Licentiate: Regime shifts in the Anthropocene
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    Licentiate: Regime shifts in the Anthropocene Licentiate: Regime shifts in the Anthropocene Presentation Transcript

    • Regime Shifts in the Anthropocene Juan-Carlos Rocha Sunday, September 1, 13
    • The Anthropocene Sunday, September 1, 13
    • The Anthropocene Social challenge: Understand patters of causes and consequences of regime shifts How common they are? What possible interactions? Where are they likely to occur? Who will be most affected? What can we do to avoid them? Sunday, September 1, 13
    • Regime Shifts Regime shifts are abrupt reorganization of a system’s structure and function. A regime correspond to characteristic behavior of the system maintained by mutually reinforcing processes or feedbacks. The shift occurs when the strength of such feedbacks change, usually driven by cumulative change in slow variables, external disturbances or shocks. collapse collapse recovery Precipitation Vegetation Precipitation Vegetation PrecipitationVegetation Precipitation Vegetation Precipitation Precipitation Precipitation Precipitation low high low high low high low high Vegetation low high Gradual Threshold Vegetation low high Vegetation low high Vegetation low high Hystersis Irreversible Stability Landscape Equilibria (Gordon et al 2008) Sunday, September 1, 13
    • Regime Shifts Regime shifts are abrupt reorganization of a system’s structure and function. A regime correspond to characteristic behavior of the system maintained by mutually reinforcing processes or feedbacks. The shift occurs when the strength of such feedbacks change, usually driven by cumulative change in slow variables, external disturbances or shocks. external forcing reverses, the response variable will flip back to the original equilibrium, but at a different Fig. 3. Catastrophe manifold illustrating that the three types of regime shifts are special cases along a continuum of internal ecosystem structure. Adapted from Jones and Walters (1976). J.S. Collie et al. / Progress in Oceanography 60 (2004) 281–302 287 (Collie 2004) Sunday, September 1, 13
    • Regime Shifts Regime shifts are abrupt reorganization of a system’s structure and function. A regime correspond to characteristic behavior of the system maintained by mutually reinforcing processes or feedbacks. The shift occurs when the strength of such feedbacks change, usually driven by cumulative change in slow variables, external disturbances or shocks. Science challenge: understand multi- causal phenomena where experimentation is rarely an option and time for action a constraint Sunday, September 1, 13
    • 1. A comparative framework: The database 2. Global drivers of Regime Shifts 3. Future developments Sunday, September 1, 13
    • 1. A comparative framework: The database Sunday, September 1, 13
    • Regime Shifts DataBase The shift substantially affect the set of ecosystem services provided by a social-ecological system Established or proposed feedback mechanisms exist that maintain the different regimes. The shift persists on time scale that impacts on people and society Sunday, September 1, 13
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    • Mechanism Existence Well established Proposed Contested Contested Proposed Well established Soil structure Marine foodwebs Monsoon weakening Termohaline circulation Encroachment Fisheries collapse Dryland degradation Forest to savanna Steppe to tundra Tundra to forest Floating plants Greenland Arctic sea ice Bivalves collapse Coral transitions Eutrophication Hypoxia Kelps transitions Peatlands River channel change Salt marshes Soil salinization Sunday, September 1, 13
    • Regime Shifts DataBase Ecosystem services Drivers ... Biodiversity Primary production Nutrient cycling Water cycling Soil Formation Fisheries Wild animals and plants food Freshwater Foodcrops Livestock Timber Woodfuel Other crops Hydropower Water purification Climate regulation Regulation of soil erosion Pest and disease regulation Natural hazard regulation Air quality regulation Pollination Recreation Aesthetic values Knowledge and educational values Spiritual and religious Livelihoods and economic activity Food and nutrition Cultural, aesthetic and recreational values Security of housing and infrastructure Health Social confict No direct impact 0 8 15 23 30 Ecosystem Services Supporting Provisioning Regulating Cultural Human well being Sunday, September 1, 13
    • Regime Shifts DataBase Ecosystem services Drivers ... 0.0 0.2 0.4 0.6 0.8 1.0 0.00.20.40.60.81.0 Proportion of Regime Shifts (n=20) ProportionofDriverssharingcausalitytoRegimeShifts(n=55) Agriculture Atmospheric CO2 Deforestation Demand Droughts Fishing Global warming Human population Nutrients inputs Urbanization Sunday, September 1, 13
    • Forks: when sharing a driver synchronize two regime shifts Causal chains: the domino effect Inconvenient feedbacks: when two shifts reinforce or dampen each other RS1 RS2 RS3 D1 RS1 RS2D1 ... RS1 RS2 D2D1 Cascading effects Arctic Icesheet collapse Bivalves collapse Coral bleaching Coral transitions Desertification Encroachment Eutrophication Fisheries collapse Floating plants Foodwebs Forest to cropland Forest to savanna Greenland icesheet collapse Hypoxia Kelp transitions Monsoon Peatlands Soil salinization Soil structure Thermohaline Tundra to forest Arctic salt marsh River channel change Sunday, September 1, 13
    • Challenges We developed a framework to compare regime shifts Issues of consistency: Drivers CLD System boundaries Uncertainty assessment: strength of feedbacks and the role of social dynamics Methods to identify leverage points for management Sunday, September 1, 13
    • 3. Global drivers of Regime Shifts Sunday, September 1, 13
    • Virtruvian Man, Leonardo Da Vinci Sunday, September 1, 13
    • Network Properties of Complex Human Disease Genes Identified through Genome-Wide Association Studies Fredrik Barrenas1. *, Sreenivas Chavali1. , Petter Holme2,3 , Reza Mobini1 , Mikael Benson1 1 The Unit for Clinical Systems Biology, University of Gothenburg, Gothenburg, Sweden, 2 Department of Physics, Umea˚ University, Umea˚, Sweden, 3 Department of Energy Science, Sungkyunkwan University, Suwon, Korea Abstract Background: Previous studies of network properties of human disease genes have mainly focused on monogenic diseases or cancers and have suffered from discovery bias. Here we investigated the network properties of complex disease genes identified by genome-wide association studies (GWAs), thereby eliminating discovery bias. Principal findings: We derived a network of complex diseases (n = 54) and complex disease genes (n = 349) to explore the shared genetic architecture of complex diseases. We evaluated the centrality measures of complex disease genes in comparison with essential and monogenic disease genes in the human interactome. The complex disease network showed that diseases belonging to the same disease class do not always share common disease genes. A possible explanation could be that the variants with higher minor allele frequency and larger effect size identified using GWAs constitute disjoint parts of the allelic spectra of similar complex diseases. The complex disease gene network showed high modularity with the size of the largest component being smaller than expected from a randomized null-model. This is consistent with limited sharing of genes between diseases. Complex disease genes are less central than the essential and monogenic disease genes in the human interactome. Genes associated with the same disease, compared to genes associated with different diseases, more often tend to share a protein-protein interaction and a Gene Ontology Biological Process. Conclusions: This indicates that network neighbors of known disease genes form an important class of candidates for identifying novel genes for the same disease. 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 Editor: Thomas Mailund, Aarhus University, Denmark Received September 15, 2009; Accepted November 3, 2009; Published November 30, 2009 Copyright: ß 2009 Barrenas et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: This work was supported by the Swedish Research Council, The European Commission, The Swedish Foundation for Strategic Research (PH), and the WCU (World Class University) program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology R31-R31- 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. Competing Interests: The authors have declared that no competing interests exist. * E-mail: fredrik.barrenas@gu.se . These authors contributed equally to this work. Introduction Systems Biology based approaches of studying human genetic diseases have brought in a shift in the paradigm of elucidating disease mechanisms from analyzing the effects of single genes to understanding the effect of molecular interaction networks. Such networks have been exploited to find novel candidate genes, based on the assumption that neighbors of a disease-causing gene in a network are more likely to cause either the same or a similar disease [1–14]. Initial studies investigating the network properties of human disease genes were based on cancers and revealed that up-regulated genes in cancerous tissues were central in the interactome and highly connected (often referred to as hubs) [1,2]. A subsequent study based on the human disease network and disease gene network derived from the Online Mendelian Inheritance in Man (OMIM) demonstrated that the products of disease genes tended (i) to have more interactions with each other than with non-disease genes, (ii) to be expressed in the same tissues and (iii) to share Gene Ontology (GO) terms [8]. Contradicting earlier reports, this latter study demonstrated that the non-essential human disease genes showed no tendency to encode hubs in the human interactome. A more recent report that evaluated the network properties of disease genes showed that genes with intermediate degrees (numbers of neighbors) were more likely to harbor germ-line disease mutations [12]. However, interpretation of this dataset might not be applicable to complex disease genes since 97% of the disease genes were monogenic. Despite this reservation, both the latter studies found a functional clustering of disease genes. Another concern is that the above studies could be confounded by discovery bias, in other words these disease genes were identified based on previous knowledge. By contrast, Genome Wide Association studies (GWAs) do not suffer from such bias [15]. In this study, we have derived networks of complex diseases and complex disease genes to explore the shared genetic architecture of complex diseases studied using GWAs. Further, we have evaluated the topological and functional properties of complex disease genes in the human interactome by comparing them with essential, monogenic and non-disease genes. We observed that diseases belonging to the same disease class do not always show a tendency to share common disease genes; the complex disease gene net- work shows high modularity comparable to that of the human PLoS ONE | www.plosone.org 1 November 2009 | Volume 4 | Issue 11 | e8090 The human disease network Kwang-Il Goh*†‡§ , Michael E. Cusick†‡¶ , David Valleʈ , Barton Childsʈ , Marc Vidal†‡¶ **, and Albert-La´szlo´ Baraba´si*†‡ ** *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 School, 77 Avenue Louis Pasteur, Boston, MA 02115; §Department of Physics, Korea University, Seoul 136-713, Korea; and ʈDepartment of Pediatrics and the McKusick–Nathans Institute of Genetic Medicine, Johns Hopkins University School of Medicine, Baltimore, MD 21205 Edited 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– gene associations offers a platform to explore in a single graph- theoretic framework all known phenotype and disease gene associ- ations, indicating the common genetic origin of many diseases. Genes associated with similar disorders show both higher likelihood of physical interactions between their products and higher expression profiling similarity for their transcripts, supporting the existence of distinct disease-specific functional modules. We find that essential human genes are likely to encode hub proteins and are expressed widely in most tissues. This suggests that disease genes also would play a central role in the human interactome. In contrast, we find that the vast majority of disease genes are nonessential and show no tendency to encode hub proteins, and their expression pattern indi- cates that they are localized in the functional periphery of the network. A selection-based model explains the observed difference between essential and disease genes and also suggests that diseases caused by somatic mutations should not be peripheral, a prediction we confirm for cancer genes. biological networks ͉ complex networks ͉ human genetics ͉ systems biology ͉ diseasome Decades-long efforts to map human disease loci, at first genet- ically and later physically (1), followed by recent positional cloning of many disease genes (2) and genome-wide association studies (3), have generated an impressive list of disorder–gene association pairs (4, 5). In addition, recent efforts to map the protein–protein interactions in humans (6, 7), together with efforts to curate an extensive map of human metabolism (8) and regulatory networks offer increasingly detailed maps of the relationships between different disease genes. Most of the successful studies building on these new approaches have focused, however, on a single disease, using network-based tools to gain a better under- standing of the relationship between the genes implicated in a selected disorder (9). Here we take a conceptually different approach, exploring whether human genetic disorders and the corresponding disease genes might be related to each other at a higher level of cellular and organismal organization. Support for the validity of this approach is provided by examples of genetic disorders that arise from mutations in more than a single gene (locus heterogeneity). For example, Zellweger syndrome is caused by mutations in any of at least 11 genes, all associated with peroxisome biogenesis (10). Similarly, there are many examples of different mutations in the same gene (allelic heterogeneity) giving rise to phenotypes cur- rently classified as different disorders. For example, mutations in TP53 have been linked to 11 clinically distinguishable cancer- related disorders (11). Given the highly interlinked internal orga- nization of the cell (12–17), it should be possible to improve the single gene–single disorder approach by developing a conceptual framework to link systematically all genetic disorders (the human ‘‘disease phenome’’) with the complete list of disease genes (the ‘‘disease genome’’), resulting in a global view of the ‘‘diseasome,’’ the combined set of all known disorder/disease gene associations. Results Construction of the Diseasome. We constructed a bipartite graph consisting of two disjoint sets of nodes. One set corresponds to all known genetic disorders, whereas the other set corresponds to all known disease genes in the human genome (Fig. 1). A disorder and a gene are then connected by a link if mutations in that gene are implicated in that disorder. The list of disorders, disease genes, and associations between them was obtained from the Online Mende- lian Inheritance in Man (OMIM; ref. 18), a compendium of human disease genes and phenotypes. As of December 2005, this list contained 1,284 disorders and 1,777 disease genes. OMIM initially focused on monogenic disorders but in recent years has expanded to include complex traits and the associated genetic mutations that confer susceptibility to these common disorders (18). Although this history introduces some biases, and the disease gene record is far from complete, OMIM represents the most complete and up-to- date repository of all known disease genes and the disorders they confer. We manually classified each disorder into one of 22 disorder classes based on the physiological system affected [see supporting information (SI) Text, SI Fig. 5, and SI Table 1 for details]. Starting from the diseasome bipartite graph we generated two biologically relevant network projections (Fig. 1). In the ‘‘human disease network’’ (HDN) nodes represent disorders, and two disorders are connected to each other if they share at least one gene in which mutations are associated with both disorders (Figs. 1 and 2a). In the ‘‘disease gene network’’ (DGN) nodes represent disease genes, and two genes are connected if they are associated with the same disorder (Figs. 1 and 2b). Next, we discuss the potential of these networks to help us understand and represent in a single framework all known disease gene and phenotype associations. Properties of the HDN. If each human disorder tends to have a distinct and unique genetic origin, then the HDN would be dis- connected into many single nodes corresponding to specific disor- ders or grouped into small clusters of a few closely related disorders. In contrast, the obtained HDN displays many connections between both individual disorders and disorder classes (Fig. 2a). Of 1,284 disorders, 867 have at least one link to other disorders, and 516 disorders form a giant component, suggesting that the genetic origins of most diseases, to some extent, are shared with other diseases. The number of genes associated with a disorder, s, has a broad distribution (see SI Fig. 6a), indicating that most disorders relate to a few disease genes, whereas a handful of phenotypes, such as deafness (s ϭ 41), leukemia (s ϭ 37), and colon cancer (s ϭ 34), relate to dozens of genes (Fig. 2a). The degree (k) distribution of HDN (SI Fig. 6b) indicates that most disorders are linked to only Author contributions: D.V., B.C., M.V., and A.-L.B. designed research; K.-I.G. and M.E.C. performed research; K.-I.G. and M.E.C. analyzed data; and K.-I.G., M.E.C., D.V., M.V., and A.-L.B. wrote the paper. The authors declare no conflict of interest. This article is a PNAS Direct Submission. Abbreviations: DGN, disease gene network; HDN, human disease network; GO, Gene Ontology; OMIM, Online Mendelian Inheritance in Man; PCC, Pearson correlation coeffi- cient. **To whom correspondence may be addressed. E-mail: alb@nd.edu or marc࿝vidal@ dfci.harvard.edu. This article contains supporting information online at www.pnas.org/cgi/content/full/ 0701361104/DC1. © 2007 by The National Academy of Sciences of the USA www.pnas.org͞cgi͞doi͞10.1073͞pnas.0701361104 PNAS ͉ May 22, 2007 ͉ vol. 104 ͉ no. 21 ͉ 8685–8690 APPLIEDPHYSICAL SCIENCES a few other disorders, whereas a few phenotypes such as colon cancer (linked to k ϭ 50 other disorders) or breast cancer (k ϭ 30) represent hubs that are connected to a large number of distinct disorders. The prominence of cancer among the most connected disorders arises in part from the many clinically distinct cancer subtypes tightly connected with each other through common tumor repressor genes such as TP53 and PTEN. Although the HDN layout was generated independently of any knowledge on disorder classes, the resulting network is naturally and visibly clustered according to major disorder classes. Yet, there are visible differences between different classes of disorders. Whereas the large cancer cluster is tightly interconnected due to the many genes associated with multiple types of cancer (TP53, KRAS, ERBB2, NF1, etc.) and includes several diseases with strong pre- disposition to cancer, such as Fanconi anemia and ataxia telangi- ectasia, metabolic disorders do not appear to form a single distinct cluster but are underrepresented in the giant component and overrepresented in the small connected components (Fig. 2a). To quantify this difference, we measured the locus heterogeneity of each disorder class and the fraction of disorders that are connected to each other in the HDN (see SI Text). We find that cancer and neurological disorders show high locus heterogeneity and also represent the most connected disease classes, in contrast with metabolic, skeletal, and multiple disorders that have low genetic heterogeneity and are the least connected (SI Fig. 7). Properties of the DGN. In the DGN, two disease genes are connected if they are associated with the same disorder, providing a comple- mentary, gene-centered view of the diseasome. Given that the links signify related phenotypic association between two genes, they represent a measure of their phenotypic relatedness, which could be used in future studies, in conjunction with protein–protein inter- actions (6, 7, 19), transcription factor-promoter interactions (20), and metabolic reactions (8), to discover novel genetic interactions. In the DGN, 1,377 of 1,777 disease genes are connected to other disease genes, and 903 genes belong to a giant component (Fig. 2b). Whereas the number of genes involved in multiple diseases de- creases rapidly (SI Fig. 6d; light gray nodes in Fig. 2b), several disease genes (e.g., TP53, PAX6) are involved in as many as 10 disorders, representing major hubs in the network. Functional Clustering of HDN and DGN. To probe how the topology of the HDN and GDN deviates from random, we randomly shuffled the associations between disorders and genes, while keep- ing the number of links per each disorder and disease gene in the bipartite network unchanged. Interestingly, the average size of the giant component of 104 randomized disease networks is 643 Ϯ 16, significantly larger than 516 (P Ͻ 10Ϫ4; for details of statistical analyses of the results reported hereafter, see SI Text), the actual size of the HDN (SI Fig. 6c). Similarly, the average size of the giant component from randomized gene networks is 1,087 Ϯ 20 genes, significantly larger than 903 (P Ͻ 10Ϫ4), the actual size of the DGN (SI Fig. 6e). These differences suggest important pathophysiological clustering of disorders and disease genes. Indeed, in the actual networks disorders (genes) are more likely linked to disorders (genes) of the same disorder class. For example, in the HDN there AR ATM BRCA1 BRCA2 CDH1 GARS HEXB KRAS LMNA MSH2 PIK3CA TP53 MAD1L1 RAD54L VAPB CHEK2 BSCL2 ALS2 BRIP1 Androgen insensitivity Breast cancer Perineal hypospadias Prostate cancer Spinal muscular atrophy Ataxia-telangiectasia Lymphoma T-cell lymphoblastic leukemia Ovarian cancer Papillary serous carcinoma Fanconi anemia Pancreatic cancer Wilms tumor Charcot-Marie-Tooth disease Sandhoff disease Lipodystrophy Amyotrophic lateral sclerosis Silver spastic paraplegia syndrome Spastic ataxia/paraplegia AR ATM BRCA1 BRCA2 CDH1 GARS HEXB KRAS LMNA MSH2 PIK3CA TP53 MAD1L1 RAD54L VAPB CHEK2 BSCL2 ALS2 BRIP1 Androgen insensitivity Breast cancer Perineal hypospadiasProstate cancer Spinal muscular atrophy Ataxia-telangiectasia Lymphoma T-cell lymphoblastic leukemia Ovarian cancer Papillary serous carcinoma Fanconi anemia Pancreatic cancer Wilms tumor Charcot-Marie-Tooth disease Sandhoff disease Lipodystrophy Amyotrophic lateral sclerosis Silver spastic paraplegia syndrome Spastic ataxia/paraplegia Human Disease Network (HDN) Disease Gene Network (DGN) disease genomedisease phenome DISEASOME Fig. 1. Construction of the diseasome bipartite network. (Center) A small subset of OMIM-based disorder–disease gene associations (18), where circles and rectangles correspond to disorders and disease genes, respectively. A link is placed between a disorder and a disease gene if mutations in that gene lead to the specific disorder. Thesizeofacircleisproportionaltothenumberofgenesparticipatinginthecorrespondingdisorder,andthecolorcorrespondstothedisorderclasstowhichthedisease 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 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, 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. 8686 ͉ www.pnas.org͞cgi͞doi͞10.1073͞pnas.0701361104 Goh et al. Sunday, September 1, 13
    • Sunday, September 1, 13
    • Methods •Bipartite network and one-mode projections: 20 Regime shifts + 55 Drivers •104 random bipartite graphs to explore significance of couplings: mean degree, co- occurrence & clustering coefficient statistics on one-mode projections. Regime shiftsDrivers Sunday, September 1, 13
    • Methods •Bipartite network and one-mode projections: 20 Regime shifts + 55 Drivers •104 random bipartite graphs to explore significance of couplings: mean degree, co- occurrence & clustering coefficient statistics on one-mode projections. Regime shiftsDrivers Sunday, September 1, 13
    • 1 3 5 7 11 16 Degree distribution Degree 05101520 ● ● ● ● ● ● ● ●● ● ●● ●● ● ● ● ●●● ● ● ● ●●● ●● ● ● ●●● ● ● ● ● ● ●● ●● ● ● ● ●●● ● ●● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 5 10 15 0100300500 Degree Betweenness Co−occurrence Index DN s−squared Density 1.4 1.6 1.8 2.0 0123456 Average Degree DN Degree Density 20 22 24 26 0.00.20.40.6 Co−occurrence Index RN s−squared Density 8 9 10 11 12 13 0.00.20.40.60.8 Average Degree RN Degree Density 12 14 16 18 0.00.20.40.6 Sunday, September 1, 13
    • Agriculture Atmospheric CO2 Deforestation Demand Droughts Fishing Global warming Human population Nutrients inputs Urbanization Global drivers of Regime Shifts Food production & climate change are the most important drivers or regime shifts globally Only 5 out of 55 drivers cause >50% of the 20 regime shifts analyzed. 11 drivers interact with >50% of other drivers when causing regime shifts. Sunday, September 1, 13
    • Encroachment Monsoonweakening Soilsalinization Drylanddegradation Foresttosavannas Fisheriescollapse Marinefoodwebs Floatingplants Peatlands Saltmarshes Soilstructure Riverchannelchange TundratoForest Greenland Thermohalinecirculation Coraltransitions Bivalvescollapse Kelpstransitions Eutrophication Hypoxia Human Indirect Activities Climate Water Biodiversity Loss Land Cover Change Biogeochemical Cycle Biophysical 0 2 4 6 8 Value 01530 Count Global drivers of Regime Shifts Food production & climate change are the most important drivers or regime shifts globally Only 5 out of 55 drivers cause >50% of the 20 regime shifts analyzed. 11 drivers interact with >50% of other drivers when causing regime shifts. Sunday, September 1, 13
    • Bivalves collapse Coral transitions Dry land degradation Encroachment Eutrophication Fisheries collapse Floating plants Forest to savannas Greenland Hypoxia Kelps transitions Marine foodwebs Monsoon weakening Peatlands River channel change Salt marshes Soil salinization Soil structure Thermohaline circulation Tundra to Forest Marine regime shifts tend to share significantly more drivers and tend to have similar feedback mechanisms, suggesting they can synchronize in space and time. By managing key drivers several regime shifts can be avoided in aquatic systems. Terrestrial regime shifts share less drivers. Higher diversity of drivers makes management more context dependent. How drivers tend to interact? Sunday, September 1, 13
    • What does it mean for management? Floating plants Bivalves collapse Eutrophication Fisheries collapse Coral transitions Hypoxia Encroachment Salt marshes Soil salinization Soil structure Forest to savannas Dry land degradation Kelps transitions Monsoon weakening Peatlands Marine foodwebs Greenland Thermohaline circulation River channel change Tundra to Forest Local National International Drivers by Management Type Proportion of RS Drivers 0.0 0.2 0.4 0.6 0.8 1.0 Half of the drivers of 75% of the regime shifts require international cooperation to manage them. Given the high diversity of drivers, focusing on well studied variables (e.g. nutrients inputs) wont preclude regime shifts from happening. Avoiding regime shifts calls for poly-centric institutions. Sunday, September 1, 13
    • Regime shifts are tightly connected both when sharing drivers and their underlying feedback dynamics. The management of immediate causes or well studied variables might not be enough to avoid such catastrophes. Food production and climate change are the main causes of regime shifts globally. Marine regime shifts share more drivers, while terrestrial regime shifts are more context dependent. Management of regime shifts requires multi-level governance: coordinating efforts across multiple scales of action. Network analysis is an useful approach to study regime shifts couplings when knowledge about system dynamics or time series of key variables are limited. Conclusions Sunday, September 1, 13
    • 4. Future developments Sunday, September 1, 13
    • Methods • Bipartite network and one- mode projections: 20 Regime shifts + 55 Drivers • 104 random bipartite graphs to explore significance of couplings: mean degree and co-occurrence statistics on one-mode projections. • ERGM models using Jaccard similarity index on the RSDB as edge covariates Regime shiftsDrivers A 1 0 1 1 0 0 0 0 1 1 1 1 0 1 0 1 B 1 0 0 0 1 1 0 0 1 1 1 0 0 1 0 1 C Regime Shift Database Ecosystem services Ecosystem processes Ecosystem type Impact on human well being Land use Spatial scale Temporal scale Reversibility Evidence ... Sunday, September 1, 13
    • Causal-loop diagrams is a technique to map out the feedback structure of a system (Sterman 2000) Work in Progress Causal Networks: Cascading effects and regime shifts controllability Sunday, September 1, 13
    • Degree centrality Topological features of Causal Networks Betweenness centrality Eigenvector centrality Sunday, September 1, 13
    • ARTICLE doi:10.1038/nature10011 Controllability of complex networks Yang-Yu Liu1,2 , Jean-Jacques Slotine3,4 & Albert-La´szlo´ Baraba´si1,2,5 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. Accordingtocontroltheory,adynamicalsystemiscontrollableif,witha suitable choice of inputs, it can be driven from any initial state to any desired final state within finite time1–3 . This definition agrees with our intuitive notion of control, capturing an ability to guide a system’s behaviourtowardsadesiredstatethroughtheappropriatemanipulation of a few input variables, like a driver prompting a car to move with the 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 circuits, manufacturing processes, communication systems4–6 , aircraft, spacecraft and robots2,3 , fundamental questions pertaining to the con- trollabilityofcomplex systemsemerging in nature andengineering have resisted advances. The difficulty is rooted in the fact that two independ- ent factors contribute to controllability, each with its own layer of unknown: (1) the system’s architecture, represented by the network encapsulating which components interact with each other; and (2) the dynamical rules that capture the time-dependent interactions between thecomponents.Thus,progresshasbeenpossibleonlyinsystemswhere both layers are well mapped, such as the control of synchronized net- works7–10 , small biological circuits11 and rate control for communica- 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 than others and how network topology affects a system’s controllability. 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- monly emerge in complex systems. Network controllability Most real systems are driven by nonlinear processes, but the controll- ability of nonlinear systems is in many aspects structurally similar to that of linear systems3 , prompting us to start our study using the of traffic that passes through a node i in a communication network24 or transcription factor concentration in a gene regulatory network25 . 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 interaction. Finally, B is the N 3 M input matrix (M # N) that iden- 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 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 nodes’. We are particularly interested in identifying the minimum number of driver nodes, denoted by ND, whose control is sufficient to fully control the system’s dynamics. The system described by equation (1) is said to be controllable if it can be driven from any initial state to any desired final state in finite time, which is possible if and only if the N3 NM controllability matrix C~(B, AB, A2 B, . . . , AN{1 B) ð2Þ has full rank, that is rank(C)~N ð3Þ This represents the mathematical condition for controllability, and is called Kalman’s controllability rank condition1,2 (Fig. 1a). In practical terms,controllabilitycanbealsoposedasfollows.Identifytheminimum 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 signalu1 offersfullcontroloverthesystem,asthestatesofnodesx1,x2,x3 and x4 are uniquely determined by the signal u1(t) (Fig. 1c). In contrast, controlling the top node in Fig. 1e is not sufficient for full control, as the difference a31x2(t) 2 a21x3(t) (where aij are the elements of A) is not Are regime shifts controllable? To what extent can we manage them? • Critics to Liu et al.: • Topology is not enough • Internal dynamics • Unmatched nodes change if the periphery of the causal networks change - The limits of the system blur • Unmatched nodes change when joining causal networks to understand cascading effects. Sunday, September 1, 13
    • ARTICLE doi:10.1038/nature10011 Controllability of complex networks Yang-Yu Liu1,2 , Jean-Jacques Slotine3,4 & Albert-La´szlo´ Baraba´si1,2,5 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. Accordingtocontroltheory,adynamicalsystemiscontrollableif,witha suitable choice of inputs, it can be driven from any initial state to any desired final state within finite time1–3 . This definition agrees with our intuitive notion of control, capturing an ability to guide a system’s behaviourtowardsadesiredstatethroughtheappropriatemanipulation of a few input variables, like a driver prompting a car to move with the 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 circuits, manufacturing processes, communication systems4–6 , aircraft, spacecraft and robots2,3 , fundamental questions pertaining to the con- trollabilityofcomplex systemsemerging in nature andengineering have resisted advances. The difficulty is rooted in the fact that two independ- ent factors contribute to controllability, each with its own layer of unknown: (1) the system’s architecture, represented by the network encapsulating which components interact with each other; and (2) the dynamical rules that capture the time-dependent interactions between thecomponents.Thus,progresshasbeenpossibleonlyinsystemswhere both layers are well mapped, such as the control of synchronized net- works7–10 , small biological circuits11 and rate control for communica- 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 than others and how network topology affects a system’s controllability. 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- monly emerge in complex systems. Network controllability Most real systems are driven by nonlinear processes, but the controll- ability of nonlinear systems is in many aspects structurally similar to that of linear systems3 , prompting us to start our study using the of traffic that passes through a node i in a communication network24 or transcription factor concentration in a gene regulatory network25 . 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 interaction. Finally, B is the N 3 M input matrix (M # N) that iden- 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 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 nodes’. We are particularly interested in identifying the minimum number of driver nodes, denoted by ND, whose control is sufficient to fully control the system’s dynamics. The system described by equation (1) is said to be controllable if it can be driven from any initial state to any desired final state in finite time, which is possible if and only if the N3 NM controllability matrix C~(B, AB, A2 B, . . . , AN{1 B) ð2Þ has full rank, that is rank(C)~N ð3Þ This represents the mathematical condition for controllability, and is called Kalman’s controllability rank condition1,2 (Fig. 1a). In practical terms,controllabilitycanbealsoposedasfollows.Identifytheminimum 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 signalu1 offersfullcontroloverthesystem,asthestatesofnodesx1,x2,x3 and x4 are uniquely determined by the signal u1(t) (Fig. 1c). In contrast, controlling the top node in Fig. 1e is not sufficient for full control, as the difference a31x2(t) 2 a21x3(t) (where aij are the elements of A) is not Are regime shifts controllable? To what extent can we manage them? • Critics to Liu et al.: • Topology is not enough • Internal dynamics • Unmatched nodes change if the periphery of the causal networks change - The limits of the system blur • Unmatched nodes change when joining causal networks to understand cascading effects. Sunday, September 1, 13
    • Thanks! Prof. Garry Peterson & Oonsie Biggs for their supervision RSDB folks for inspiring discussion and writing examples Funding sources: FORMAS, SSEESS, CSS. Questions?? e-mail: juan.rocha@stockholmresilience.su.se News and papers on regime shifts: @juanrocha Research blog: http://criticaltransitions.wordpress.com/ Sunday, September 1, 13
    • Holling’s logic in reverse Reduce complexity: a handful of variables will reproduce regime shifts. But which ones? 1. Resilience surrogates 2. Leverage points 3. Fast / slow processes Sunday, September 1, 13
    • Parallel projects & collaboration 1. Text mining to infer potential ecosystem services affected by regime shifts (with Robin Wikström - Abo University) 2. Networks of Drivers and Ecosystem Services consequences of Marine Regime Shifts (with Peterson, Biggs, Blenckner & Yletyinen) 3. Experimental economics in Colombia: how people respond to abrupt ecosystem change? (with Schill, Crepin & Lindahl) 4. Resource - trade networks: Can we detect cascading effects among regime shifts by tracing trade signals? 5. Holling’s logic in reverse: Can networks infer resilience surrogates in SES? Sunday, September 1, 13
    • Data quality (time series) Knowledgeofthe system Statistics: Autocorrelation and variance Bayesian networks - models Models & Jacobians Web crawlers & local knowledge Research agenda on Regime Shifts High High Low Low Sunday, September 1, 13
    • Data quality (time series) Knowledgeofthe system Statistics: Autocorrelation and variance Bayesian networks - models Models & Jacobians Web crawlers & local knowledge Research agenda on Regime Shifts High High Low Low Sunday, September 1, 13
    • Data quality (time series) Knowledgeofthe system Statistics: Autocorrelation and variance Bayesian networks - models Models & Jacobians Web crawlers & local knowledge Research agenda on Regime Shifts ? High High Low Low Sunday, September 1, 13
    • TundratoForest Greenland Termohalinecirculation Saltmarshes Marinefoodwebs Fisheriescollapse Soilstructure Riverchannelchange Floatingplants Peatlands Coraltransitions Kelpstransitions Bivalvescollapse Eutrophication Hypoxia Foresttosavannas Drylanddegradation Encroachment Monsoonweakening Soilsalinization Soil salinization Monsoon weakening Encroachment Dry land degradation Forest to savannas Hypoxia Eutrophication Bivalves collapse Kelps transitions Coral transitions Peatlands Floating plants River channel change Soil structure Fisheries collapse Marine foodwebs Salt marshes Termohaline circulation Greenland Tundra to Forest Regime shifts 0 0.4 0.8 Value 0100 Color Key and Histogram Count Average Degree in simulated Regime Shifts Networks Mean Degree Density 12 13 14 15 16 17 18 19 0.00.10.20.30.40.50.60.7 Regime Shifts Network Co−occurrence Index s−squared Density 8 9 10 11 12 13 0.00.20.40.60.8 Bivalves collapse Coral transitions Dry land degradation Encroachment Eutrophication Fisheries collapse Forest to Savannas Hypoxia Kelps transitions Marine foodwebs Floating plants River channel change Salt marshes Soil salinization Soil structure Tundra to Forest Monsoon weakening Peatlands Greenland Thermohaline circulation The co-occurrence of regime shifts is not random. Aquatic systems tend to share more drivers suggesting that their underlying processes are also similar Sunday, September 1, 13
    • Turbidity Disease Pollutants Sediments Thermalanomaliesinsummer Oceanacidification Hurricanes Lowtides Waterstratification Impoundments Rainfallvariability Landscapefragmentation Flushing Urbanstormwaterrunoff Urbanization Nutrientsinputs Fishing Demand Deforestation Humanpopulation Agriculture Erosion Floods Fertilizersuse Sewage Productionintensification Foodprices Laboravailability Ranching(livestock) Waterinfrastructure Aquifers Wateravailability Upwellings ENSOlikeevents Tragedyofthecommons Accesstomarkets Subsidies Infrastructuredevelopment Immigration Logging Droughts Firefrequency Irrigation Globalwarming AtmosphericCO2 Precipitation Fishingtechnology Foodsupply Invasivespecies Sealevelrise Temperature Greenhousegases Developmentpolicies Drainage Seasurfacetemperature Sea surface temperature Drainage Development policies Green house gases Temperature Sea level rise Invasive species Food supply Fishing technology Precipitation Atmospheric CO2 Global warming Irrigation Fire frequency Droughts Logging Immigration Infrastructure development Subsidies Access to markets Tragedy of the commons ENSO like events Upwellings Water availability Aquifers Water infrastructure Ranching (livestock) Labor availability Food prices Production intensification Sewage Fertilizers use Floods Erosion Agriculture Human population Deforestation Demand Fishing Nutrients inputs Urbanization Urban storm water runoff Flushing Landscape fragmentation Rainfall variability Impoundments Water stratification Low tides Hurricanes Ocean acidification Thermal anomalies in summer Sediments Pollutants Disease Turbidity Drivers 0 0.4 0.8 Value 01000 Color Key and Histogram Count Average Degree in simulated Drivers Networks Mean Degree Density 20 21 22 23 24 25 26 0.00.10.20.30.40.50.60.7 Drivers Network Co−occurrence Index s−squared Density 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 0123456 The co-occurrence of driver is not random. Drivers tend to cluster according to the ecosystem type where the regime shift takes place. AgricultureAtmospheric CO2 Deforestation Demand Droughts ENSO like events Erosion Fertilizers use Fishing Floods Global warming Human population Irrigation Nutrients inputs Precipitation Sewage Upwellings Urbanization Marine General Terrestrial Sunday, September 1, 13
    • Marine Regime Shifts Local centrality Global centrality 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.000.020.040.060.080.100.12 Eigenvector Betweenness Agriculture Algae Atmospheric CO2 Biodiversity Bivalves abundance Canopy−forming algae Consumption preferences Coral abundance Daily relative coolingDeforestation DemandDensity contrast in the water column Disease outbreak Dissolved oxygen DroughtsENSO−like events frequency Erosion Fertilizers useFish Fishing Floods Flushing Global warming Greenhouse gases Habitat structural complexity Herbivores Human populationHurricanesImpoundmentsInvasive speciesIrrigationLandscape fragmentation/conversion Leakage Lobsters and meso−predators Local water movementsLow tides frequency Macroalgae abundance Macrophytes Mid−predators Mortality rate Nekton Noxious gases Nutrients input Ocean acidification Organic matter Other competitorsPerverse incentives Phosphorous in water Phytoplankton Planktivore fish Plankton and filamentous algae PollutantsPrecipitationSedimentsSewage Space SST StratificationSubsidiesSulfide releaseTechnologyThermal annomalies Thermal low pressure Top predators TradeTragedy of the commons Turbidity Turf−forming algae Unpalatability Upwellings Urban growth Urban storm water runoff Urchin barrenWater column density contrast Water mixing Water temperature Water vapor Wind stress Zooplankton Zooxanthellae 0 5 10 15 0510 Indegree Outdegree Agriculture Algae Atmospheric CO2 Biodiversity Bivalves abundance Canopy−forming algae Consumption preferences Coral abundance Daily relative cooling Deforestation Demand Density contrast in the water column Disease outbreak Dissolved oxygen Droughts ENSO−like events frequency Erosion Fertilizers use Fish Fishing Floods Flushing Global warming Greenhouse gases Habitat structural complexity Herbivores Human population Hurricanes ImpoundmentsInvasive species Irrigation Landscape fragmentation/conversion Leakage Lobsters and meso−predators Local water movements Low tides frequency Macroalgae abundance Macrophytes Mid−predators Mortality rate Nekton Noxious gases Nutrients input Ocean acidification Organic matterOther competitors Perverse incentives Phosphorous in water PhytoplanktonPlanktivore fish Plankton and filamentous algae Pollutants Precipitation SedimentsSewage Space SST Stratification Subsidies Sulfide releaseTechnologyThermal annomalies Thermal low pressure Top predators Trade Tragedy of the commons Turbidity Turf−forming algae Unpalatability Upwellings Urban growth Urban storm water runoff Urchin barren Water column density contrastWater mixing Water temperature Water vapor Wind stress Zooplankton Zooxanthellae Sunday, September 1, 13
    • Terrestrial Regime Shifts Local centrality Global centrality 0 2 4 6 8 02468 Indegree Outdegree Absorption of solar radiationAdvectionAerosol concentration Agriculture Albedo Aquifers Atmospheric CO2 Atmospheric temperature Biomass Brown cloudsCarbon storage Cropland−Grassland area Deforestation Demand Droughts DustENSO−like events frequency ErosionEvapotranspiration Fertilizers use Fire frequency Floods Forest Global warming Grass dominance Grazers Grazing Ground water table Human population Illegal logging Immigration Infrastructure development Irrigation Land conversion Land−Ocean pressure gradient Land−Ocean temperature gradient Latent heat release Lifting condensation levelLogging industryMoisture Monsoon circulation Native vegetation Palatability Precipitation Productivity Rainfall deficit Rainfall variability Ranching Roughness Savanna Sea tides Shadow_rooting Soil impermeability Soil moistureSoil productivity Soil quality Soil salinitySolar radiation SpaceSST Temperature Tree maturity Vapor VegetationWater availability Water consumption Water demandWater infrastructure Wind stress Woody plants dominance 0.00 0.02 0.04 0.06 0.08 0.000.020.040.060.08 Eigenvector Betweenness Absorption of solar radiation Advection Aerosol concentration Agriculture Albedo Aquifers Atmospheric CO2 Atmospheric temperature Biomass Brown clouds Carbon storage Cropland−Grassland area Deforestation Demand Droughts Dust ENSO−like events frequency Erosion Evapotranspiration Fertilizers use Fire frequency Floods Forest Global warming Grass dominance Grazers Grazing Ground water table Human populationIllegal loggingImmigrationInfrastructure development Irrigation Land conversion Land−Ocean pressure gradient Land−Ocean temperature gradient Latent heat release Lifting condensation level Logging industry Moisture Monsoon circulation Native vegetation Palatability Precipitation Productivity Rainfall deficit Rainfall variability Ranching Roughness Savanna Sea tides Shadow_rooting Soil impermeability Soil moisture Soil productivity Soil quality Soil salinity Solar radiation Space SST Temperature Tree maturity Vapor Vegetation Water availability Water consumption Water demand Water infrastructure Wind stress Woody plants dominance Sunday, September 1, 13