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The slides of my talk given at the European Conference of Complex Systems 2012

The slides of my talk given at the European Conference of Complex Systems 2012

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  • \n
  • human population has grown six-fold, the world’s economy 50-fold and energy consumption 40-fold (Steffen et al. 2007)\n\n
  • Phase transitions, critical transitions, phase shifts.\n
  • Speak slowly.\n\n
  • Speak slowly.\n\n
  • Speak slowly.\n\n
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  • methods from physics and social sciences applied to medicine to figure out multicausality patterns.\n
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  • sequential importance sampling algorithm\n89 variables coded on the RSDB\n
  • 20RS - 55 Drivers, 186 links, density 6.3%\n
  • 82% density\n\nTop 5 RS in degree are in aquatic environments\n
  • Temperate areas are also strongly connected (tundra - greenland - thermohaline)\nMarine RS are tightly connected: water as a transport media for disturbances: turbidity, SST, pollutants, sediments, etc. \n
  • \n
  • 38% density\nGlobal warming: floods, droughts, precipitation, GHG\nAgriculture: fishing, deforestation, irrigation, fertilizers use, erosion, nutrient inputs\nHuman pop growth: urbanization, sewage \n
  • Purple: Marine Ecosystems\nBlue: Common to all types but also present in aquatic (marine + eutrophication and river change)\nOrange: More common on terrestrial ecosystems, less clustering, more context dependent for management.\n
  • CLD: consist on variables connected by arrows denoting causal influence. Each relationship must have a positive (+) or negative (-) polarity, intended to represent the effect of the dependent variable given a change in the independent variable. A positive link means that if the cause change, the effect will change in the same direction. A negative link means that if the cause change in one direction, the effect change in the opposite way. Closed paths thus conform the feedback mechanisms that could be reinforcing if their overall polarity is positive or balancing if negative.\n
  • 19 Regime Shifts\n204 nodes, 529 links, Density: 0.017 or 17%\nDegree:The number edges a vertex is connected to (Newman 2010): In-degree and Out-degree\nBTW: The extent to which a vertex lies on paths between other vertices\nEigenvector: A vertex is important if it is directly or indirectly connected to other vertices that are in turn important\n\n
  • Outdegree: Variables which have a lot of causal links to other variables.\nIndegree: Variables hard to manage because they receive a lot of causal connections\n
  • Few nodes have a lot of links!\nMost connections are positive.\n
  • Few nodes have a lot of links!\nMost connections are positive.\n
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ECCS12 ECCS12 Presentation Transcript

  • The Network of Driving Forces of Global Environmental Change Juan-Carlos Rocha, Oonsie Biggs & Garry Peterson Stockholm Resilience Centre Stockholm University
  • The challengeThe Anthropocene: an era wherehuman impact on Earth is strongenough to change global scaledynamics.Frequency and intensity of regimeshifts are likely to increase.Society and economy could bepotentially affected through impactson ecosystem services. Vulnerable areas? Possible synergistic effects? Cross-scale interactions?
  • Regime shifts: Large, abrupt, persistent change in the structure and function of a system.Policy relevant: Substantial change in ecosystem services - the goods people receive from nature
  • Research agenda on Regime Shifts High Bayesian networks - Web crawlers & models local knowledge Knowledge of the Models & Jacobians system Statistics: Autocorrelation and variance Low Low Data quality High (time series)
  • Research agenda on Regime Shifts High Bayesian networks - Web crawlers & models local knowledge Knowledge of the Models & Jacobians system Statistics: Autocorrelation and variance Low Low Data quality High (time series)
  • Research agenda on Regime Shifts High Bayesian networks - Web crawlers & models local knowledge Knowledge of the Models & Jacobians system ? Statistics: Autocorrelation and variance Low Low Data quality High (time series)
  • Virtruvian Man, Leonardo Da Vinci
  • The human disease network Network Properties of Complex Human Disease GenesKwang-Il Goh*†‡§, Michael E. Cusick†‡¶, David Valleʈ, Barton Childsʈ, Marc Vidal†‡¶**, ´ ´ and Albert-Laszlo ´ Barabasi*†‡***Center for Complex Network Research and Department of Physics, University of Notre Dame, Notre Dame, IN 46556; †Center for Cancer Systems Biology Identified through Genome-Wide Association Studies(CCSB) and ¶Department of Cancer Biology, Dana–Farber Cancer Institute, 44 Binney Street, Boston, MA 02115; ‡Department of Genetics, Harvard MedicalSchool, 77 Avenue Louis Pasteur, Boston, MA 02115; §Department of Physics, Korea University, Seoul 136-713, Korea; and ʈDepartment of Pediatrics and the Fredrik Barrenas1.*, Sreenivas Chavali1., Petter Holme2,3, Reza Mobini1, Mikael Benson1McKusick–Nathans Institute of Genetic Medicine, Johns Hopkins University School of Medicine, Baltimore, MD 21205 ˚ ˚ 1 The Unit for Clinical Systems Biology, University of Gothenburg, Gothenburg, Sweden, 2 Department of Physics, Umea University, Umea, Sweden, 3 Department ofEdited by H. Eugene Stanley, Boston University, Boston, MA, and approved April 3, 2007 (received for review February 14, 2007) Energy Science, Sungkyunkwan University, Suwon, KoreaA network of disorders and disease genes linked by known disorder– known genetic disorders, whereas the other set corresponds to allgene associations offers a platform to explore in a single graph- known disease genes in the human genome (Fig. 1). A disorder andtheoretic framework all known phenotype and disease gene associ- a gene are then connected by a link if mutations in that gene are Abstractations, indicating the common genetic origin of many diseases. Genes implicated in that disorder. The list of disorders, disease genes, and DISEASOMEassociated with similar disorders show both higher likelihood of associations between them was obtained from the Online Mende- Background: Previous studies of network properties of human disease genes have mainly focused on monogenic diseasesphysical interactions between their products and higher expression lian Inheritance in Man (OMIM; ref. 18), a compendium of human or cancers and have suffered from discovery bias. Here we investigated the network properties of complex disease genesprofiling similarity for their transcripts, supporting the existence of disease genes and phenotypes. As of December 2005, this list identified by genome-wide association studies (GWAs), thereby eliminating discovery bias.distinct disease-specific functional modules. Wedisease phenome find that essential disease genome contained 1,284 disorders and 1,777 disease genes. OMIM initially Human Disease Networkhuman genes are likely to encode hub proteins and are expressed Disease Gene Network Principal findings: We derived a network of complex diseases (n = 54) and complex disease genes (n = 349) to explore the Ataxia-telangiectasia focused on AR monogenic disorders but in recent years has expanded (HDN)widely in most tissues. This suggests that disease genes hypospadias Perineal also would Androgen insensitivity (DGN) to include complex traits and the associated genetic mutations that ATM shared genetic architecture of complex diseases. We evaluated the centrality measures of complex disease genes inplay a central role in the human interactome. In contrast, we find that confer susceptibility to these common disorders (18). Although this comparison with essential and monogenic disease genes in the human interactome. The complex disease network showed T-cell lymphoblastic leukemiathe vast majority of disease genes are nonessential and show no Charcot-Marie-Tooth disease Papillary serous carcinoma BRCA1 history introduces some biases, LMNA the disease gene record is far and HEXB that diseases belonging to the same disease class do not always share common disease genes. A possible explanation couldtendency to encode hubLipodystrophy and their expression pattern indi- proteins, BRCA2 from complete, OMIM represents the most complete and up-to- ALS2 be that the variants with higher minor allele frequency and larger effect size identified using GWAs constitute disjoint parts APPLIED PHYSICAL Prostate cancercates that ataxia/paraplegia localized paraplegia syndrome Spastic they are Silver spastic in the functional periphery of the CDH1 BSCL2 date repository of all known VAPBdisease genes and the disorders they of the allelic spectra of similar complex diseases. The complex disease gene network showed high modularity with the size SCIENCESnetwork. A selection-basedSandhoff disease model explains the observed difference Ovarian cancer GARS Amyotrophic lateral sclerosis confer. We manually classified each disorder into one of 22 disorder GARS of the largest component being smaller than expected from a randomized null-model. This is consistent with limited sharingbetween essential and disease genes and also suggests that diseases Lymphoma classes based on the physiological system affected [see supporting HEXB of genes between diseases. Complex disease genes are less central than the essential and monogenic disease genes in thecaused by somatic mutations should not be peripheral, a prediction Spinal muscular atrophy information (SI) Text, SI Fig. 5, and SI Table 1 for details]. KRAS AR human interactome. Genes associated with the same disease, compared to genes associated with different diseases, morewe confirm for cancer genes. insensitivity Androgen Prostate cancer Breast cancer Starting LMNA the diseasome bipartite graph we generated two from ATM often tend to share a protein-protein interaction and a Gene Ontology Biological Process. Perineal hypospadiasbiological networks ͉ complex networks ͉ human genetics Pancreatic cancer ͉ systems biologically relevant network projections (Fig. 1). In the ‘‘human MSH2 BRIP1 BRCA2biology ͉ diseasome Lymphoma disease network’’ (HDN) nodes represent disorders, and two PIK3CA BRCA1 Conclusions: This indicates that network neighbors of known disease genes form an important class of candidates for Wilms tumor Breast cancer Wilms tumor disorders are connected to each otherKRAS TP53 RAD54L if they share at least one gene identifying novel genes for the same disease. Ovarian cancer in which mutations are associated with both TP53 disorders (Figs. 1 andD Spinal muscular atrophy ecades-long efforts to map human disease loci,Sandhoff disease Pancreatic cancer at first genet- MAD1L1 2a). In the ‘‘disease gene network’’MAD1L1 (DGN) nodes represent disease ically and later physically (1), followed by recent positional Fanconi anemia Papillary serous carcinoma Lipodystrophy two CHEK2 genes, andRAD54L genes are connected if they are associated with the Citation: Barrenas F, Chavali S, Holme P, Mobini R, Benson M (2009) Network Properties of Complex Human Disease Genes Identified through Genome-Widecloning of many disease T-cell lymphoblastic and genome-wide association genes (2) leukemia Charcot-Marie-Tooth disease PIK3CA same disorder (Figs. 1 and 2b). Next, we discuss the potential of VAPB Association Studies. PLoS ONE 4(11): e8090. doi:10.1371/journal.pone.0008090studies (3), have generated an impressive list of disorder–gene Ataxia-telangiectasia these networks to help us understand and MSH2 CHEK2 CDH1 represent in a single Editor: Thomas Mailund, Aarhus University, Denmarkassociation pairs (4, 5). In addition, recent efforts to map the Amyotrophic lateral sclerosis frameworkBSCL2 known disease gene and phenotype associations. all Received September 15, 2009; Accepted November 3, 2009; Published November 30, 2009protein–protein interactions in humans (6, 7), together paraplegia syndrome Silver spastic with efforts ALS2to curate an extensive map of human metabolism (8) and regulatory Spastic ataxia/paraplegia Copyright: ß 2009 Barrenas et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits Properties BRIP1the HDN. If each human disorder tends to have a ofnetworks offer increasingly detailed maps of theFanconi anemia relationships unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.between different disease genes. Most of the successful studies distinct and unique genetic origin, then the HDN would be dis- connected into many single nodes corresponding to specific disor- Funding: This work was supported by the Swedish Research Council, The European Commission, The Swedish Foundation for Strategic Research (PH), and thebuilding on these new approaches have focused, however, on a WCU (World Class University) program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology R31-R31-single disease, using network-based tools to gain a better under- ders or grouped into small clusters of a few closely related disorders. 2008-000-10029-0 (PH). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. In contrast, the obtained HDN displays many connections betweenFig. 1. Construction of the diseasome bipartite network. (Center) A small subset of OMIM-based disorder– disease gene associations (18), where circles and rectanglesstanding of the relationship between the genes implicated in acorrespond to disorders and disease genes, respectively. A link is placed between a disorder and aindividual disorders and disorder classes (Fig. 2a). Of 1,284 disease gene if mutations in that gene lead to the specific disorder. Competing Interests: The authors have declared that no competing interests exist.selected circle is proportional to the number of genes participating in the corresponding both and the color corresponds to the disorder class to which the diseaseThe size of adisorder (9). disorder,belongs. (Left) The HDN a conceptually different approach, which two disorders are connected there Here we take projection of the diseasome bipartite graph, in exploring disorders, 867ifhave is a gene that is implicatedother disorders,ofand 516 at least one link to in both. The width * E-mail: fredrik.barrenas@gu.sea link is proportional to the number of genes and are implicated in both diseases. For example, three genes area giant component, cancer and prostate cancer, geneticwhether human genetic disorders that the corresponding disease disorders form implicated in both breast suggesting that the . These authors contributed equally to this work.resulting in a link ofrelated to each other at a higher level of cellular andtwo genes are connected if they are involved in the same disorder.shared with othergenes might be weight three between them. (Right) The DGN projection where origins of most diseases, to some extent, are The width ofa link is proportional to the number of diseases with which the two genes are commonly diseases. A full number of genes associated with Fig. 13. associated. The diseasome bipartite map is provided as SI a disorder, s, has aorganismal organization. Support for the validity of this approachis provided by examples of genetic disorders that arise from broad distribution (see SI Fig. 6a), indicating that most disorders relate to a few disease genes, whereas a handful of phenotypes, such Introduction human interactome. A more recent report that evaluated thea few otherin more than a singlefew phenotypes such as colon Formentary, gene-centered view of the diseasome. Given that the linksmutations disorders, whereas a gene (locus heterogeneity). network properties of disease genes showed that genes withcancer (linked to k ϭ 50 other disorders) orby mutations (k ϭ 30) atsignify deafnessphenotypicleukemia (s ϭ 37), and colon cancer (s ϭ 34),example, Zellweger syndrome is caused breast cancer in any of as related (s ϭ 41), association between two genes, they Systems Biology based approaches of studying human genetic intermediate degrees (numbers of neighbors) were more likely toleast 11 hubs that associated with peroxisome biogenesis (10).represent a to dozens of genes (Fig. 2a). The degree (k) distribution ofrepresent genes, all are connected to a large number of distinct relate measure of their phenotypic relatedness, which could be diseases have brought in a shift in the paradigm of elucidating harbor germ-line disease mutations [12]. However, interpretationdisorders. The prominence of cancer among the most connected theusedHDN (SI Fig. 6b) in conjunction with protein–proteinlinked to onlySimilarly, there are many examples of different mutations in in future studies, indicates that most disorders are inter- disease mechanisms from analyzing the effects of single genes todisorders arises in part from the many clinically distinct cancercur-actions (6, 7, 19), transcription factor-promoter interactions (20),same gene (allelic heterogeneity) giving rise to phenotypes of this dataset might not be applicable to complex disease genes understanding the effect of molecular interaction networks. Suchsubtypes tightly connected withdisorders. For example, mutations inand metabolic reactions (8), toM.V., and A.-L.B. designed research; K.-I.G. and M.E.C.rently classified as different each other through common tumor Author contributions: D.V., B.C., discover novel genetic interactions. since 97% of the disease genes were monogenic. Despite thisTP53 have been linked to 11 clinically distinguishable cancer-In the DGN, research;of 1,777 disease genes data; connected to other M.V., andrepressor genes such as TP53 and PTEN. performed 1,377 K.-I.G. and M.E.C. analyzed are and K.-I.G., M.E.C., D.V., networks have been exploited to find novel candidate genes, based reservation, both the latter studies found a functional clustering ofrelated disorders (11). Given the highly interlinked internal orga-disease genes, and paper. Although the HDN layout was generated independently of any A.-L.B. wrote the 903 genes belong to a giant component (Fig. 2b). on the assumption that neighbors of a disease-causing gene in a disease genes. Another concern is that the above studies could beknowledge on disorder classes,itthe resultingpossible to improve theWhereas the number of genesinterest.nization of the cell (12–17), should be network is naturally The authors declare no conflict of involved in multiple diseases de- network are more likely to cause either the same or a similar confounded by discovery bias, in other words these disease genesand visibly clustered accordingapproachdisorder classes. Yet, theresingle gene–single disorder to major by developing a conceptualcreases article is a (SI Fig. 6d; light gray nodes in Fig. 2b), several This rapidly PNAS Direct Submission. disease [1–14]. Initial studies investigating the network properties were identified based on previous knowledge. By contrast,framework to link systematically all genetic disorders (the humandisease genes (e.g., TP53, PAX6) are involved in as many as 10 GO, Geneare visible differences between different classes of disorders. Abbreviations: DGN, disease gene network; HDN, human disease network; of human disease genes were based on cancers and revealed thatWhereas the large cancer cluster is tightly interconnected due to the(thedisorders, representing major hubs in the network. Pearson correlation coeffi-‘‘disease phenome’’) with the complete list of disease genes Genome Wide Association studies (GWAs) do not suffer from Ontology; OMIM, Online Mendelian Inheritance in Man; PCC, up-regulated genes in cancerous tissues were central in themany genes associated with multiple global view of (TP53, KRAS,‘‘disease genome’’), resulting in a types of cancer the ‘‘diseasome,’’ cient. such bias [15].ERBB2, NF1, etc.) of all known several diseases with strong pre- **To whom correspondence and DGN. To probe how the topologythe combined set and includes disorder/disease gene associations.Functional Clustering of HDN may be addressed. E-mail: alb@nd.edu or marc࿝vidal@ interactome and highly connected (often referred to as hubs) In this study, we have derived networks of complex diseases anddisposition to cancer, such as Fanconi anemia and ataxia telangi- of thedfci.harvard.edu. GDN deviates from random, we randomly HDN and [1,2]. A subsequent study based on the human disease network complex disease genes to explore the shared genetic architecture of Resultsectasia, metabolic disorders do not appear to form a single distinct shuffledarticle contains supporting information online at www.pnas.org/cgi/content/full/ This the associations between disorders and genes, while keep- and disease gene network derived from the Online Mendelian complex diseases studied using GWAs. Further, we have evaluatedcluster but are underrepresented in constructed a bipartite graphing the number of links per each disorder and disease gene in the Construction of the Diseasome. We the giant component and 0701361104/DC1. Inheritance in Man (OMIM) demonstrated that the products of the topological and functional properties of complex disease genesoverrepresented in disjoint sets of nodes. One set corresponds to allbipartite network unchanged. Interestingly, the average size of the consisting of two the small connected components (Fig. 2a). To © 2007 by The National Academy of Sciences of the USA disease genes tended (i) to have more interactions with each other in the human interactome by comparing them with essential,quantify this difference, we measured the locus heterogeneity of giant component of 104 randomized disease networks is 643 Ϯ 16,each disorder class and the fraction of disorders that are connected significantly larger than 516 (P Ͻ 10Ϫ4; for details of statistical than with non-disease genes, (ii) to be expressed in the same tissues monogenic and non-disease genes. We observed that diseases www.pnas.org͞cgi͞doi͞10.1073͞pnas.0701361104to each other in the HDN (see SI Text). We find that cancer and analyses of the results reported hereafter, ͉see SI104 ͉ no. 21 ͉ 8685– 8690 PNAS ͉ May 22, 2007 vol. Text), the actual and (iii) to share Gene Ontology (GO) terms [8]. Contradicting belonging to the same disease class do not always show a tendencyneurological disorders show high locus heterogeneity and also size of the HDN (SI Fig. 6c). Similarly, the average size of the giant earlier reports, this latter study demonstrated that the non-essential to share common disease genes; the complex disease gene net-represent the most connected disease classes, in contrast with component from randomized gene networks is 1,087 Ϯ 20 genes, human disease genes showed no tendency to encode hubs in the work shows high modularity comparable to that of the humanmetabolic, skeletal, and multiple disorders that have low genetic significantly larger than 903 (P Ͻ 10Ϫ4), the actual size of the DGNheterogeneity and are the least connected (SI Fig. 7). (SI Fig. 6e). These differences suggest important pathophysiological clustering of disorders and disease genes. Indeed, in the actual PLoS ONE | www.plosone.org 1 November 2009 | Volume 4 | Issue 11 | e8090Properties of the DGN. In the DGN, two disease genes are connected networks disorders (genes) are more likely linked to disordersif they are associated with the same disorder, providing a comple- (genes) of the same disorder class. For example, in the HDN there8686 ͉ www.pnas.org͞cgi͞doi͞10.1073͞pnas.0701361104 Goh et al.
  • Regime shift database
  • Regime shift database
  • Regime shift database Description of the alternative regimes and reinforcing feedbacks The drivers that precipitate the regime shift Impacts on ecosystem services and human well-being Management options www.regimeshifts.org
  • N Policy relevant regime shifts Mechanism Reversibility 1 Bivalves collapse Established H 2 Coral transitions Established H 3 Desertification Contested H, I 4 Encroachment Established H 5 Eutrophication Established H, I, RData: 6 Fisheries collapse 7 Marine foodwebs collapse Contested Contested U U 8 Forest - Savanna Established I 9 Hypoxia Established H, R 10 Kelp transitions Established H, R20 policy relevant regime shifts: 11 Soil salinization Established H, I 12 Steppe - Tundra Established I 13 Tundra - Forest Established I 8 terrestrial 14 Monsoon circulation Established I 9 aquatic 15 Thermohaline circulation collapse Established I 2 global + 1 polar 16 Greenland ice sheet collapse Established I 17 Arctic salt marshes Established I 18 Peatlands Established I 19 River channel position Established I 20 Soil structure Established H, I Reversibility: H = Hysteretic; I = Irreversible; R= Reversible; U = Unknown
  • Methods• Bipartite network and one- mode projections: 20 Regime shifts + 55 Drivers Drivers Regime shifts• 104 random bipartite graphs to explore significance of Regime Shift Database couplings: mean degree and A 1 0 1 1 0 0 0 0 1 1 1 1 0 1 0 1 co-occurrence statistics on B C 1 0 0 0 1 1 0 0 1 1 1 0 0 1 0 1 one-mode projections.• ERGM models using Jaccard Ecosystem services Spatial scale similarity index on the RSDB Ecosystem processes Temporal scale as edge covariates Ecosystem type Reversibility Impact on human well being Evidence Land use ...
  • 20 Number of vertex5 10 0 15 1 3 5 7 10 12 16 19 Degree Regime Shifts - Drivers 20 Regime shifts Bipartite Network
  • Greenland Monsoon weakening Tundra to Soil Forest Coral transitions structure Dry land degradationThermohaline Kelps transitionscirculation Forest to Savannas Soil Eutrophication salinization Fisheries collapse Bivalves Encroachment collapse Salt marshes Peatlands Marine foodwebs Hypoxia Floating plants River channel change Regime Shifts Network Top 5 occur in aquatic ecosystems
  • Color Key Greenland Monsoon weakening and Histogram Tundra to Forest Coral transitions Soil structure Regime shiftsCount Dry land 100 degradation Thermohaline Kelps transitions circulation Forest to Savannas Soil 0 Eutrophication salinization Fisheries collapse Bivalves 0 0.4 0.8 Encroachment collapse Value Salt marshes Peatlands Marine foodwebs Hypoxia Tundra to Forest Floating plants River channel Greenland change Termohaline circulation Average Degree in simulated Salt marshes Regime Shifts Networks 0.7 Marine foodwebs Fisheries collapse 0.6 Soil structure 0.5 River channel change 0.4 Density Floating plants 0.3 Peatlands Coral transitions 0.2 Kelps transitions 0.1 Bivalves collapse 0.0 Eutrophication 12 13 14 15 16 17 18 19 Hypoxia Mean Degree Forest to savannas Regime Shifts Network Dry land degradation Co−occurrence Index Encroachment 0.8 Monsoon weakening Soil salinization 0.6 River channel change Floating plants Tundra to Forest Soil structure Greenland Termohaline circulation Salt marshes Marine foodwebs Fisheries collapse Peatlands Coral transitions Kelps transitions Bivalves collapse Eutrophication Hypoxia Forest to savannas Dry land degradation Encroachment Monsoon weakening Soil salinization Density 0.4 0.2 0.0 The co-occurrence of regime shifts is not random. Aquatic 8 9 10 s−squared 11 12 13 systems tend to share more drivers suggesting that their underlying processes are also similar
  • ERGM models results Parameters Base model Full model Log-likelihood -84.6 -73.2 AIC 173.21 168.38 The likelihood of Network structure sharing Edges -0.70 0.52 Edges covariates drivers increase Regime Shift Database 6.95 ** when regime Ecosystem services -1.54 Ecosystem processes -1.47 shifts happen in Human well being -0.34 the same ecosystem and Ecosystem type 2.59 * Land use 2.69 · Scale -0.54 under similar land use practices. Reversibility 2.63 ** Evidence 1.6 * Mechanism 0.02 Existence 0.27
  • Upwellings Precipitation Erosion Fishing 300 Nutrients inputs Irrigation 250 Atmospheric CO2 AgricultureNumber of links Demand 200 Global warming Human population Fertilizers use 150 Urbanization 100 Deforestation ENSO like events Sewage 50 Droughts Floods 0 1 2 3 4 5 6 7 8 9 10 Number of Regime Shifts jointly caused Drivers Network Agriculture and Climate change
  • Upwellings Precipitation Erosion Fishing 300 Nutrients inputs Irrigation 250 Atmospheric CO2 AgricultureNumber of links Demand 200 Global warming Human population Fertilizers use 150 Urbanization 100 Deforestation ENSO like events Sewage 50 Droughts Floods 0 1 2 3 4 5 6 7 8 9 10 Number of Regime Shifts jointly caused Drivers Network Agriculture and Climate change
  • Color Key Upwellings Erosion Precipitation and Histogram Count Drivers 0 1000 Fishing Nutrients inputs Irrigation Atmospheric CO2 Agriculture Demand Global warming Human population Marine General Terrestrial Fertilizers use 0 0.4 0.8 Value Urbanization Deforestation ENSO like events Sewage Droughts Turbidity Floods Disease Pollutants Sediments Thermal anomalies in summer Ocean acidification Hurricanes Average Degree in simulated Low tides Drivers Networks 0.7 Water stratification Impoundments Rainfall variability 0.6 Landscape fragmentation Flushing Urban storm water runoff 0.5 Urbanization Nutrients inputs Fishing 0.4 Demand Density Deforestation Human population 0.3 Agriculture Erosion Floods 0.2 Fertilizers use Sewage Production intensification 0.1 Food prices Labor availability Ranching (livestock) 0.0 Water infrastructure Aquifers Water availability 20 21 22 23 24 25 26 Upwellings Mean Degree ENSO like events Tragedy of the commons Access to markets Subsidies Infrastructure development Immigration Drivers Network Logging Co−occurrence Index Droughts Fire frequency 6 Irrigation Global warming Atmospheric CO2 Precipitation 5 Fishing technology Food supply Invasive species 4 Sea level rise Temperature Density Green house gases Development policies 3 Drainage Sea surface temperature 2 Turbidity Disease Pollutants Sediments Thermal anomalies in summer Ocean acidification Hurricanes Low tides Water stratification Impoundments Rainfall variability Landscape fragmentation Flushing Urban storm water runoff Urbanization Nutrients inputs Fishing Demand Deforestation Labor availability Ranching (livestock) Human population Agriculture Erosion Floods Fertilizers use Sewage Production intensification Food prices Water infrastructure Aquifers Water availability Upwellings ENSO like events Tragedy of the commons Access to markets Subsidies Infrastructure development Immigration Logging Droughts Fire frequency Irrigation Global warming Atmospheric CO2 Precipitation Fishing technology Food supply Invasive species Sea level rise Temperature Green house gases Development policies Drainage Sea surface temperatureThe co-occurrence of driver is not random. Drivers tend to 1cluster according to the ecosystem type where the regime 0 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1shift takes place. s−squared
  • Work in ProgressCausal Networks of Regime Shifts Causal-loop diagrams is a technique to map out thefeedback structure of a system (Sterman 2000)
  • Topological features of Causal NetworksDegree centrality Betweenness centrality Eigenvector centrality
  • 1. What are the major global change drivers of regime shifts? 80 60Numbervertex vertex Number vertexvertex 50 60 40 of Number of of Number of 40 30 20 20 10 0 0 1 2 3 4 5 6 7 8 9 11 12 14 15 17 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 19 22 Outgoing links Outdegree Incoming links Indegree Few nodes have a lot of links!
  • Marine Regime Shifts Local centrality Global centrality 0.12 0.10 Nutrients input 10 Phytoplankton Nutrients input Fishing 0.08 Dissolved oxygenMid−predators Noxious gases Global warming Betweenness Algae Bivalves abundanceOutdegree Agriculture Bivalves abundance 0.06 Floods Zooplankton 5 Top predators Space GlobalUrban Macrophytes Phytoplankton Planktivore fish warminggrowth Dissolved oxygen Turbidity SST Erosion SST ENSO−like Water temperature events frequency Canopy−forming algae algae Turf−forming Biodiversity Fishing 0.04 Greenhouse gasesand meso−predators Disease outbreak Urchin barren Lobsters Nekton Coral abundance Unpalatability AtmosphericDemand Water vapor CO2 Plankton and Macroalgae abundance Human population Upwellings ConsumptionFertilizers use runoff filamentous algae Precipitation Flushing Coral abundance Urban Sewage Deforestation Sediments preferences Localstorm water Herbivores Landscape fragmentation/conversion water movements Disease outbreak Tragedy of thecolumn acidification Impoundments densityLeakage Water frequency OceanIrrigation contrast Thermal annomalies species Invasive Droughts Perverse incentives mixing TechnologyWater Zooxanthellae Low tides commons Sulfide stress Wind release Stratification relative cooling structural complexity Mortality rate Habitat Density Thermal Fishmatter Daily competitors SubsidiesPollutants low pressurecolumn Hurricanescontrast in the water Noxious gases Trade Other Organic Phosphorous in water Water vapor 0.02 Biodiversity Zooplankton Nekton Space Upwellings 0 Mid−predators Turbidity Algae Water temperature Greenhouse gases Floods Thermal low pressureErosion Macrophytes Turf−forming algae Macroalgae abundance Flushing Lobsters and meso−predatorsTop predators Wind stress Water column density contrast Urchin barren Herbivores Canopy−forming algae Habitat structural complexity Phosphorous in growth Urban Density contrast inOrganic matter and filamentous algae Leakage Plankton 0.00 Zooxanthellae mixing water ENSO−like events water column Mortality the Unpalatability frequency Droughts OceanHumanPerverseDemand rate Agriculture Planktivore fish AtmosphericWater Technology preferences Landscape coolingwater incentives fragmentation/conversion acidification theuse Other competitors Sediments DailyInvasiveLocalSewage runoff Low PollutantsFish Subsidies population HurricanesCO2 release Consumption relativePrecipitationTrade Deforestation movements Thermal annomalies of water tidesUrban Stratificationcommons storm Fertilizers Irrigation frequency Tragedy Impoundments species Sulfide 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0 5 10 15 Eigenvector Indegree
  • Terrestrial Regime Shifts Local centrality Global centrality 0.08 8 Fire frequency Precipitation 0.06 Global warming Precipitation Agriculture Woody plants dominance 6 Fire frequency Forest Grass dominance Deforestation Cropland−Grassland area Deforestation BetweennessOutdegree Agriculture Irrigation Albedo 0.04 Albedo Grass dominance 4 Irrigation Rainfall variability Soil productivity Forest Droughts DemandLand−Ocean temperature Rainfall deficit Savanna Native vegetation gradient Woody plants dominance Demand Productivity Land−Ocean temperature gradient Atmospheric temperature Erosion Savanna SST Atmospheric temperature Floodsdemand Grazing Water infrastructure Evapotranspiration Water Erosion Vegetation Space Water availability 2 Atmospheric CO2 0.02 Human population Palatability Soil moisture productivity Soil Vegetation Water infrastructure Water availability Advection Carbon storage Global warming Soil impermeability Solar radiation Infrastructure developmentstress WindTree release maturity Aquifers LatentSoil quality heatevents Monsoon circulation ENSO−likeDust frequency Vapor Soil salinity Soil salinity Biomass Logging industryShadow_rooting level ImmigrationWater consumption Land−Ocean pressure gradient concentration Productivity Aerosol concentration Soil moisture Rainfall deficit use Moisture Carbon storage Lifting Ranching condensation Advection FertilizersAbsorption of solar radiation Aerosol Brown radiation Solar clouds Illegal logging Sea tides Brown clouds Roughness Temperature Land conversion Ground water table Grazers Absorption of solar radiation Aquifers Evapotranspiration variability Land conversion Rainfall Cropland−Grassland area Vapor Droughts Native vegetation Ground Waterstress frequencyGrazers ENSO−like events SSTMonsoon Land−Ocean water table pressure gradient circulation Wind demand WaterTemperature Shadow_rooting Moisture Dust LiftingRoughnessTree maturity Soil quality consumptioncondensation level Palatability 0 0.00 RanchingFloods Grazing Space Soil impermeabilityBiomass population Human Latent heat Logginglogging Atmospheric CO2 Fertilizers Illegal development Immigration Sea tides releaseindustry Infrastructure use 0 2 4 6 8 0.00 0.02 0.04 0.06 0.08 Indegree Eigenvector
  • Are regime shifts controllable?To what extent can we manage them?• Critics to Liu et al.: ARTICLE doi:10.1038/nature10011 • Topology is not enough Controllability of complex networks Yang-Yu Liu1,2, Jean-Jacques Slotine3,4 & Albert-Laszlo Barabasi1,2,5 ´ ´ ´ • Internal dynamics The ultimate proof of our understanding of natural or technological systems is reflected in our ability to control them. Although control theory offers mathematical tools for steering engineered and natural systems towards a desired state, a framework to control complex self-organized systems is lacking. Here we develop analytical tools to study the• Unmatched nodes change if controllability of an arbitrary complex directed network, identifying the set of driver nodes with time-dependent control that can guide the system’s entire dynamics. We apply these tools to several real networks, finding that the number of driver nodes is determined mainly by the network’s degree distribution. We show that sparse inhomogeneous networks, which emerge in many real complex systems, are the most difficult to control, but that the periphery of the causal dense and homogeneous networks can be controlled using a few driver nodes. Counterintuitively, we find that in both model and real systems the driver nodes tend to avoid the high-degree nodes. networks change - The limits of According to control theory, a dynamical system is controllable if, with a suitable choice of inputs, it can be driven from any initial state to any of traffic that passes through a node i in a communication network24 or transcription factor concentration in a gene regulatory network25. the system blur desired final state within finite time1–3. This definition agrees with our intuitive notion of control, capturing an ability to guide a system’s behaviour towards a desired state through the appropriate manipulation The N 3 N matrix A describes the system’s wiring diagram and the interaction strength between the components, for example the traffic on individual communication links or the strength of a regulatory of a few input variables, like a driver prompting a car to move with the interaction. Finally, B is the N 3 M input matrix (M # N) that iden- desired speed and in the desired direction by manipulating the pedals tifies the nodes controlled by an outside controller. The system is and the steering wheel. Although control theory is a mathematically controlled using the time-dependent input vector u(t) 5 (u1(t), …, highly developed branch of engineering with applications to electric uM(t))T imposed by the controller (Fig. 1a), where in general the same circuits, manufacturing processes, communication systems4–6, aircraft, signal ui(t) can drive multiple nodes. If we wish to control a system, we• Unmatched nodes change spacecraft and robots2,3, fundamental questions pertaining to the con- first need to identify the set of nodes that, if driven by different signals, trollability of complex systems emerging in nature and engineering have can offer full control over the network. We will call these ‘driver resisted advances. The difficulty is rooted in the fact that two independ- nodes’. We are particularly interested in identifying the minimum when joining causal networks ent factors contribute to controllability, each with its own layer of number of driver nodes, denoted by ND, whose control is sufficient unknown: (1) the system’s architecture, represented by the network to fully control the system’s dynamics. encapsulating which components interact with each other; and (2) the The system described by equation (1) is said to be controllable if it dynamical rules that capture the time-dependent interactions between to understand cascading can be driven from any initial state to any desired final state in finite the components. Thus, progress has been possible only in systems where time, which is possible if and only if the N 3 NM controllability matrix both layers are well mapped, such as the control of synchronized net- works7–10, small biological circuits11 and rate control for communica- C~(B, AB, A2 B, . . . , AN{1 B) ð2Þ effects. tion networks4–6. Recent advances towards quantifying the topological characteristics of complex networks12–16 have shed light on factor (1), prompting us to wonder whether some networks are easier to control has full rank, that is rank(C)~N ð3Þ than others and how network topology affects a system’s controllability. Despite some pioneering conceptual work17–23 (Supplementary This represents the mathematical condition for controllability, and is Information, section II), we continue to lack general answers to these called Kalman’s controllability rank condition1,2 (Fig. 1a). In practical questions for large weighted and directed networks, which most com- terms, controllability can be also posed as follows. Identify the minimum monly emerge in complex systems. number of driver nodes such that equation (3) is satisfied. For example, equation (3) predicts that controlling node x1 in Fig. 1b with the input Network controllability signal u1 offers full control over the system, as the states of nodes x1, x2, x3 Most real systems are driven by nonlinear processes, but the controll- and x4 are uniquely determined by the signal u1(t) (Fig. 1c). In contrast,
  • ConclusionsRegime shifts are tightly connected both when sharing drivers andtheir underlying feedback dynamics. The management of immediatecauses or well studied variables might not be enough to avoid suchcatastrophes.Agricultural processes and global warming are the main causes ofregime shifts.Marine regime shifts tend to share more drivers, while terrestrialregime shifts are more context dependent.Network analysis is an useful approach to study regime shiftscouplings when knowledge about system dynamics or time series ofkey variables are limited. Network controllability opens a window ofopportunity to address causality relationships in systems with highuncertainty.
  • Thanks! Prof. Garry Peterson & Oonsie Biggs for their supervision RSDB folks for inspiring discussion and writing examples SRC for an inspiring research place and Sweden FORMAS and MISTRA funding!Questions??e-mail: juan.rocha@stockholmresilience.su.seTwitter: @juanrochaBlog: http://criticaltransitions.wordpress.com/