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Rocha comple net2012-melbourne

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Slides presented in Melbourne 120309

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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
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  • methods from physics and social sciences applied to medicine to figure out multicausality patterns.\n
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  • 20RS - 67 Drivers, 239 links, density 6.3%\n
  • 82% density\nMarine RS are tightly connected: water as a transport media for disturbances: turbidity, SST, pollutants, sediments, etc.\n
  • 48% density\nGlobal warming: floods, droughts, GHG\nAgriculture: fishing, deforestation, irrigation, fertilizers use, erosion, nutrient inputs\nHuman pop growth: urbanization, sewage \n
  • 48% density\nGlobal warming: floods, droughts, GHG\nAgriculture: fishing, deforestation, irrigation, fertilizers use, erosion, nutrient inputs\nHuman pop growth: urbanization, sewage \n
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  • \n204 nodes, 529 links, Density: 0.017 or 17%\n
  • Global centrality\n
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  • 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
  • MANAGEMENT CHALLENGES\n1.the increasing forcing on global change drivers should slow down enough to allow species adaptation and keep food webs stable.\n2. New methods to close the nutrient cycle on farms are needed.\nseparate on 3 slides for each question\n
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  • Transcript

    • 1. The Network of Driving Forces of Global Environmental Change Juan-Carlos Rocha, Oonsie Biggs & Garry Peterson Stockholm Resilience Centre Stockholm University
    • 2. The challengeFrequency and intensity ofregime shifts are likely toincrease.ES’s may be substantiallyaffected. Where? Vulnerable areas? Possible synergistic effects? Cross-scale interactions? Rockström et al., 2009
    • 3. Regime shifts that matter to peopleRegime shifts: Large, abrupt, persistent change in the structure and function of asystem.Policy relevant = Substantial change in Ecosystem Services
    • 4. Research agenda on RS: Early warnings!! Bayesian Web crawlers & networks - local knowledge models Knowledge of the Models & Jacobians system Statistics: Autocorrelation and variance Data quality (time series)
    • 5. Research agenda on RS: Early warnings!! Bayesian Web crawlers & networks - local knowledge models Knowledge of the Models & Jacobians system ? Statistics: Autocorrelation and variance Data quality (time series)
    • 6. Virtruvian Man, Leonardo Da Vinci
    • 7. Network Properties of Complex Human Disease GenesThe human disease network Identified through Genome-Wide Association Studies ´ ´ ´Kwang-Il Goh*†‡§, Michael E. Cusick†‡¶, David Valleʈ, Barton Childsʈ, Marc Vidal†‡¶**, and Albert-Laszlo Barabasi*†‡** Fredrik Barrenas1.*, Sreenivas Chavali1., Petter Holme2,3, Reza Mobini1, Mikael Benson1*Center for Complex Network Research and Department of Physics, University of Notre Dame, Notre Dame, IN 46556; †Center for Cancer Systems Biology(CCSB) and ¶Department of Cancer Biology, Dana–Farber Cancer Institute, 44 Binney Street, Boston, MA 02115; ‡Department of Genetics, Harvard Medical ˚ ˚ 1 The Unit for Clinical Systems Biology, University of Gothenburg, Gothenburg, Sweden, 2 Department of Physics, Umea University, Umea, Sweden, 3 Department ofSchool, 77 Avenue Louis Pasteur, Boston, MA 02115; §Department of Physics, Korea University, Seoul 136-713, Korea; and ʈDepartment of Pediatrics and the Energy Science, Sungkyunkwan University, Suwon, KoreaMcKusick–Nathans Institute of Genetic Medicine, Johns Hopkins University School of Medicine, Baltimore, MD 21205Edited by H. Eugene Stanley, Boston University, Boston, MA, and approved April 3, 2007 (received for review February 14, 2007)A network of disorders and disease genes linked by known disorder– known genetic disorders, whereas the other set corresponds to all Abstractgene 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 Background: Previous studies of network properties of human disease genes have mainly focused on monogenic diseasesations, indicating the common genetic origin of many diseases. Genes implicated in that disorder. The list of disorders, disease genes, and or cancers and have suffered from discovery bias. Here we investigated the network properties of complex disease genesassociated with similar disorders show both higher likelihood of associations between them was obtained from the Online Mende- identified by genome-wide association studies (GWAs), thereby eliminating discovery bias.physical interactions between their products and higher expression lian Inheritance in Man (OMIM; ref. 18), a compendium of humanprofiling similarity for their transcripts, supporting the existence of disease genes and phenotypes. As of December 2005, this list Principal findings: We derived a network of complex diseases (n = 54) and complex disease genes (n = 349) to explore thedistinct disease-specific functional modules. We find that essential contained 1,284 disorders and 1,777 disease genes. OMIM initiallyhuman genes are likely to encode hub proteins and are expressed shared genetic architecture of complex diseases. We evaluated the centrality measures of complex disease genes in focused on monogenic disorders but in recent years has expanded comparison with essential and monogenic disease genes in the human interactome. The complex disease network showedwidely in most tissues. This suggests that disease genes also would to include complex traits and the associated genetic mutations thatplay a central role in the human interactome. In contrast, we find that that diseases belonging to the same disease class do not always share common disease genes. A possible explanation could confer susceptibility to these common disorders (18). Although thisthe vast majority of disease genes are nonessential and show no history introduces some biases, and the disease gene record is far be that the variants with higher minor allele frequency and larger effect size identified using GWAs constitute disjoint partstendency to encode hub proteins, and their expression pattern indi- from complete, OMIM represents the most complete and up-to- of the allelic spectra of similar complex diseases. The complex disease gene network showed high modularity with the size APPLIED PHYSICALcates that they are localized in the functional periphery of the of the largest component being smaller than expected from a randomized null-model. This is consistent with limited sharing date repository of all known disease genes and the disorders they SCIENCESnetwork. A selection-based model explains the observed difference confer. We manually classified each disorder into one of 22 disorder of genes between diseases. Complex disease genes are less central than the essential and monogenic disease genes in thebetween essential and disease genes and also suggests that diseases classes based on the physiological system affected [see supporting human interactome. Genes associated with the same disease, compared to genes associated with different diseases, morecaused by somatic mutations should not be peripheral, a prediction information (SI) Text, SI Fig. 5, and SI Table 1 for details]. often tend to share a protein-protein interaction and a Gene Ontology Biological Process.we confirm for cancer genes. Starting from the diseasome bipartite graph we generated twobiological networks ͉ complex networks ͉ human genetics ͉ systems biologically relevant network projections (Fig. 1). In the ‘‘human Conclusions: This indicates that network neighbors of known disease genes form an important class of candidates forbiology ͉ diseasome disease network’’ (HDN) nodes represent disorders, and two identifying novel genes for the same disease. disorders are connected to each other if they share at least one gene DISEASOME in which mutations are associated with both disorders (Figs. 1 andD ecades-long efforts to map human disease loci, at first genet- ically and later physically (1), followed by recent positionalcloning of many disease genes (2) and genome-wide association phenome 2a). In the ‘‘disease gene network’’ (DGN) nodes represent disease genes, and two 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-Wide Association Studies. PLoS ONE 4(11): e8090. doi:10.1371/journal.pone.0008090 disease same disorder (Figs. 1 andgenome we discuss the potential of disease 2b). Next,studies (3), have generated an impressive list of disorder–gene Editor: Thomas Mailund, Aarhus University, Denmarkassociation Human Disease Network these networks to help us understand andDiseasein a single represent Gene Network pairs (4, 5). In addition, recent efforts to map Ataxia-telangiectasia the Received September 15, 2009; Accepted November 3, 2009; Published November 30, 2009 framework all known diseaseAR gene and phenotype associations.protein–protein interactions in humans (6, 7), together with efforts hypospadias (HDN)to curate an extensive map of human metabolism (8) and regulatory insensitivity Perineal Androgen ATM (DGN) 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 of the HDN. If each human disorder tends to have a unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.networks offer increasingly detailed maps of the relationships T-cell lymphoblastic leukemia Charcot-Marie-Tooth diseasebetween different disease genes. Most of the successful studies serous carcinoma Papillary distinct and unique geneticBRCA1 then the HDN would be dis- origin, HEXB 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 Prostate cancer Lipodystrophy a connected into many single BRCA2 corresponding to specific disor- nodes ALS2 LMNA WCU (World Class University) program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology R31-R31- Spastic ataxia/paraplegiasingle disease, using network-based tools tosyndromea better under- Silver spastic paraplegia gain ders or grouped into small clusters of a few closely related disorders.BSCL2 CDH1 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.standing of the relationship between the genes implicated in Ovarian cancer a In contrast, the obtained HDN displays many connections between VAPB GARS Competing Interests: The authors have declared that no competing interests exist.selected disorder (9). Amyotrophic lateral sclerosis Sandhoff disease both individual disorders and disorder classes (Fig. 2a). Of 1,284 GARS Here we take a conceptually different approach, exploring disorders, 867 have at least HEXB link to other disorders, and 516 Lymphoma one * E-mail: fredrik.barrenas@gu.se Spinal muscular atrophywhether human genetic disorders and the corresponding disease disorders form a giant component, suggesting that the genetic KRAS AR . These authors contributed equally to this work.genes might be related to each Androgenat a higher level of cellular and cancer other insensitivity origins of most diseases, to some extent, are shared with other Breastorganismal organization. Support hypospadiasvalidity of this approach Prostate cancer Perineal for the diseases. The number of genes associated with a disorder, s, has a LMNA ATM BRCA2is provided by examples of genetic disorders that arise from broad distribution (see SI Fig. 6a), indicating that most disorders MSH2 BRIP1 Pancreatic cancermutations in more than a single gene (locus heterogeneity). For Lymphoma relate to a few disease genes,PIK3CA whereas a handful of phenotypes, such BRCA1 Introduction human interactome. A more recent report that evaluated theexample, Zellweger syndrome is caused by mutations in any of at tumordeafness (s ϭ 41), leukemia (s ϭ 37), and colon cancer (s KRAS Wilms tumor Wilms as ϭ 34), network properties of disease genes showed that genes with TP53least 11 genes, all associated with peroxisome biogenesis Spinal muscular atrophyto dozens of genes (Fig. 2a). The degree (k) distribution of Breast cancer Ovarian cancer (10). relate RAD54L TP53 Systems Biology based approaches of studying human genetic intermediate degrees (numbers of neighbors) were more likely toSimilarly, there are many examples of different mutations in the Pancreatic cancer HDN (SI Fig. 6b) indicatesMAD1L1most disorders are linked to only that diseases have brought in a shift in the paradigm of elucidating harbor germ-line disease mutations [12]. However, interpretationsame gene (allelic heterogeneity) giving rise to phenotypes cur- disease Papillary serous carcinoma Sandhoff RAD54L MAD1L1 CHEK2 disease mechanisms from analyzing the effects of single genes to of this dataset might not be applicable to complex disease genes Fanconi anemiarently classified as different disorders. For example, mutations in T-cell lymphoblastic leukemia Lipodystrophy PIK3CA understanding the effect of molecular interaction networks. Such Author contributions: D.V., B.C., M.V., and A.-L.B. designed research; K.-I.G. and M.E.C. VAPB since 97% of the disease genes were monogenic. Despite thisTP53 have been linked to 11 clinically distinguishable cancer- Charcot-Marie-Tooth disease performed research; K.-I.G. and M.E.C. analyzed data; and K.-I.G., M.E.C., D.V., M.V., andrelated disorders (11). Given the highly interlinked internalAmyotrophic lateral sclerosis the paper. Ataxia-telangiectasia orga- A.-L.B. wrote CHEK2 CDH1 MSH2 networks have been exploited to find novel candidate genes, based reservation, both the latter studies found a functional clustering ofnization of the cell (12–17), it should be possible to improve the The authors declare no conflict of interest. BSCL2 on the assumption that neighbors of a disease-causing gene in a disease genes. Another concern is that the above studies could besingle gene–single disorder approach by developing a conceptual Silver spastic paraplegia syndrome This article is a PNAS Direct Submission. network are more likely to cause either the same or a similar confounded by discovery bias, in other words these disease genesframework to link systematically all genetic disorders (the human ataxia/paraplegiaSpastic ALS2 disease [1–14]. Initial studies investigating the network properties Abbreviations: DGN, disease gene network; HDN, human disease network; GO, Gene were identified based on previous knowledge. By contrast,‘‘disease phenome’’) with the complete list of disease genes (the anemia BRIP1 Fanconi Ontology; OMIM, Online Mendelian Inheritance in Man; PCC, Pearson correlation coeffi-‘‘disease genome’’), resulting in a global view of the ‘‘diseasome,’’ of human disease genes were based on cancers and revealed that Genome Wide Association studies (GWAs) do not suffer from cient.the combined set of all known disorder/disease gene associations. **To whom correspondence may be addressed. E-mail: alb@nd.edu or marc࿝vidal@ up-regulated genes in cancerous tissues were central in the such bias [15]. dfci.harvard.edu. interactome and highly connected (often referred to as hubs) In this study, we have derived networks of complex diseases andResults This article contains supporting information online at www.pnas.org/cgi/content/full/ [1,2]. A subsequent study based on the human disease network Fig. 1. Construction of the diseasome bipartite network. (Center) A small0701361104/DC1. subset of OMIM-based disorder– disease gene associations (18), where circles and rectangles complex disease genes to explore the shared genetic architecture ofConstruction of the Diseasome. We constructed a bipartite graph and disease gene network derived from the Online Mendelian complex diseases studied using GWAs. Further, we have evaluatedconsisting ofto disorders and disease genes, respectively. A link isto all between aThe National Academy of Sciences ofif mutations in that gene lead to the specific disorder. correspond two disjoint sets of nodes. One set corresponds placed © 2007 by disorder and a disease gene the USA The size of a circle is proportional to the number of genes participating in the corresponding disorder, and the color corresponds to the disorder class to which the disease Inheritance in Man (OMIM) demonstrated that the products of the topological and functional properties of complex disease genes belongs. (Left) The HDN projection of the diseasome bipartite graph, in which two disorders are connected if there is a gene that is implicated in both. The width of disease genes tended (i) to have more interactions with each other in the human interactome by comparing them with essential,www.pnas.org͞cgi͞doi͞10.1073͞pnas.0701361104 PNAS ͉ May 22, 2007 ͉ vol. 104 ͉ no. 21 ͉ 8685– 8690 a link is proportional to the number of genes that are implicated in both diseases. For example, three genes are implicated in both breast cancer and prostate cancer, than with non-disease genes, (ii) to be expressed in the same tissues monogenic and non-disease genes. We observed that diseases resulting in a link of weight three between them. (Right) The DGN projection where two genes are connected if they are involved in the same disorder. The width of a link is proportional to the number of diseases with which the two genes are commonly associated. A full diseasome bipartite map is provided as SI Fig. 13. and (iii) to share Gene Ontology (GO) terms [8]. Contradicting belonging to the same disease class do not always show a tendency earlier reports, this latter study demonstrated that the non-essential to share common disease genes; the complex disease gene net- human disease genes showed no tendency to encode hubs in the work shows high modularity comparable to that of the human a few other disorders, whereas a few phenotypes such as colon mentary, gene-centered view of the diseasome. Given that the links cancer (linked to k ϭ 50 other disorders) or breast cancer (k ϭ 30) signify related phenotypic association between two genes, they represent hubs that are connected to a large number of distinct represent a measure of their phenotypic relatedness, which could be PLoS ONE | www.plosone.org 1 November 2009 | Volume 4 | Issue 11 | e8090 disorders. The prominence of cancer among the most connected used in future studies, in conjunction with protein–protein inter- disorders arises in part from the many clinically distinct cancer actions (6, 7, 19), transcription factor-promoter interactions (20), subtypes tightly connected with each other through common tumor and metabolic reactions (8), to discover novel genetic interactions. repressor genes such as TP53 and PTEN. In the DGN, 1,377 of 1,777 disease genes are connected to other Although the HDN layout was generated independently of any disease genes, and 903 genes belong to a giant component (Fig. 2b). knowledge on disorder classes, the resulting network is naturally Whereas the number of genes involved in multiple diseases de- and visibly clustered according to major disorder classes. Yet, there creases rapidly (SI Fig. 6d; light gray nodes in Fig. 2b), several are visible differences between different classes of disorders. disease genes (e.g., TP53, PAX6) are involved in as many as 10 Whereas the large cancer cluster is tightly interconnected due to the disorders, representing major hubs in the network. many genes associated with multiple types of cancer (TP53, KRAS, ERBB2, NF1, etc.) and includes several diseases with strong pre- Functional Clustering of HDN and DGN. To probe how the topology
    • 8. Regime shift database
    • 9. Regime shift database
    • 10. 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
    • 11. 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, R 6 Fisheries collapse Contested U 7 Marine foodwebs collapse Contested U 8 Forest - Savanna Established I 9 Hypoxia Established H, R 10 Kelp transitions Established H, R 11 Soil salinization Established H, I 12 Steppe - Tundra Established I 13 Tundra - Forest Established I 14 Monsoon circulation Established I 15 Thermohaline circulation collapse Established I 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, IReversibility: H = Hysteretic; I = Irreversible; R= Reversible; U = Unknown Current data: 20 Regime Shifts in Social-Ecological Systems
    • 12. Hurricanes tides Thermal anomalies in summerLow Ocean acidification Sea level rise Disease Fishing technology Pollutants Wind stress 25 Thermal low pressure Upwellings Water column density contrast Invasive species Sediments Tragedy of the commons Urban storm water runoff Fishing Water vapor Turbidity Urbanization Sea surface temperature Sewage 20 Daily Relative cooling Coral.transitions Logging Salt.marshes Marine.foodwebs Nutrients inputs Fisheries.collapse house consumption preferences Green Fish gases Water stratification Kelps.transitions Precipitation Bivalves.collapseNumber of vertex 15 River.channel.change Hypoxia Floating.plants Flushing Fertilizers use ENSO like events Erosion Food supply Eutrophication Subsidies Floods Demand Global warming Impoundments Human population Agriculture Access to markets 10 Deforestation Leaking Termohaline.circulation Forest.to.savannas Rainfall variability Landscape fragmentation Immigration Greenland Peatlands Monsoon.weakening Soil.salinization Irrigation 5 Encroachment Tundra.to.Forest Dry.land.degradation Infrastructure development Droughts Migration Aquifers Drainage Fire frequency Temperature Dry−spells 0 Atmospheric CO2 Irrigation infrastructure Soil.structure Managerial practices diversity 1 2 3 4 5 6 7 9 10 11 12 13 14 15 16 18 19 20 22 23 26 Ranching (livestock) Water infrastructure Degree Water availability Development policies Production intensification cycles Length of production Labor availability Food prices Regime Shifts - Drivers Bipartite Network
    • 13. Soil.structure 40 Dry.land.degradation Soil.salinization Peatlands Fisheries.collapse Salt.marshes Bivalves.collapse 30 EncroachmentNumber of links Greenland Coral.transitions Hypoxia Eutrophication River.channel.ch 20 Forest.to.savannas Kelps.transitions Tundra.to.Forest 10 Floating.plants Termohaline.circulation Monsoon.weakening Marine.foodwebs 0 1 2 3 4 5 6 7 8 10 11 12 13 15 17 Number of Drivers shared Regime Shifts Network
    • 14. 500 400Number of links 300 200 100 0 1 2 3 4 5 6 7 8 9 10 11 Number of Regime Shifts jointly caused Drivers Network
    • 15. 500 400Number of links 300 200 100 0 1 2 3 4 5 6 7 8 9 10 11 Number of Regime Shifts jointly caused Drivers Network
    • 16. Green house gases 500 Global warming 400 TurbidityNumber of links Fishing Food supply 300 Nutrients inputs Irrigation 200 Fertilizers use Agriculture Human population Demand 100 Sewage Deforestation Floods 0 1 2 3 4 5 6 7 8 9 10 11 Urbanization Number of Regime Shifts jointly caused Erosion Droughts Drivers Network
    • 17. How our results differ from random? Average Degree in simulated DN Co−occurrence Index 2500 3000 2500 2000 2000 1500Frequency Frequency 1500 1000 1000 500 500 0 0 29 30 31 32 33 34 35 36 −1776.6 −1776.4 −1776.2 −1776.0 −1775.8 Mean Degree s−squared
    • 18. Causal-loop diagrams is a N Policy relevant Regime Shifts Mechanism Reversibility technique to map out the 1 Bivalves collapse Established H feedback structure of a system 2 Coral transitions Established H (Sterman 2000) 3 Coral bleaching Established H 4 Desertification Contested H, I 5 Encroachment Established H 6 Eutrophication Established H, I, R 7 Fisheries collapse Contested U 8 Marine foodwebs collapse Contested U 9 Forest - Savanna Established I 10 Hypoxia Established H, R 11 Kelp transitions Established H, R 12 Soil salinization Established H, I 13 Steppe - Tundra Established I 14 Tundra - Forest Established I 15 Monsoon circulation Established I 16 Thermohaline circulation collapse Established I 17 Greenland ice sheet collapse Established I 18 Arctic salt marshes Established I 19 Arctic ice collapse Established IReversibility: H = Hysteretic; I = Irreversible; R= Reversible; U = Unknown Current data: 19 Regime Shifts descriptions + CLD.
    • 19. Topological features of Causal Network Centrality Definition Degree The number edges a vertex is connected to (Newman 2010): In-degree and Out-degree Betweenness The extent to which a vertex lies on paths between other vertices (Newman 2010) Eigenvector A vertex is important if it is directly or Degree centrality indirectly connected to other vertices that are in turn important (Allesina and Pascual 2009), like Google PageRank
    • 20. Topological features of Causal Network Centrality Definition Degree The number edges a vertex is connected to (Newman 2010): In-degree and Out-degree Betweenness The extent to which a vertex lies on paths between other vertices (Newman 2010) Eigenvector A vertex is important if it is directly or Betweenness centrality indirectly connected to other vertices that are in turn important (Allesina and Pascual 2009), like Google PageRank
    • 21. Topological features of Causal Network Centrality Definition Degree The number edges a vertex is connected to (Newman 2010): In-degree and Out-degree Betweenness The extent to which a vertex lies on paths between other vertices (Newman 2010) Eigenvector A vertex is important if it is directly or Eigenvector centrality indirectly connected to other vertices that are in turn important (Allesina and Pascual 2009), like Google PageRank
    • 22. D1 1. What are the major global change drivers of regime shifts? RS1 RS2 RS3 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!
    • 23. D1 Marine Regime Shifts RS1 RS2 RS3 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
    • 24. D1 Terrestrial Regime Shifts RS1 RS2 RS3 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
    • 25. Interaction of regime shifts drivers?Regime shifts are tightly connected. Themanagement of immediate causes or wellstudied variables might not be enough toavoid such catastrophes.Agricultural processes and global warmingare the main causes of regime shifts.Network analysis might be a usefulapproach to address causality relationships
    • 26. Thanks! Drs. Oonsie Biggs & Garry Peterson for their supervision RSDB folks for inspiring discussion and writing examples SRC for an inspiring research space and funding!Questions??e-mail: juan.rocha@stockholmresilience.su.seTwitter: @juanrochaBlog: http://criticaltransitions.wordpress.com/ What is a regime shift? Science pub May 2009 - SRC
    • 27. Are RS controllable? ARTICLE doi:10.1038/nature10011• Critics to Liu et al.: Controllability of complex networks Yang-Yu Liu1,2, Jean-Jacques Slotine3,4 & Albert-Laszlo Barabasi1,2,5 ´ ´ ´ • Topology is not enough 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 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 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. • Internal dynamics According to control theory, a dynamical system is controllable if, with a of traffic that passes through a node i in a communication network24 suitable choice of inputs, it can be driven from any initial state to any or transcription factor concentration in a gene regulatory network25. desired final state within finite time1–3. This definition agrees with our The N 3 N matrix A describes the system’s wiring diagram and the intuitive notion of control, capturing an ability to guide a system’s interaction strength between the components, for example the traffic behaviour towards a desired state through the appropriate manipulation 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-• Unmatched nodes change if desired speed and in the desired direction by manipulating the pedals and the steering wheel. Although control theory is a mathematically highly developed branch of engineering with applications to electric tifies the nodes controlled by an outside controller. The system is controlled using the time-dependent input vector u(t) 5 (u1(t), …, uM(t))T imposed by the controller (Fig. 1a), where in general the same the periphery of the CLD circuits, manufacturing processes, communication systems4–6, aircraft, spacecraft and robots2,3, fundamental questions pertaining to the con- trollability of complex systems emerging in nature and engineering have signal ui(t) can drive multiple nodes. If we wish to control a system, we first need to identify the set of nodes that, if driven by different signals, can offer full control over the network. We will call these ‘driver change resisted advances. The difficulty is rooted in the fact that two independ- nodes’. We are particularly interested in identifying the minimum 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 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• Unmatched nodes change tion networks4–6. Recent advances towards quantifying the topological has full rank, that is characteristics of complex networks12–16 have shed light on factor (1), prompting us to wonder whether some networks are easier to control rank(C)~N ð3Þ than others and how network topology affects a system’s controllability. when joining CLD’s to Despite some pioneering conceptual work17–23 (Supplementary Information, section II), we continue to lack general answers to these questions for large weighted and directed networks, which most com- This represents the mathematical condition for controllability, and is called Kalman’s controllability rank condition1,2 (Fig. 1a). In practical terms, controllability can be also posed as follows. Identify the minimum understand cascading effects. 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, ability of nonlinear systems is in many aspects structurally similar to controlling the top node in Fig. 1e is not sufficient for full control, as the that of linear systems3, prompting us to start our study using the difference a31x2(t) 2 a21x3(t) (where aij are the elements of A) is not canonical linear, time-invariant dynamics uniquely determined by u1(t) (see Fig. 1f and Supplementary Information section III.A). To gain full control, we must simultaneously dx(t) control node x1 and any two nodes among {x2, x3, x4} (see Fig. 1h, i for a ~Ax(t)zBu(t) ð1Þ dt more complex example). T where the vector x(t) 5 (x1(t), …, xN(t)) captures the state of a To apply equations (2) and (3) to an arbitrary network, we need to system of N nodes at time t. For example, xi(t) can denote the amount know the weight of each link (that is, the aij), which for most real