatial networks and particularly the effect of node heterogeneity. We extend the master stability function formalism to inhomogeneous biregular networks having two types of spatial nodes. Notably, this class of systems also allows the investigation of certain types of dynamics on higher-order networks. Combined with the generalized modeling approach to study the linear stability of steady states, this is a powerful tool to numerically asses the stability of large ensembles of systems. We analyze the stability of ecological metacommunities with two distinct types of habitats analytically and numerically in order to identify several sets of conditions under which the dynamics can become stabilized by dispersal. Our analytical approach allows general insights into stabilizing and destabilizing effects in metapopulations. Specifically, we identify self-regulation and negative feedback loops between source and sink populations as stabilizing mechanisms and we show that maladaptive dispersal may be stable under certain conditions.
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Affiliation(s)
- Alexander Krauß
- Institute for Condensed Matter Physics, Technical University of Darmstadt, 64289 Darmstadt, Germany
| | - Thilo Gross
- Helmholtz Institute for Functional Marine Biodiversity, University of Oldenburg, 26129 Oldenburg, Germany
- Alfred-Wegener-Institute for Marine and Polar Research, 27570 Bremerhaven, Germany
- Institute for Chemistry and Biology of the Marine Environment, University of Oldenburg, 26129 Oldenburg, Germany
| | - Barbara Drossel
- Institute for Condensed Matter Physics, Technical University of Darmstadt, 64289 Darmstadt, Germany
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8
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Barter E, Brechtel A, Drossel B, Gross T. A closed form for Jacobian reconstruction from time series and its application as an early warning signal in network dynamics. Proc Math Phys Eng Sci 2022; 477:20200742. [PMID: 35153548 PMCID: PMC8300673 DOI: 10.1098/rspa.2020.0742] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2020] [Accepted: 02/18/2021] [Indexed: 11/12/2022] Open
Abstract
The Jacobian matrix of a dynamical system describes its response to perturbations. Conversely, one can estimate the Jacobian matrix by carefully monitoring how the system responds to environmental noise. We present a closed-form analytical solution for the calculation of a system’s Jacobian from a time series. Being able to access the Jacobian enables a broad range of mathematical analyses by which deeper insights into the system can be gained. Here we consider in particular the computation of the leading Jacobian eigenvalue as an early warning signal for critical transitions. To illustrate this approach, we apply it to ecological meta-foodweb models, which are strongly nonlinear dynamical multi-layer networks. Our analysis shows that accurate results can be obtained, although the data demand of the method is still high.
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Affiliation(s)
- Edmund Barter
- Department of Engineering Mathematics, University of Bristol, Merchant Venturers Building, Woodland Road, Bristol BS8 1UB, UK
| | - Andreas Brechtel
- TU Darmstadt, Fachbereich Physik, Hochschulstrasse, 6, 64289 Darmstadt, Germany
| | - Barbara Drossel
- TU Darmstadt, Fachbereich Physik, Hochschulstrasse, 6, 64289 Darmstadt, Germany
| | - Thilo Gross
- HIFMB Helmholtz Institute for Functional Marine Biodiversity, Ammerländer Heerstr. 231, Oldenburg, Germany.,Alfred-Wegener-Institute for Marine and Polar Research, Am Handelshaven 12, Bremerhaven, Germany.,University of Oldenburg, Institute for Chemistry and Biology of the Marine Environment, Carl-von-Ossietzky 9-11 Str., Germany.,UC Davis, Department of Computer Science, 1 Shields Avenue Davis, CA 95616, USA
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9
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Zhivkoplias EK, Vavulov O, Hillerton T, Sonnhammer ELL. Generation of Realistic Gene Regulatory Networks by Enriching for Feed-Forward Loops. Front Genet 2022; 13:815692. [PMID: 35222536 PMCID: PMC8872634 DOI: 10.3389/fgene.2022.815692] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2021] [Accepted: 01/13/2022] [Indexed: 11/13/2022] Open
Abstract
The regulatory relationships between genes and proteins in a cell form a gene regulatory network (GRN) that controls the cellular response to changes in the environment. A number of inference methods to reverse engineer the original GRN from large-scale expression data have recently been developed. However, the absence of ground-truth GRNs when evaluating the performance makes realistic simulations of GRNs necessary. One aspect of this is that local network motif analysis of real GRNs indicates that the feed-forward loop (FFL) is significantly enriched. To simulate this properly, we developed a novel motif-based preferential attachment algorithm, FFLatt, which outperformed the popular GeneNetWeaver network generation tool in reproducing the FFL motif occurrence observed in literature-based biological GRNs. It also preserves important topological properties such as scale-free topology, sparsity, and average in/out-degree per node. We conclude that FFLatt is well-suited as a network generation module for a benchmarking framework with the aim to provide fair and robust performance evaluation of GRN inference methods.
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Affiliation(s)
- Erik K. Zhivkoplias
- Department of Biochemistry and Biophysics, Science for Life Laboratory, Stockholm University, Solna, Sweden
| | - Oleg Vavulov
- Bioinformatics Institute, St. Petersburg, Russia
| | - Thomas Hillerton
- Department of Biochemistry and Biophysics, Science for Life Laboratory, Stockholm University, Solna, Sweden
| | - Erik L. L. Sonnhammer
- Department of Biochemistry and Biophysics, Science for Life Laboratory, Stockholm University, Solna, Sweden
- *Correspondence: Erik L. L. Sonnhammer,
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10
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Anderson KE, Fahimipour AK. Body size dependent dispersal influences stability in heterogeneous metacommunities. Sci Rep 2021; 11:17410. [PMID: 34465802 PMCID: PMC8408130 DOI: 10.1038/s41598-021-96629-5] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2021] [Accepted: 08/12/2021] [Indexed: 11/25/2022] Open
Abstract
Body size affects key biological processes across the tree of life, with particular importance for food web dynamics and stability. Traits influencing movement capabilities depend strongly on body size, yet the effects of allometrically-structured dispersal on food web stability are less well understood than other demographic processes. Here we study the stability properties of spatially-arranged model food webs in which larger bodied species occupy higher trophic positions, while species’ body sizes also determine the rates at which they traverse spatial networks of heterogeneous habitat patches. Our analysis shows an apparent stabilizing effect of positive dispersal rate scaling with body size compared to negative scaling relationships or uniform dispersal. However, as the global coupling strength among patches increases, the benefits of positive body size-dispersal scaling disappear. A permutational analysis shows that breaking allometric dispersal hierarchies while preserving dispersal rate distributions rarely alters qualitative aspects of metacommunity stability. Taken together, these results suggest that the oft-predicted stabilizing effects of large mobile predators may, for some dimensions of ecological stability, be attributed to increased patch coupling per se, and not necessarily coupling by top trophic levels in particular.
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Affiliation(s)
- Kurt E Anderson
- Department of Evolution, Ecology, and Organismal Biology, University of California, Riverside, CA, USA.
| | - Ashkaan K Fahimipour
- Department of Computer Science, University of California, Davis, CA, USA.,Institute of Marine Sciences, University of California, Santa Cruz, CA, USA
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11
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Eichenwald AJ, Reed JM. An Expanded Framework for Community Viability Analysis. Bioscience 2021. [DOI: 10.1093/biosci/biab034] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Abstract
Community viability analysis (CVA) has been put forth as an analogue for population viability analysis (PVA), an accepted conservation tool for evaluating species-specific threat and management scenarios. The original proposal recommended that CVAs examine resistance-based questions. PVAs, however, are broadly applicable to multiple types of viability questions, suggesting that the original CVA definition may be too narrow. In the present article, we advance an expanded framework in which CVA includes any analysis assessing the status, threats, or management options of an ecological community. We discuss viability questions that can be investigated with CVA. We group those inquiries into categories of resistance, resilience, and persistence, and provide case studies for each. Finally, we broadly present the steps in a CVA.
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Affiliation(s)
- Adam J Eichenwald
- PhD candidate, Tufts University, Medford, Massachusetts, United States
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12
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Awender S, Wackerbauer R, Breed GA. Stability of generalized ecological-network models. CHAOS (WOODBURY, N.Y.) 2021; 31:023106. [PMID: 33653073 DOI: 10.1063/5.0029934] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2020] [Accepted: 01/14/2021] [Indexed: 06/12/2023]
Abstract
The stability of ecological networks of varying topologies and predator-prey relationships is explored by applying the concept of generalized modeling. The effects of omnivory, complexity, enrichment, number of top predators, and predatory response are discussed. The degree of omnivory plays a large role in governing web stability at steady state. Complexity as measured from connectance and network size is not a perfect indicator of stability; large, highly connected webs can be just as stable as smaller, less connected ones. Learning behavior as expressed in Holling's type III predatory response is stabilizing for food webs and provides exceptions to the paradox of enrichment for some topologies.
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Affiliation(s)
- Stefan Awender
- Department of Physics, University of Alaska Fairbanks, Fairbanks, Alaska 99775, USA
| | - Renate Wackerbauer
- Department of Physics, University of Alaska Fairbanks, Fairbanks, Alaska 99775, USA
| | - Greg A Breed
- Department of Biology and Wildlife, University of Alaska Fairbanks, Fairbanks, Alaska 99775, USA
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13
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Gross T, Allhoff KT, Blasius B, Brose U, Drossel B, Fahimipour AK, Guill C, Yeakel JD, Zeng F. Modern models of trophic meta-communities. Philos Trans R Soc Lond B Biol Sci 2020; 375:20190455. [PMID: 33131442 PMCID: PMC7662193 DOI: 10.1098/rstb.2019.0455] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 03/17/2020] [Indexed: 02/06/2023] Open
Abstract
Dispersal and foodweb dynamics have long been studied in separate models. However, over the past decades, it has become abundantly clear that there are intricate interactions between local dynamics and spatial patterns. Trophic meta-communities, i.e. meta-foodwebs, are very complex systems that exhibit complex and often counterintuitive dynamics. Over the past decade, a broad range of modelling approaches have been used to study these systems. In this paper, we review these approaches and the insights that they have revealed. We focus particularly on recent papers that study trophic interactions in spatially extensive settings and highlight the common themes that emerged in different models. There is overwhelming evidence that dispersal (and particularly intermediate levels of dispersal) benefits the maintenance of biodiversity in several different ways. Moreover, some insights have been gained into the effect of different habitat topologies, but these results also show that the exact relationships are much more complex than previously thought, highlighting the need for further research in this area. This article is part of the theme issue 'Integrative research perspectives on marine conservation'.
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Affiliation(s)
- Thilo Gross
- University of California Davis, Department of Computer Science, 1 Shields Avenue, Davis, CA 95616, USA
- Alfred Wegener Institut. Helmholtz Zentrum für Polar und Meeresforschung, Am Handelshafen 12, 27570 Bremerhaven, Germany
- Univeristät Oldenburg, Institut für Chemie und Biologie des Meeres, Carl-von-Ossietzky-Strasse 9-11, 26111 Oldenburg, Germany
- Helmholtz Institute for Functional Marine Bidiversity, Ammerländer Heerstrasse 231, Oldenburg, Germany
| | - Korinna T. Allhoff
- Universität Tübingen, Department of Biology, Auf der Morgenstelle 5, 72076 Tübingen, Germany
| | - Bernd Blasius
- Alfred Wegener Institut. Helmholtz Zentrum für Polar und Meeresforschung, Am Handelshafen 12, 27570 Bremerhaven, Germany
- Univeristät Oldenburg, Institut für Chemie und Biologie des Meeres, Carl-von-Ossietzky-Strasse 9-11, 26111 Oldenburg, Germany
| | - Ulrich Brose
- German Centre for Integrative Biodiversity Research, Deutscher Platz 5e, 04103 Leipzig, Germany
- Institute for Biodiversity, Friedrich Schiller University Jena, Dornburger-Strasse 159, 07743 Jena, Germany
| | - Barbara Drossel
- TU Darmstadt, Institut für Festkörperphysik, Hochschulstrasse 6, 64289 Darmstadt, Germany
| | - Ashkaan K. Fahimipour
- National Oceanic and Atmospheric Administration, Southwest Fisheries Science Center, 110 McAllister Way, Santa Cruz, CA 95060, USA
| | - Christian Guill
- Universität Potsdam, Institut für Biochemie und Biologie, Karl-Liebknecht-Strasse 24-25, 14476 Potsdam, Germany
| | - Justin D. Yeakel
- University of California, Merced, School of Natural Sciences, 5200 North Lake Road, Merced, CA 95343, USA
| | - Fanqi Zeng
- University of Bristol, Department of Engineering Mathematics, Merchant Venturers Building, Bristol BS8 1UB, UK
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14
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Adamson MW, Morozov AY. Identifying the sources of structural sensitivity in partially specified biological models. Sci Rep 2020; 10:16926. [PMID: 33037267 PMCID: PMC7547730 DOI: 10.1038/s41598-020-73710-z] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2020] [Accepted: 09/14/2020] [Indexed: 12/02/2022] Open
Abstract
Biological systems are characterised by a high degree of uncertainty and complexity, which implies that exact mathematical equations to describe biological processes cannot generally be justified. Moreover, models can exhibit sensitivity to the precise formulations of their component functions—a property known as structural sensitivity. Structural sensitivity can be revealed and quantified by considering partially specified models with uncertain functions, but this goes beyond well-established, parameter-based sensitivity analysis, and currently presents a mathematical challenge. Here we build upon previous work in this direction by addressing the crucial question of identifying the processes which act as the major sources of model uncertainty and those which are less influential. To achieve this goal, we introduce two related concepts: (1) the gradient of structural sensitivity, accounting for errors made in specifying unknown functions, and (2) the partial degree of sensitivity with respect to each function, a global measure of the uncertainty due to possible variation of the given function while the others are kept fixed. We propose an iterative framework of experiments and analysis to inform a heuristic reduction of structural sensitivity in a model. To demonstrate the framework introduced, we investigate the sources of structural sensitivity in a tritrophic food chain model.
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Affiliation(s)
- Matthew W Adamson
- Institute of Mathematics, Institute of Environmental Systems Research, University of Osnabrück, Osnabrück, 49076, Germany.
| | - Andrew Yu Morozov
- Department of Mathematics, University of Leicester, Leicester, LE1 7RH, UK.,Institute of Ecology and Evolution, Russian Academy of Sciences, 33 Leninskii pr., Moscow, Russia, 119071.,N.I. Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
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15
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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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16
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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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17
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Doizy A, Barter E, Memmott J, Varnham K, Gross T. Impact of cyber-invasive species on a large ecological network. Sci Rep 2018; 8:13245. [PMID: 30185798 PMCID: PMC6125364 DOI: 10.1038/s41598-018-31423-4] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2018] [Accepted: 08/02/2018] [Indexed: 11/20/2022] Open
Abstract
As impacts of introduced species cascade through trophic levels, they can cause indirect and counter-intuitive effects. To investigate the impact of invasive species at the network scale, we use a generalized food web model, capable of propagating changes through networks with a series of ecologically realistic criteria. Using data from a small British offshore island, we quantify the impacts of four virtual invasive species (an insectivore, a herbivore, a carnivore and an omnivore whose diet is based on a rat) and explore which clusters of species react in similar ways. We find that the predictions for the impacts of invasive species are ecologically plausible, even in large networks. Species in the same taxonomic group are similarly impacted by a virtual invasive species. However, interesting differences within a given taxonomic group can occur. The results suggest that some native species may be at risk from a wider range of invasives than previously believed. The implications of these results for ecologists and land managers are discussed.
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Affiliation(s)
- Anna Doizy
- Université Paris-Sud, 91400 Orsay, France and AgroParisTech, 75005, Paris, France.
| | - Edmund Barter
- Queen's Building, University Walk, Bristol, BS8 1TR, UK
| | - Jane Memmott
- School of Biological Sciences, Life Sciences Building, Tyndall Avenue, Bristol, BS8 1TQ, UK
| | - Karen Varnham
- Royal Society for the Protection of Birds, The Lodge, Beds, Sandy, SG19 2DL, UK
| | - Thilo Gross
- Merchant Venturers Building, Woodland Road, Bristol, BS8 1UB, UK
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18
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Brechtel A, Gramlich P, Ritterskamp D, Drossel B, Gross T. Master stability functions reveal diffusion-driven pattern formation in networks. Phys Rev E 2018; 97:032307. [PMID: 29776185 DOI: 10.1103/physreve.97.032307] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2017] [Indexed: 11/07/2022]
Abstract
We study diffusion-driven pattern formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing random walks, while they can be created or destroyed by reactions between or within a layer. We show that the stability of homogeneous steady states can be analyzed with a master stability function approach that reveals a deep analogy between pattern formation in networks and pattern formation in continuous space. For illustration, we consider a generalized model of ecological meta-food webs. This fairly complex model describes the dispersal of many different species across a region consisting of a network of individual habitats while subject to realistic, nonlinear predator-prey interactions. In this example, the method reveals the intricate dependence of the dynamics on the spatial structure. The ability of the proposed approach to deal with this fairly complex system highlights it as a promising tool for ecology and other applications.
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Affiliation(s)
- Andreas Brechtel
- Institute of Condensed Matter Physics, Technische Universität Darmstadt, 64289 Darmstadt, Germany
| | - Philipp Gramlich
- Institute of Condensed Matter Physics, Technische Universität Darmstadt, 64289 Darmstadt, Germany
| | - Daniel Ritterskamp
- Department of Engineering Mathematics, Merchant Venturers School of Engineering, University of Bristol, Woodland Road, Bristol BS8 1UB, United Kingdom
| | - Barbara Drossel
- Institute of Condensed Matter Physics, Technische Universität Darmstadt, 64289 Darmstadt, Germany
| | - Thilo Gross
- Department of Engineering Mathematics, Merchant Venturers School of Engineering, University of Bristol, Woodland Road, Bristol BS8 1UB, United Kingdom
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19
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Ritterskamp D, Demirel G, MacCarthy BL, Rudolf L, Champneys AR, Gross T. Revealing instabilities in a generalized triadic supply network: A bifurcation analysis. CHAOS (WOODBURY, N.Y.) 2018; 28:073103. [PMID: 30070537 DOI: 10.1063/1.5026746] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2018] [Accepted: 06/13/2018] [Indexed: 06/08/2023]
Abstract
Supply networks are exposed to instabilities and thus a high level of risk. To mitigate this risk, it is necessary to understand how instabilities are formed in supply networks. In this paper, we focus on instabilities in inventory dynamics that develop due to the topology of the supply network. To be able to capture these topology-induced instabilities, we use a method called generalized modeling, a minimally specified modeling approach adopted from ecology. This method maps the functional dependencies of production rates on the inventory levels of different parts and products, which are imposed by the network topology, to a set of elasticity parameters. We perform a bifurcation analysis to investigate how these elasticities affect the stability. First, we show that dyads and serial supply chains are immune to topology-induced instabilities. In contrast, in a simple triadic network, where a supplier acts as both a first and a second tier supplier, we can identify instabilities that emerge from saddle-node, Hopf, and global homoclinic bifurcations. These bifurcations lead to different types of dynamical behavior, including exponential convergence to and divergence from a steady state, temporary oscillations around a steady state, and co-existence of different types of dynamics, depending on initial conditions. Finally, we discuss managerial implications of the results.
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Affiliation(s)
- Daniel Ritterskamp
- Department of Engineering Mathematics, University of Bristol, Bristol BS8 1UB, United Kingdom
| | - Güven Demirel
- Management Science and Entrepreneurship, Essex Business School, University of Essex, Southend-on-Sea SS1 1LW, United Kingdom
| | - Bart L MacCarthy
- Operations Management & Information Systems, Business School, University of Nottingham, Nottingham NG8 1BB, United Kingdom
| | - Lars Rudolf
- Department of Engineering Mathematics, University of Bristol, Bristol BS8 1UB, United Kingdom
| | - Alan R Champneys
- Department of Engineering Mathematics, University of Bristol, Bristol BS8 1UB, United Kingdom
| | - Thilo Gross
- Department of Engineering Mathematics, University of Bristol, Bristol BS8 1UB, United Kingdom
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20
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Aldebert C, Kooi BW, Nerini D, Poggiale JC. Is structural sensitivity a problem of oversimplified biological models? Insights from nested Dynamic Energy Budget models. J Theor Biol 2018; 448:1-8. [PMID: 29550453 DOI: 10.1016/j.jtbi.2018.03.019] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2017] [Revised: 03/01/2018] [Accepted: 03/13/2018] [Indexed: 10/17/2022]
Abstract
Many current issues in ecology require predictions made by mathematical models, which are built on somewhat arbitrary choices. Their consequences are quantified by sensitivity analysis to quantify how changes in model parameters propagate into an uncertainty in model predictions. An extension called structural sensitivity analysis deals with changes in the mathematical description of complex processes like predation. Such processes are described at the population scale by a specific mathematical function taken among similar ones, a choice that can strongly drive model predictions. However, it has only been studied in simple theoretical models. Here, we ask whether structural sensitivity is a problem of oversimplified models. We found in predator-prey models describing chemostat experiments that these models are less structurally sensitive to the choice of a specific functional response if they include mass balance resource dynamics and individual maintenance. Neglecting these processes in an ecological model (for instance by using the well-known logistic growth equation) is not only an inappropriate description of the ecological system, but also a source of more uncertain predictions.
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Affiliation(s)
- Clement Aldebert
- Mediterranean Institute of Oceanography, Aix-Marseille University, Toulon University, CNRS/INSU,IRD, MIO, UM 110, Marseille, Cedex 09 13288, France; University of Zurich, Institute of Evolutionary Biology and Environmental Studies, Winterthurerstrasse 190, Zurich 8057, Switzerland.
| | - Bob W Kooi
- Faculty of Science, VU University, de Boelelaan 1085,HV Amsterdam 1081, The Netherlands
| | - David Nerini
- Mediterranean Institute of Oceanography, Aix-Marseille University, Toulon University, CNRS/INSU,IRD, MIO, UM 110, Marseille, Cedex 09 13288, France.
| | - Jean-Christophe Poggiale
- Mediterranean Institute of Oceanography, Aix-Marseille University, Toulon University, CNRS/INSU,IRD, MIO, UM 110, Marseille, Cedex 09 13288, France.
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21
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Dougoud M, Vinckenbosch L, Rohr RP, Bersier LF, Mazza C. The feasibility of equilibria in large ecosystems: A primary but neglected concept in the complexity-stability debate. PLoS Comput Biol 2018; 14:e1005988. [PMID: 29420532 PMCID: PMC5821382 DOI: 10.1371/journal.pcbi.1005988] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2017] [Revised: 02/21/2018] [Accepted: 01/19/2018] [Indexed: 11/18/2022] Open
Abstract
The consensus that complexity begets stability in ecosystems was challenged in the seventies, a result recently extended to ecologically-inspired networks. The approaches assume the existence of a feasible equilibrium, i.e. with positive abundances. However, this key assumption has not been tested. We provide analytical results complemented by simulations which show that equilibrium feasibility vanishes in species rich systems. This result leaves us in the uncomfortable situation in which the existence of a feasible equilibrium assumed in local stability criteria is far from granted. We extend our analyses by changing interaction structure and intensity, and find that feasibility and stability is warranted irrespective of species richness with weak interactions. Interestingly, we find that the dynamical behaviour of ecologically inspired architectures is very different and richer than that of unstructured systems. Our results suggest that a general understanding of ecosystem dynamics requires focusing on the interplay between interaction strength and network architecture.
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Affiliation(s)
- Michaël Dougoud
- Department of Mathematics, University of Fribourg, Fribourg, Switzerland
| | - Laura Vinckenbosch
- Department of Mathematics, University of Fribourg, Fribourg, Switzerland
- University of Applied Sciences Western Switzerland - HES-SO, Yverdon-les-Bains, Switzerland
| | - Rudolf P. Rohr
- Department of Biology, Unit of Ecology and Evolution, University of Fribourg, Fribourg, Switzerland
| | - Louis-Félix Bersier
- Department of Biology, Unit of Ecology and Evolution, University of Fribourg, Fribourg, Switzerland
| | - Christian Mazza
- Department of Mathematics, University of Fribourg, Fribourg, Switzerland
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22
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Calcagno V, Jarne P, Loreau M, Mouquet N, David P. Diversity spurs diversification in ecological communities. Nat Commun 2017; 8:15810. [PMID: 28598423 PMCID: PMC5494188 DOI: 10.1038/ncomms15810] [Citation(s) in RCA: 38] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2016] [Accepted: 05/05/2017] [Indexed: 11/19/2022] Open
Abstract
Diversity is a fundamental, yet threatened, property of ecological systems. The idea that diversity can itself favour diversification, in an autocatalytic process, is very appealing but remains controversial. Here, we study a generalized model of ecological communities and investigate how the level of initial diversity influences the possibility of evolutionary diversification. We show that even simple models of intra- and inter-specific ecological interactions can predict a positive effect of diversity on diversification: adaptive radiations may require a threshold number of species before kicking-off. We call this phenomenon DDAR (diversity-dependent adaptive radiations) and identify mathematically two distinct pathways connecting diversity to diversification, involving character displacement and the positive diversity-productivity relationship. Our results may explain observed delays in adaptive radiations at the macroscale and diversification patterns reported in experimental microbial communities, and shed new light on the dynamics of ecological diversity, the diversity-dependence of diversification rates, and the consequences of biodiversity loss. Diversification may be driven by diversity, a concept Calcagno et al. explore using models of intra- and inter-specific ecological interactions. A threshold number of species is sometimes required before adaptive radiations can occur; a phenomenon they term diversity-dependent adaptive radiation.
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Affiliation(s)
- Vincent Calcagno
- Université Côte d'Azur, CNRS, INRA, ISA, Sophia Antipolis 06900, France
| | - Philippe Jarne
- CEFE UMR 5175, CNRS-Univ. of Montpellier-Univ. P. Valery Montp.-EPHE, Montpellier 34090, France
| | - Michel Loreau
- Theoretical and Experimental Ecology Station, CNRS-Univ. Paul Sabatier, Moulis 09200, France
| | - Nicolas Mouquet
- MARBEC, CNRS-IFREMER-IRD-Univ. of Montpellier, Montpellier 34095, France
| | - Patrice David
- CEFE UMR 5175, CNRS-Univ. of Montpellier-Univ. P. Valery Montp.-EPHE, Montpellier 34090, France
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23
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Goldental A, Uzan H, Sardi S, Kanter I. Oscillations in networks of networks stem from adaptive nodes with memory. Sci Rep 2017; 7:2700. [PMID: 28578398 PMCID: PMC5457433 DOI: 10.1038/s41598-017-02814-w] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2017] [Accepted: 04/19/2017] [Indexed: 11/29/2022] Open
Abstract
We present an analytical framework that allows the quantitative study of statistical dynamic properties of networks with adaptive nodes that have memory and is used to examine the emergence of oscillations in networks with response failures. The frequency of the oscillations was quantitatively found to increase with the excitability of the nodes and with the average degree of the network and to decrease with delays between nodes. For networks of networks, diverse cluster oscillation modes were found as a function of the topology. Analytical results are in agreement with large-scale simulations and open the horizon for understanding network dynamics composed of finite memory nodes as well as their different phases of activity.
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Affiliation(s)
- Amir Goldental
- Department of Physics, Bar-Ilan University, Ramat-Gan, 52900, Israel
| | - Herut Uzan
- Department of Physics, Bar-Ilan University, Ramat-Gan, 52900, Israel
| | - Shira Sardi
- Department of Physics, Bar-Ilan University, Ramat-Gan, 52900, Israel
| | - Ido Kanter
- Department of Physics, Bar-Ilan University, Ramat-Gan, 52900, Israel.
- Gonda Interdisciplinary Brain Research Center and the Goodman Faculty of Life Sciences, Bar-Ilan University, Ramat-Gan, 52900, Israel.
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24
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25
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Aldebert C, Nerini D, Gauduchon M, Poggiale J. Structural sensitivity and resilience in a predator–prey model with density-dependent mortality. ECOLOGICAL COMPLEXITY 2016. [DOI: 10.1016/j.ecocom.2016.05.004] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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26
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Adamson MW, Morozov AY, Kuzenkov OA. Quantifying uncertainty in partially specified biological models: how can optimal control theory help us? Proc Math Phys Eng Sci 2016; 472:20150627. [PMID: 27713655 PMCID: PMC5046979 DOI: 10.1098/rspa.2015.0627] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2015] [Accepted: 08/18/2016] [Indexed: 11/12/2022] Open
Abstract
Mathematical models in biology are highly simplified representations of a complex underlying reality and there is always a high degree of uncertainty with regards to model function specification. This uncertainty becomes critical for models in which the use of different functions fitting the same dataset can yield substantially different predictions-a property known as structural sensitivity. Thus, even if the model is purely deterministic, then the uncertainty in the model functions carries through into uncertainty in model predictions, and new frameworks are required to tackle this fundamental problem. Here, we consider a framework that uses partially specified models in which some functions are not represented by a specific form. The main idea is to project infinite dimensional function space into a low-dimensional space taking into account biological constraints. The key question of how to carry out this projection has so far remained a serious mathematical challenge and hindered the use of partially specified models. Here, we propose and demonstrate a potentially powerful technique to perform such a projection by using optimal control theory to construct functions with the specified global properties. This approach opens up the prospect of a flexible and easy to use method to fulfil uncertainty analysis of biological models.
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Affiliation(s)
- M. W. Adamson
- Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK
| | - A. Y. Morozov
- Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK
- Shirshov Institute of Oceanology, Moscow, 117997, Russia
| | - O. A. Kuzenkov
- Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, Russia
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27
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28
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Gramlich P, Plitzko SJ, Rudolf L, Drossel B, Gross T. The influence of dispersal on a predator-prey system with two habitats. J Theor Biol 2016; 398:150-61. [PMID: 27038668 DOI: 10.1016/j.jtbi.2016.03.015] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2015] [Revised: 02/12/2016] [Accepted: 03/11/2016] [Indexed: 11/19/2022]
Abstract
Dispersal between different habitats influences the dynamics and stability of populations considerably. Furthermore, these effects depend on the local interactions of a population with other species. Here, we perform a general and comprehensive study of the simplest possible system that includes dispersal and local interactions, namely a 2-patch 2-species system. We evaluate the impact of dispersal on stability and on the occurrence of bifurcations, including pattern forming bifurcations that lead to spatial heterogeneity, in 19 different classes of models with the help of the generalized modelling approach. We find that dispersal often destabilizes equilibria, but it can stabilize them if it increases population losses. If dispersal is nonrandom, i.e. if emigration or immigration rates depend on population densities, the correlation of stability with dispersal rates is positive in part of the models. We also find that many systems show all four types of bifurcations and that antisynchronous oscillations occur mostly with nonrandom dispersal.
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Affiliation(s)
- P Gramlich
- Institute for Condensed Matter Physics, Technische Universität Darmstadt, Hochschulstraße, 6 D-64289 Darmstadt, Germany.
| | - S J Plitzko
- Institute for Condensed Matter Physics, Technische Universität Darmstadt, Hochschulstraße, 6 D-64289 Darmstadt, Germany.
| | - L Rudolf
- Department of Engineering Mathematics, University of Bristol, Bristol, UK.
| | - B Drossel
- Institute for Condensed Matter Physics, Technische Universität Darmstadt, Hochschulstraße, 6 D-64289 Darmstadt, Germany.
| | - T Gross
- Department of Engineering Mathematics, University of Bristol, Bristol, UK.
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29
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Lafferty KD, DeLeo G, Briggs CJ, Dobson AP, Gross T, Kuris AM. ECOLOGICAL THEORY. A general consumer-resource population model. Science 2015; 349:854-7. [PMID: 26293960 DOI: 10.1126/science.aaa6224] [Citation(s) in RCA: 59] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Food-web dynamics arise from predator-prey, parasite-host, and herbivore-plant interactions. Models for such interactions include up to three consumer activity states (questing, attacking, consuming) and up to four resource response states (susceptible, exposed, ingested, resistant). Articulating these states into a general model allows for dissecting, comparing, and deriving consumer-resource models. We specify this general model for 11 generic consumer strategies that group mathematically into predators, parasites, and micropredators and then derive conditions for consumer success, including a universal saturating functional response. We further show how to use this framework to create simple models with a common mathematical lineage and transparent assumptions. Underlying assumptions, missing elements, and composite parameters are revealed when classic consumer-resource models are derived from the general model.
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Affiliation(s)
- Kevin D Lafferty
- Western Ecological Research Center, U.S. Geological Survey, Marine Science Institute, University of California-Santa Barbara, Santa Barbara, CA, USA.
| | - Giulio DeLeo
- Hopkins Marine Station Woods Institute for the Environment, Stanford University, Stanford, CA, USA
| | - Cheryl J Briggs
- Ecology, Evolution and Marine Biology, University of California-Santa Barbara, Santa Barbara, CA, USA
| | - Andrew P Dobson
- Ecology and Evolutionary Biology, Princeton University, Princeton, NJ, USA. Santa Fe Institute, Hyde Park Road, Santa Fe, NM, USA
| | - Thilo Gross
- Department of Engineering Mathematics, University of Bristol, Bristol, UK
| | - Armand M Kuris
- Ecology, Evolution and Marine Biology, University of California-Santa Barbara, Santa Barbara, CA, USA
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30
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An empirical model of the Baltic Sea reveals the importance of social dynamics for ecological regime shifts. Proc Natl Acad Sci U S A 2015; 112:11120-5. [PMID: 26283344 DOI: 10.1073/pnas.1504954112] [Citation(s) in RCA: 51] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Regime shifts triggered by human activities and environmental changes have led to significant ecological and socioeconomic consequences in marine and terrestrial ecosystems worldwide. Ecological processes and feedbacks associated with regime shifts have received considerable attention, but human individual and collective behavior is rarely treated as an integrated component of such shifts. Here, we used generalized modeling to develop a coupled social-ecological model that integrated rich social and ecological data to investigate the role of social dynamics in the 1980s Baltic Sea cod boom and collapse. We showed that psychological, economic, and regulatory aspects of fisher decision making, in addition to ecological interactions, contributed both to the temporary persistence of the cod boom and to its subsequent collapse. These features of the social-ecological system also would have limited the effectiveness of stronger fishery regulations. Our results provide quantitative, empirical evidence that incorporating social dynamics into models of natural resources is critical for understanding how resources can be managed sustainably. We also show that generalized modeling, which is well-suited to collaborative model development and does not require detailed specification of causal relationships between system variables, can help tackle the complexities involved in creating and analyzing social-ecological models.
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31
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Neutel AM, Thorne MAS. Linking saturation, stability and sustainability in food webs with observed equilibrium structure. THEOR ECOL-NETH 2015. [DOI: 10.1007/s12080-015-0270-z] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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32
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Murabito E, Verma M, Bekker M, Bellomo D, Westerhoff HV, Teusink B, Steuer R. Monte-Carlo modeling of the central carbon metabolism of Lactococcus lactis: insights into metabolic regulation. PLoS One 2014; 9:e106453. [PMID: 25268481 PMCID: PMC4182131 DOI: 10.1371/journal.pone.0106453] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2014] [Accepted: 08/07/2014] [Indexed: 11/18/2022] Open
Abstract
Metabolic pathways are complex dynamic systems whose response to perturbations and environmental challenges are governed by multiple interdependencies between enzyme properties, reactions rates, and substrate levels. Understanding the dynamics arising from such a network can be greatly enhanced by the construction of a computational model that embodies the properties of the respective system. Such models aim to incorporate mechanistic details of cellular interactions to mimic the temporal behavior of the biochemical reaction system and usually require substantial knowledge of kinetic parameters to allow meaningful conclusions. Several approaches have been suggested to overcome the severe data requirements of kinetic modeling, including the use of approximative kinetics and Monte-Carlo sampling of reaction parameters. In this work, we employ a probabilistic approach to study the response of a complex metabolic system, the central metabolism of the lactic acid bacterium Lactococcus lactis, subject to perturbations and brief periods of starvation. Supplementing existing methodologies, we show that it is possible to acquire a detailed understanding of the control properties of a corresponding metabolic pathway model that is directly based on experimental observations. In particular, we delineate the role of enzymatic regulation to maintain metabolic stability and metabolic recovery after periods of starvation. It is shown that the feedforward activation of the pyruvate kinase by fructose-1,6-bisphosphate qualitatively alters the bifurcation structure of the corresponding pathway model, indicating a crucial role of enzymatic regulation to prevent metabolic collapse for low external concentrations of glucose. We argue that similar probabilistic methodologies will help our understanding of dynamic properties of small-, medium- and large-scale metabolic networks models.
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Affiliation(s)
- Ettore Murabito
- Manchester Institute of Biotechnology, School of Chemical Engineering and Analytical Sciences (CEAS), Manchester Centre for Integrative Systems Biology (MCISB), The University of Manchester, Manchester, United Kingdom
- * E-mail: (EM); (RS)
| | - Malkhey Verma
- Manchester Institute of Biotechnology, School of Chemical Engineering and Analytical Sciences (CEAS), Manchester Centre for Integrative Systems Biology (MCISB), The University of Manchester, Manchester, United Kingdom
| | - Martijn Bekker
- Molecular Microbial Physiology, Swammerdam Institute for Life Sciences, University of Amsterdam, Amsterdam, The Netherlands
| | - Domenico Bellomo
- Systems Bioinformatics IBIVU and Netherlands Institute for Systems Biology (NISB), VU University Amsterdam, Amsterdam, The Netherlands
| | - Hans V. Westerhoff
- Manchester Institute of Biotechnology, School of Chemical Engineering and Analytical Sciences (CEAS), Manchester Centre for Integrative Systems Biology (MCISB), The University of Manchester, Manchester, United Kingdom
- Synthetic Systems Biology, Swammerdam Institute for Life Sciences, University of Amsterdam, Amsterdam, The Netherlands
- Molecular Cell Physiology, FALW, VU University Amsterdam, Amsterdam, The Netherlands
| | - Bas Teusink
- Systems Bioinformatics IBIVU and Netherlands Institute for Systems Biology (NISB), VU University Amsterdam, Amsterdam, The Netherlands
| | - Ralf Steuer
- CzechGlobe - Global Change Research Center, Academy of Sciences of the Czech Republic, Brno, Czech Republic
- Humboldt-University Berlin, Institute for Theoretical Biology, Berlin, Germany
- * E-mail: (EM); (RS)
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33
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Abstract
The dynamics of ecosystem collapse are fundamental to determining how and why biological communities change through time, as well as the potential effects of extinctions on ecosystems. Here, we integrate depictions of mammals from Egyptian antiquity with direct lines of paleontological and archeological evidence to infer local extinctions and community dynamics over a 6,000-y span. The unprecedented temporal resolution of this dataset enables examination of how the tandem effects of human population growth and climate change can disrupt mammalian communities. We show that the extinctions of mammals in Egypt were nonrandom and that destabilizing changes in community composition coincided with abrupt aridification events and the attendant collapses of some complex societies. We also show that the roles of species in a community can change over time and that persistence is predicted by measures of species sensitivity, a function of local dynamic stability. To our knowledge, our study is the first high-resolution analysis of the ecological impacts of environmental change on predator-prey networks over millennial timescales and sheds light on the historical events that have shaped modern animal communities.
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Bifurcation analysis of models with uncertain function specification: how should we proceed? Bull Math Biol 2014; 76:1218-40. [PMID: 24789567 DOI: 10.1007/s11538-014-9951-9] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2013] [Accepted: 03/13/2014] [Indexed: 10/25/2022]
Abstract
When we investigate the bifurcation structure of models of natural phenomena, we usually assume that all model functions are mathematically specified and that the only existing uncertainty is with respect to the parameters of these functions. In this case, we can split the parameter space into domains corresponding to qualitatively similar dynamics, separated by bifurcation hypersurfaces. On the other hand, in the biological sciences, the exact shape of the model functions is often unknown, and only some qualitative properties of the functions can be specified: mathematically, we can consider that the unknown functions belong to a specific class of functions. However, the use of two different functions belonging to the same class can result in qualitatively different dynamical behaviour in the model and different types of bifurcation. In the literature, the conventional way to avoid such ambiguity is to narrow the class of unknown functions, which allows us to keep patterns of dynamical behaviour consistent for varying functions. The main shortcoming of this approach is that the restrictions on the model functions are often given by cumbersome expressions and are strictly model-dependent: biologically, they are meaningless. In this paper, we suggest a new framework (based on the ODE paradigm) which allows us to investigate deterministic biological models in which the mathematical formulation of some functions is unspecified except for some generic qualitative properties. We demonstrate that in such models, the conventional idea of revealing a concrete bifurcation structure becomes irrelevant: we can only describe bifurcations with a certain probability. We then propose a method to define the probability of a bifurcation taking place when there is uncertainty in the parameterisation in our model. As an illustrative example, we consider a generic predator-prey model where the use of different parameterisations of the logistic-type prey growth function can result in different dynamics in terms of the type of the Hopf bifurcation through which the coexistence equilibrium loses stability. Using this system, we demonstrate a framework for evaluating the probability of having a supercritical or subcritical Hopf bifurcation.
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35
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Calçada D, Vianello D, Giampieri E, Sala C, Castellani G, de Graaf A, Kremer B, van Ommen B, Feskens E, Santoro A, Franceschi C, Bouwman J. The role of low-grade inflammation and metabolic flexibility in aging and nutritional modulation thereof: a systems biology approach. Mech Ageing Dev 2014; 136-137:138-47. [PMID: 24462698 DOI: 10.1016/j.mad.2014.01.004] [Citation(s) in RCA: 69] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2013] [Revised: 01/10/2014] [Accepted: 01/13/2014] [Indexed: 02/07/2023]
Abstract
Aging is a biological process characterized by the progressive functional decline of many interrelated physiological systems. In particular, aging is associated with the development of a systemic state of low-grade chronic inflammation (inflammaging), and with progressive deterioration of metabolic function. Systems biology has helped in identifying the mediators and pathways involved in these phenomena, mainly through the application of high-throughput screening methods, valued for their molecular comprehensiveness. Nevertheless, inflammation and metabolic regulation are dynamical processes whose behavior must be understood at multiple levels of biological organization (molecular, cellular, organ, and system levels) and on multiple time scales. Mathematical modeling of such behavior, with incorporation of mechanistic knowledge on interactions between inflammatory and metabolic mediators, may help in devising nutritional interventions capable of preventing, or ameliorating, the age-associated functional decline of the corresponding systems.
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Affiliation(s)
- Dulce Calçada
- TNO, Microbiology and Systems Biology Group, Utrechtseweg 48, 3704 HE Zeist, The Netherlands; Wageningen University, Department of Human Nutrition, Wageningen, The Netherlands
| | - Dario Vianello
- University of Bologna, Department of Experimental, Diagnostic and Specialty Medicine, Via San Giacomo 12, 40126 Bologna, Italy
| | - Enrico Giampieri
- University of Bologna, Department of Physics and Astronomy, 40127 Bologna, Italy
| | - Claudia Sala
- University of Bologna, Department of Physics and Astronomy, 40127 Bologna, Italy
| | - Gastone Castellani
- University of Bologna, Department of Physics and Astronomy, 40127 Bologna, Italy
| | - Albert de Graaf
- TNO, Microbiology and Systems Biology Group, Utrechtseweg 48, 3704 HE Zeist, The Netherlands
| | - Bas Kremer
- TNO, Microbiology and Systems Biology Group, Utrechtseweg 48, 3704 HE Zeist, The Netherlands
| | - Ben van Ommen
- TNO, Microbiology and Systems Biology Group, Utrechtseweg 48, 3704 HE Zeist, The Netherlands
| | - Edith Feskens
- Wageningen University, Department of Human Nutrition, Wageningen, The Netherlands
| | - Aurelia Santoro
- University of Bologna, Department of Experimental, Diagnostic and Specialty Medicine, Via San Giacomo 12, 40126 Bologna, Italy
| | - Claudio Franceschi
- University of Bologna, Department of Experimental, Diagnostic and Specialty Medicine, Via San Giacomo 12, 40126 Bologna, Italy; University of Bologna, Interdepartmental Centre "L. Galvani" (CIG), 40126 Bologna, Italy
| | - Jildau Bouwman
- TNO, Microbiology and Systems Biology Group, Utrechtseweg 48, 3704 HE Zeist, The Netherlands.
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36
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Aufderheide H, Rudolf L, Gross T, Lafferty KD. How to predict community responses to perturbations in the face of imperfect knowledge and network complexity. Proc Biol Sci 2013; 280:20132355. [PMID: 24197416 PMCID: PMC3826232 DOI: 10.1098/rspb.2013.2355] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2013] [Accepted: 10/14/2013] [Indexed: 11/12/2022] Open
Abstract
Recent attempts to predict the response of large food webs to perturbations have revealed that in larger systems increasingly precise information on the elements of the system is required. Thus, the effort needed for good predictions grows quickly with the system's complexity. Here, we show that not all elements need to be measured equally well, suggesting that a more efficient allocation of effort is possible. We develop an iterative technique for determining an efficient measurement strategy. In model food webs, we find that it is most important to precisely measure the mortality and predation rates of long-lived, generalist, top predators. Prioritizing the study of such species will make it easier to understand the response of complex food webs to perturbations.
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Affiliation(s)
- Helge Aufderheide
- Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
- Merchant Venturers School of Engineering, University of Bristol, Bristol, UK
| | - Lars Rudolf
- Merchant Venturers School of Engineering, University of Bristol, Bristol, UK
| | - Thilo Gross
- Merchant Venturers School of Engineering, University of Bristol, Bristol, UK
| | - Kevin D. Lafferty
- US Geological Survey, Western Ecological Research Center, Marine Science Institute, University of California, Santa Barbara, CA 93106, USA
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37
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Höfener JM, Sethia GC, Gross T. Amplitude death in networks of delay-coupled delay oscillators. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2013; 371:20120462. [PMID: 23960220 DOI: 10.1098/rsta.2012.0462] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Amplitude death is a dynamical phenomenon in which a network of oscillators settles to a stable state as a result of coupling. Here, we study amplitude death in a generalized model of delay-coupled delay oscillators. We derive analytical results for degree homogeneous networks which show that amplitude death is governed by certain eigenvalues of the network's adjacency matrix. In particular, these results demonstrate that in delay-coupled delay oscillators amplitude death can occur for arbitrarily large coupling strength k. In this limit, we find a region of amplitude death which already occurs at small coupling delays that scale with 1/k. We show numerically that these results remain valid in random networks with heterogeneous degree distribution.
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Affiliation(s)
- Johannes M Höfener
- Biological Physics Section, Max Planck Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, Dresden 01187, Germany
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38
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Scheff JD, Calvano SE, Androulakis IP. Predicting critical transitions in a model of systemic inflammation. J Theor Biol 2013; 338:9-15. [PMID: 23973206 DOI: 10.1016/j.jtbi.2013.08.011] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2013] [Revised: 05/13/2013] [Accepted: 08/12/2013] [Indexed: 12/14/2022]
Abstract
The human body can be viewed as a dynamical system, with physiological states such as health and disease broadly representing steady states. From this perspective, and given inter- and intra-individual heterogeneity, an important task is identifying the propensity to transition from one steady state to another, which in practice can occur abruptly. Detecting impending transitions between steady states is of significant importance in many fields, and thus a variety of methods have been developed for this purpose, but lack of data has limited applications in physiology. Here, we propose a model-based approach towards identifying critical transitions in systemic inflammation based on a minimal amount of assumptions about the availability of data and the structure of the system. We derived a warning signal metric to identify forthcoming abrupt transitions occurring in a mathematical model of systemic inflammation with a gradually increasing bacterial load. Intervention to remove the inflammatory stimulus was successful in restoring homeostasis if undertaken when the warning signal was elevated rather than waiting for the state variables of the system themselves to begin moving to a new steady state. The proposed combination of data and model-based analysis for predicting physiological transitions represents a step forward towards the quantitative study of complex biological systems.
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Affiliation(s)
- Jeremy D Scheff
- Department of Biomedical Engineering, Rutgers University, 599 Taylor Road, Piscataway, NJ 08854, USA.
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39
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40
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Mu N, Liao X, Huang T. Approach to design neural cryptography: a generalized architecture and a heuristic rule. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:062804. [PMID: 23848726 DOI: 10.1103/physreve.87.062804] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2013] [Indexed: 06/02/2023]
Abstract
Neural cryptography, a type of public key exchange protocol, is widely considered as an effective method for sharing a common secret key between two neural networks on public channels. How to design neural cryptography remains a great challenge. In this paper, in order to provide an approach to solve this challenge, a generalized network architecture and a significant heuristic rule are designed. The proposed generic framework is named as tree state classification machine (TSCM), which extends and unifies the existing structures, i.e., tree parity machine (TPM) and tree committee machine (TCM). Furthermore, we carefully study and find that the heuristic rule can improve the security of TSCM-based neural cryptography. Therefore, TSCM and the heuristic rule can guide us to designing a great deal of effective neural cryptography candidates, in which it is possible to achieve the more secure instances. Significantly, in the light of TSCM and the heuristic rule, we further expound that our designed neural cryptography outperforms TPM (the most secure model at present) on security. Finally, a series of numerical simulation experiments are provided to verify validity and applicability of our results.
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Affiliation(s)
- Nankun Mu
- College of Computer Science, Chongqing University, Chongqing, 400044, China.
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41
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Reznik E, Kaper TJ, Segrè D. The dynamics of hybrid metabolic-genetic oscillators. CHAOS (WOODBURY, N.Y.) 2013; 23:013132. [PMID: 23556969 DOI: 10.1063/1.4793573] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
The synthetic construction of intracellular circuits is frequently hindered by a poor knowledge of appropriate kinetics and precise rate parameters. Here, we use generalized modeling (GM) to study the dynamical behavior of topological models of a family of hybrid metabolic-genetic circuits known as "metabolators." Under mild assumptions on the kinetics, we use GM to analytically prove that all explicit kinetic models which are topologically analogous to one such circuit, the "core metabolator," cannot undergo Hopf bifurcations. Then, we examine more detailed models of the metabolator. Inspired by the experimental observation of a Hopf bifurcation in a synthetically constructed circuit related to the core metabolator, we apply GM to identify the critical components of the synthetically constructed metabolator which must be reintroduced in order to recover the Hopf bifurcation. Next, we study the dynamics of a re-wired version of the core metabolator, dubbed the "reverse" metabolator, and show that it exhibits a substantially richer set of dynamical behaviors, including both local and global oscillations. Prompted by the observation of relaxation oscillations in the reverse metabolator, we study the role that a separation of genetic and metabolic time scales may play in its dynamics, and find that widely separated time scales promote stability in the circuit. Our results illustrate a generic pipeline for vetting the potential success of a circuit design, simply by studying the dynamics of the corresponding generalized model.
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Affiliation(s)
- Ed Reznik
- Department of Biomedical Engineering, Boston University, Boston, Massachusetts 02215, USA
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42
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Intrinsic feedbacks in MAPK signaling cascades lead to bistability and oscillations. Acta Biotheor 2013; 61:59-78. [PMID: 23400325 DOI: 10.1007/s10441-013-9177-5] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2012] [Accepted: 01/22/2013] [Indexed: 10/27/2022]
Abstract
Previous studies have demonstrated that double phosphorylation of a protein can lead to bistability if some conditions are fulfilled. It was also shown that the signaling behavior of a covalent modification cycle can be quantitatively and, more importantly, qualitatively modified when this cycle is coupled to a signaling pathway as opposed to being isolated. This property was named retroactivity. These two results are studied together in this paper showing the existence of interesting phenomena--oscillations and bistability--in signaling cascades possessing at least one stage with a double-phosphorylation cycle as in MAPK cascades.
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43
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44
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Ackermann E, Weiel EM, Pfaff T, Drossel B. Boolean versus continuous dynamics in modules with two feedback loops. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2012; 35:107. [PMID: 23096153 DOI: 10.1140/epje/i2012-12107-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2012] [Revised: 09/20/2012] [Accepted: 09/26/2012] [Indexed: 06/01/2023]
Abstract
We investigate the dynamical behavior of simple networks, namely loops with an additional internal regulating connection. Continuous dynamics for mRNA and protein concentrations is compared to a Boolean model for gene activity. Using a generalized method and within a single framework, we study different continuous models and different types of regulatory functions, and establish conditions under which the system can display stable oscillations or stable fixed points. These conditions depend only on general features such as the degree of cooperativity of the regulating interactions and the logical structure of the interactions. There are no simple rules for deciding when Boolean and continuous dynamics agree with each other, but we identify several relevant criteria.
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Affiliation(s)
- Eva Ackermann
- Institut für Festkörperphysik, TU Darmstadt, Hochschulstraße 6, 64289, Darmstadt, Germany.
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45
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Plitzko SJ, Drossel B, Guill C. Complexity-stability relations in generalized food-web models with realistic parameters. J Theor Biol 2012; 306:7-14. [PMID: 22575485 DOI: 10.1016/j.jtbi.2012.04.008] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2011] [Revised: 04/05/2012] [Accepted: 04/06/2012] [Indexed: 11/26/2022]
Abstract
We investigate the relation between complexity and stability in model food webs by evaluating the local stability of fixed points of the population dynamics using the recently developed method of generalized modeling. We first determine general conditions that lead to positive complexity-stability relations. These include (1) high resource abundance and (2) strong density-dependent mortality effects that limit consumer populations. The parameters that constitute a generalized model have clear biological meanings. In this work, emphasis is placed on using realistic values for these generalized parameters. They are derived from conventional ordinary differential equations which are commonly used to describe population dynamics and for which empirical parameter estimates exist. We find that the empirically supported generalized parameters fall in regions of the parameter space that allow for a positive relation between food-web complexity and stability.
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Affiliation(s)
- Sebastian J Plitzko
- Institut für Festkörperphysik, TU Darmstadt, Hochschulstrasse 6, D-64289 Darmstadt, Germany.
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46
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Lade SJ, Gross T. Early warning signals for critical transitions: a generalized modeling approach. PLoS Comput Biol 2012; 8:e1002360. [PMID: 22319432 PMCID: PMC3271022 DOI: 10.1371/journal.pcbi.1002360] [Citation(s) in RCA: 79] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2011] [Accepted: 12/09/2011] [Indexed: 11/18/2022] Open
Abstract
Critical transitions are sudden, often irreversible, changes that can occur in a large variety of complex systems; signals that warn of critical transitions are therefore highly desirable. We propose a new method for early warning signals that integrates multiple sources of information and data about the system through the framework of a generalized model. We demonstrate our proposed approach through several examples, including a previously published fisheries model. We regard our method as complementary to existing early warning signals, taking an approach of intermediate complexity between model-free approaches and fully parameterized simulations. One potential advantage of our approach is that, under appropriate conditions, it may reduce the amount of time series data required for a robust early warning signal.
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Affiliation(s)
- Steven J Lade
- Max Planck Institute for the Physics of Complex Systems, Dresden, Germany.
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47
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Gehrmann E, Glässer C, Jin Y, Sendhoff B, Drossel B, Hamacher K. Robustness of glycolysis in yeast to internal and external noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:021913. [PMID: 21929026 DOI: 10.1103/physreve.84.021913] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2011] [Indexed: 05/31/2023]
Abstract
Glycolysis is one of the most essential intracellular networks, found in a wide range of organisms. Due to its importance and due to its wide industrial applications, many experimental studies on all details of this process have been performed. Until now, however, to the best of our knowledge, there has been no comprehensive investigation of the robustness of this important process with respect to internal and external noise. To close this gap, we applied two complementary and mutually supporting approaches to a full-scale model of glycolysis in yeast: (a) a linear stability analysis based on a generalized modeling that deals only with those effective parameters of the system that are relevant for its stability, and (b) a numerical integration of the rate equations in the presence of noise, which accounts for imperfect mixing. The results suggest that the occurrence of metabolite oscillations in part of the parameter space is a side effect of the optimization of the system for maintaining a constant adenosine triphosphate level in the face of a varying energy demand and of fluctuations in the parameters and metabolite concentrations.
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Affiliation(s)
- Eva Gehrmann
- Institut für Festkörperphysik, TU Darmstadt, Hochschulstraße 6, D-64289 Darmstadt, Germany
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48
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Henkel S, Nägele T, Hörmiller I, Sauter T, Sawodny O, Ederer M, Heyer AG. A systems biology approach to analyse leaf carbohydrate metabolism in Arabidopsis thaliana. EURASIP JOURNAL ON BIOINFORMATICS & SYSTEMS BIOLOGY 2011; 2011:2. [PMID: 21910921 PMCID: PMC3171179 DOI: 10.1186/1687-4153-2011-2] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/29/2010] [Accepted: 06/17/2011] [Indexed: 12/01/2022]
Abstract
Plant carbohydrate metabolism comprises numerous metabolite interconversions, some of which form cycles of metabolite degradation and re-synthesis and are thus referred to as futile cycles. In this study, we present a systems biology approach to analyse any possible regulatory principle that operates such futile cycles based on experimental data for sucrose (Scr) cycling in photosynthetically active leaves of the model plant Arabidopsis thaliana. Kinetic parameters of enzymatic steps in Scr cycling were identified by fitting model simulations to experimental data. A statistical analysis of the kinetic parameters and calculated flux rates allowed for estimation of the variability and supported the predictability of the model. A principal component analysis of the parameter results revealed the identifiability of the model parameters. We investigated the stability properties of Scr cycling and found that feedback inhibition of enzymes catalysing metabolite interconversions at different steps of the cycle have differential influence on stability. Applying this observation to futile cycling of Scr in leaf cells points to the enzyme hexokinase as an important regulator, while the step of Scr degradation by invertases appears subordinate.
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Affiliation(s)
- Sebastian Henkel
- Biologisches Institut, Abteilung Pflanzenbiotechnologie, Universität Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart, Germany.
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49
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Zumsande M, Stiefs D, Siegmund S, Gross T. General analysis of mathematical models for bone remodeling. Bone 2011; 48:910-7. [PMID: 21185412 DOI: 10.1016/j.bone.2010.12.010] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 09/30/2010] [Revised: 12/08/2010] [Accepted: 12/12/2010] [Indexed: 11/29/2022]
Abstract
Bone remodeling is regulated by pathways controlling the interplay of osteoblasts and osteoclasts. In this work, we apply the method of generalized modeling to systematically analyse a large class of models of bone remodeling. Our analysis shows that osteoblast precursors can play an important role in the regulation of bone remodeling. Further, we find that the parameter regime most likely realized in nature lies close to bifurcation lines, marking qualitative changes in the dynamics. Although proximity to a bifurcation facilitates adaptive responses to changing external conditions, it entails the danger of losing dynamical stability. Some evidence implicates such dynamical transitions as a potential mechanism leading to forms of Paget's disease.
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Affiliation(s)
- Martin Zumsande
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany.
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50
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Malka R, Rom-Kedar V. Bacteria-phagocyte dynamics, axiomatic modelling and mass-action kinetics. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2011; 8:475-502. [PMID: 21631141 DOI: 10.3934/mbe.2011.8.475] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Axiomatic modeling is ensued to provide a family of models that describe bacterial growth in the presence of phagocytes, or, more generally, prey dynamics in a large spatially homogenous eco-system. A classification of the possible bifurcation diagrams that arise in such models is presented. It is shown that other commonly used models that do not belong to this class may miss important features that are associated with the limited growth curve of the bacteria (prey) and the saturation associated with the phagocytosis (predator kill) term. Notably, these features appear at relatively low concentrations, much below the saturation range. Finally, combining this model with a model of neutrophil dynamics in the blood after chemotherapy treatments we obtain new insights regarding the development of infections under neutropenic conditions.
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Affiliation(s)
- Roy Malka
- Department of Computer Science and Applied Mathematics, The Weizmann Institute, Rehovot, Israel.
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