Post on 11-Jun-2015
Regime Shifts in the Anthropocene Juan-Carlos Rocha
The Anthropocene
The Anthropocene
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?
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
Prec
ipita
tion
Vegetation Prec
ipita
tion
Vegetation Prec
ipita
tion
Vegetation Prec
ipita
tion
Vegetation
Precipitation Precipitation Precipitation Precipitation
low high low high low high low high
Vegetation
low
high
Gradual Threshold
Vegetation
low
high
Vegetation
low
highVegetation
low
high
Hystersis Irreversible
StabilityLandscape
Equilibria
(Gordon et al 2008)
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 differentlevel. Human activities can move the system along both of the horizontal axes. For example, fishing can actas external forcing by reducing the population rate of increase and also alter the internal trophic structure.
4. Modeling regime shifts
We concentrate here on general classes of model that can exhibit multiple equilibria for certain com-binations of parameter values. It is important to note that the three different types of regime shifts (smooth,abrupt, and discontinuous) can be generated from the same general models with different parameters. Thus,the three types are, apparently, special cases of the same general models, corresponding to different regionsof parameter space. There are large tracts of parameter space for which only a single equilibrium exists,corresponding to smooth or more abrupt regime shifts. This hierarchical modeling framework permitsstatistical tests of which type of regime shift fits the data best.
Our treatment summarizes the main features of these models that could be mechanisms for regime shifts,starting with models of single populations and progressing to coupled models of two or more species. Oneproblem with using models to describe the mechanisms that can lead to regime shifts is that, according tothe definition of regime shift that we have adopted here, several species or trophic levels should exhibit theshift. However, the simplest models describe only one population variable; two or three variables or trophiclevels rapidly develop very complicated responses. Thus, the models described here must be considered as‘‘samples’’ from a community responding as a regime. An alternative approach would be to start withecosystem models and to study the system dynamics. Models with many species are known to exhibitcomplex dynamics, thereby increasing the likelihood of discontinuous regime shifts.
Fig. 3. Catastrophe manifold illustrating that the three types of regime shifts are special cases along a continuum of internal ecosystemstructure. Adapted from Jones and Walters (1976).
J.S. Collie et al. / Progress in Oceanography 60 (2004) 281–302 287
(Collie 2004)
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
1. A comparative framework: The database 2. Global drivers of Regime Shifts 3. Future developments
1. A comparative framework: The database
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
Mechanism
Exist
ence
Well established
Proposed
Contested
Contested
Proposed
Well established
Soil structureMarine foodwebs Monsoon weakening Termohaline circulation
Encroachment Fisheries collapse Marine Eutrophication
Dryland degradation Forest to savanna Steppe to tundra Mangroves collapse
Tundra to forest
Floating plants Greenland Arctic sea ice West Antarctica Ice Sheet
Bivalves collapse Coral transitions Lake Eutrophication Hypoxia Kelps transitions Sea grass Peatlands River channel change Salt marshes Soil salinization
Regime Shifts DataBase
Ecosystem services !
Drivers ...
Ecosystem Services
BiodiversityPrimary production
Nutrient cyclingWater cycling
Soil FormationFisheries
Wild animals and plants foodFreshwaterFoodcrops
LivestockTimber
WoodfuelOther cropsHydropower
Water purificationClimate regulation
Regulation of soil erosionPest and disease regulation
Natural hazard regulationAir quality regulation
PollinationRecreation
Aesthetic valuesKnowledge and educational values
Spiritual and religiousLivelihoods and economic activity
Food and nutritionCultural, aesthetic and recreational values
Security of housing and infrastructureHealth
Social confictNo direct impact
0 8 15 23 30
SupportingProvisioningRegulatingCulturalHuman well being
Regime Shifts DataBase
Ecosystem services !
Drivers ...
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Proportion of Regime Shifts (n=20)
Prop
ortio
n of
Driv
ers
shar
ing
caus
ality
to R
egim
e Sh
ifts
(n=5
5)
Agriculture
Atmospheric CO2
Deforestation
Demand
DroughtsFishing
Global warming
Human populationNutrients inputs
Urbanization
2. Global drivers of Regime Shifts
Virtruvian Man, Leonardo Da Vinci
Network Properties of Complex Human Disease GenesIdentified through Genome-Wide Association StudiesFredrik Barrenas1.*, Sreenivas Chavali1., Petter Holme2,3, Reza Mobini1, Mikael Benson1
1 The Unit for Clinical Systems Biology, University of Gothenburg, Gothenburg, Sweden, 2Department of Physics, Umea University, Umea, Sweden, 3Department of
Energy Science, Sungkyunkwan University, Suwon, Korea
Abstract
Background: Previous studies of network properties of human disease genes have mainly focused on monogenic diseasesor cancers and have suffered from discovery bias. Here we investigated the network properties of complex disease genesidentified 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 theshared genetic architecture of complex diseases. We evaluated the centrality measures of complex disease genes incomparison with essential and monogenic disease genes in the human interactome. The complex disease network showedthat diseases belonging to the same disease class do not always share common disease genes. A possible explanation couldbe that the variants with higher minor allele frequency and larger effect size identified using GWAs constitute disjoint partsof the allelic spectra of similar complex diseases. The complex disease gene network showed high modularity with the sizeof the largest component being smaller than expected from a randomized null-model. This is consistent with limited sharingof genes between diseases. Complex disease genes are less central than the essential and monogenic disease genes in thehuman interactome. Genes associated with the same disease, compared to genes associated with different diseases, moreoften 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 foridentifying 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-WideAssociation 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: ! 2009 Barrenas et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permitsunrestricted 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 theWCU (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 geneticdiseases have brought in a shift in the paradigm of elucidatingdisease mechanisms from analyzing the effects of single genes tounderstanding the effect of molecular interaction networks. Suchnetworks have been exploited to find novel candidate genes, basedon the assumption that neighbors of a disease-causing gene in anetwork are more likely to cause either the same or a similardisease [1–14]. Initial studies investigating the network propertiesof human disease genes were based on cancers and revealed thatup-regulated genes in cancerous tissues were central in theinteractome and highly connected (often referred to as hubs)[1,2]. A subsequent study based on the human disease networkand disease gene network derived from the Online MendelianInheritance in Man (OMIM) demonstrated that the products ofdisease genes tended (i) to have more interactions with each otherthan with non-disease genes, (ii) to be expressed in the same tissuesand (iii) to share Gene Ontology (GO) terms [8]. Contradictingearlier reports, this latter study demonstrated that the non-essentialhuman disease genes showed no tendency to encode hubs in the
human interactome. A more recent report that evaluated thenetwork properties of disease genes showed that genes withintermediate degrees (numbers of neighbors) were more likely toharbor germ-line disease mutations [12]. However, interpretationof this dataset might not be applicable to complex disease genessince 97% of the disease genes were monogenic. Despite thisreservation, both the latter studies found a functional clustering ofdisease genes. Another concern is that the above studies could beconfounded by discovery bias, in other words these disease geneswere identified based on previous knowledge. By contrast,Genome Wide Association studies (GWAs) do not suffer fromsuch bias [15].In this study, we have derived networks of complex diseases and
complex disease genes to explore the shared genetic architecture ofcomplex diseases studied using GWAs. Further, we have evaluatedthe topological and functional properties of complex disease genesin the human interactome by comparing them with essential,monogenic and non-disease genes. We observed that diseasesbelonging to the same disease class do not always show a tendencyto 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 networkKwang-Il Goh*†‡§, Michael E. Cusick†‡¶, David Valle!, Barton Childs!, 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(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 !Department of Pediatrics and theMcKusick–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. Genesassociated with similar disorders show both higher likelihood ofphysical interactions between their products and higher expressionprofiling similarity for their transcripts, supporting the existence ofdistinct disease-specific functional modules. We find that essentialhuman genes are likely to encode hub proteins and are expressedwidely in most tissues. This suggests that disease genes also wouldplay a central role in the human interactome. In contrast, we find thatthe vast majority of disease genes are nonessential and show notendency to encode hub proteins, and their expression pattern indi-cates that they are localized in the functional periphery of thenetwork. A selection-based model explains the observed differencebetween essential and disease genes and also suggests that diseasescaused by somatic mutations should not be peripheral, a predictionwe confirm for cancer genes.
biological networks " complex networks " human genetics " systemsbiology " 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 associationstudies (3), have generated an impressive list of disorder–geneassociation pairs (4, 5). In addition, recent efforts to map theprotein–protein interactions in humans (6, 7), together with effortsto curate an extensive map of human metabolism (8) and regulatorynetworks offer increasingly detailed maps of the relationshipsbetween different disease genes. Most of the successful studiesbuilding on these new approaches have focused, however, on asingle disease, using network-based tools to gain a better under-standing of the relationship between the genes implicated in aselected disorder (9).
Here we take a conceptually different approach, exploringwhether human genetic disorders and the corresponding diseasegenes might be related to each other at a higher level of cellular andorganismal organization. Support for the validity of this approachis provided by examples of genetic disorders that arise frommutations in more than a single gene (locus heterogeneity). Forexample, Zellweger syndrome is caused by mutations in any of atleast 11 genes, all associated with peroxisome biogenesis (10).Similarly, there are many examples of different mutations in thesame gene (allelic heterogeneity) giving rise to phenotypes cur-rently classified as different disorders. For example, mutations inTP53 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 thesingle gene–single disorder approach by developing a conceptualframework 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.
ResultsConstruction of the Diseasome. We constructed a bipartite graphconsisting of two disjoint sets of nodes. One set corresponds to all
known genetic disorders, whereas the other set corresponds to allknown disease genes in the human genome (Fig. 1). A disorder anda gene are then connected by a link if mutations in that gene areimplicated in that disorder. The list of disorders, disease genes, andassociations between them was obtained from the Online Mende-lian Inheritance in Man (OMIM; ref. 18), a compendium of humandisease genes and phenotypes. As of December 2005, this listcontained 1,284 disorders and 1,777 disease genes. OMIM initiallyfocused on monogenic disorders but in recent years has expandedto include complex traits and the associated genetic mutations thatconfer susceptibility to these common disorders (18). Although thishistory introduces some biases, and the disease gene record is farfrom complete, OMIM represents the most complete and up-to-date repository of all known disease genes and the disorders theyconfer. We manually classified each disorder into one of 22 disorderclasses based on the physiological system affected [see supportinginformation (SI) Text, SI Fig. 5, and SI Table 1 for details].
Starting from the diseasome bipartite graph we generated twobiologically relevant network projections (Fig. 1). In the ‘‘humandisease network’’ (HDN) nodes represent disorders, and twodisorders are connected to each other if they share at least one genein which mutations are associated with both disorders (Figs. 1 and2a). In the ‘‘disease gene network’’ (DGN) nodes represent diseasegenes, and two genes are connected if they are associated with thesame disorder (Figs. 1 and 2b). Next, we discuss the potential ofthese networks to help us understand and represent in a singleframework all known disease gene and phenotype associations.
Properties of the HDN. If each human disorder tends to have adistinct 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 betweenboth individual disorders and disorder classes (Fig. 2a). Of 1,284disorders, 867 have at least one link to other disorders, and 516disorders form a giant component, suggesting that the geneticorigins of most diseases, to some extent, are shared with otherdiseases. The number of genes associated with a disorder, s, has abroad distribution (see SI Fig. 6a), indicating that most disordersrelate to a few disease genes, whereas a handful of phenotypes, suchas deafness (s ! 41), leukemia (s ! 37), and colon cancer (s ! 34),relate to dozens of genes (Fig. 2a). The degree (k) distribution ofHDN (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., andA.-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, GeneOntology; 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.org#cgi#doi#10.1073#pnas.0701361104 PNAS " May 22, 2007 " vol. 104 " no. 21 " 8685–8690
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a few other disorders, whereas a few phenotypes such as coloncancer (linked to k ! 50 other disorders) or breast cancer (k ! 30)represent hubs that are connected to a large number of distinctdisorders. The prominence of cancer among the most connecteddisorders arises in part from the many clinically distinct cancersubtypes tightly connected with each other through common tumorrepressor genes such as TP53 and PTEN.
Although the HDN layout was generated independently of anyknowledge on disorder classes, the resulting network is naturallyand visibly clustered according to major disorder classes. Yet, thereare visible differences between different classes of disorders.Whereas the large cancer cluster is tightly interconnected due to themany 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 distinctcluster but are underrepresented in the giant component andoverrepresented in the small connected components (Fig. 2a). Toquantify this difference, we measured the locus heterogeneity ofeach disorder class and the fraction of disorders that are connectedto each other in the HDN (see SI Text). We find that cancer andneurological disorders show high locus heterogeneity and alsorepresent the most connected disease classes, in contrast withmetabolic, skeletal, and multiple disorders that have low geneticheterogeneity and are the least connected (SI Fig. 7).
Properties of the DGN. In the DGN, two disease genes are connectedif they are associated with the same disorder, providing a comple-
mentary, gene-centered view of the diseasome. Given that the linkssignify related phenotypic association between two genes, theyrepresent a measure of their phenotypic relatedness, which could beused 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 otherdisease 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), severaldisease genes (e.g., TP53, PAX6) are involved in as many as 10disorders, representing major hubs in the network.
Functional Clustering of HDN and DGN. To probe how the topologyof the HDN and GDN deviates from random, we randomlyshuffled the associations between disorders and genes, while keep-ing the number of links per each disorder and disease gene in thebipartite network unchanged. Interestingly, the average size of thegiant component of 104 randomized disease networks is 643 " 16,significantly larger than 516 (P # 10$4; for details of statisticalanalyses of the results reported hereafter, see SI Text), the actualsize of the HDN (SI Fig. 6c). Similarly, the average size of the giantcomponent from randomized gene networks is 1,087 " 20 genes,significantly larger than 903 (P # 10$4), the actual size of the DGN(SI Fig. 6e). These differences suggest important pathophysiologicalclustering of disorders and disease genes. Indeed, in the actualnetworks 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 carcinomaFanconi anemia
Pancreatic cancer
Wilms tumor
Charcot-Marie-Tooth disease
Sandhoff disease
Lipodystrophy
Amyotrophic lateral sclerosis
Silver spastic paraplegia syndromeSpastic 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 rectanglescorrespond 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.Thesizeofacircle isproportional tothenumberofgenesparticipating inthecorrespondingdisorder,andthecolorcorrespondstothedisorderclass towhichthediseasebelongs. (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 ofa 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 ofa 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.org"cgi"doi"10.1073"pnas.0701361104 Goh et al.
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
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
1 3 5 7 9 12 14 16 19
Degree distribution
Degree
05
1015
2025
30
Clustering Coefficient
Clustering coefficient
Den
sity
0.20 0.25 0.30 0.35 0.40
05
1020
30
Drivers Network Co−occurrence Index
s−squared
Den
sity
1.8 2.0 2.2 2.4 2.6
01
23
45
6
Regime Shifts Network Co−occurrence Index
s−squared
Den
sity
10 11 12 13 14 15 16
0.0
0.2
0.4
0.6
0.8
Average Degree in simulated Drivers Networks
Mean Degree
Den
sity
22 23 24 25 26 27 28 29
0.0
0.2
0.4
0.6
Average Degree in simulated Regime Shifts Networks
Mean Degree
Den
sity
18 19 20 21 22 23
0.0
0.2
0.4
0.6
Agriculture
Atmospheric CO2
Deforestation
Demand
Droughts
Erosion Fishing
Floods
Global warming
Human population
Landscape fragmentation
Nutrients inputs Rainfall variability
Sea level rise
Sea surface temperature
Sediments
Sewage
Temperature
Upwellings
Urbanization
Arctic sea ice
Bivalves collapse
Coral transitions
Dry land degradation
Encroachment
Eutrophication
Fisheries collapse
Floating plants
Forest to savannas
Greenland
Hypoxia
Kelps transitions
Mangroves collapse
Marine Eutrophication
Marine foodwebs
Monsoon weakening
Peatlands
River channel change
Salt marshes
Sea grass
Soil salinization Soil structure
Thermohaline circulation
Tundra to Forest
Western Antarctic IceSheet Collapse
Simulation results for 25 Regime Shifts across the globe
AgricultureAtmospheric CO2
DeforestationDemand
Droughts
Fishing
Global warming
Human population
Nutrients inputsUrbanization
Global drivers of Regime Shifts
Food production & climate change drive the most frequent drivers of regime shifts
Few frequent drivers: Only 5 out of 55 drivers influence more than 1/2 of the regime shifts analyzed.
More shared drivers: 11 drivers interact with >50% of other drivers when causing regime shifts.
Encroachment
Mon
soon
wea
keni
ngS
oil s
alin
izat
ion
Dry
land
deg
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tion
Fore
st to
sav
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sFi
sher
ies
colla
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Mar
ine
food
web
sFl
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ants
Peatlands
Sal
t mar
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Soi
l stru
ctur
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iver
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Tund
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For
est
Greenland
Ther
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atio
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oral
tran
sitio
nsB
ival
ves
colla
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Kel
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ansi
tions
Eutrophication
Hypoxia
Human Indirect Activities
Climate
Water
Biodiversity Loss
Land Cover Change
Biogeochemical Cycle
Biophysical
0 2 4 6 8Value
015
30Count
Global drivers of Regime Shifts
Food production & climate change drive the most frequent drivers of regime shifts
Few frequent drivers: Only 5 out of 55 drivers influence more than 1/2 of the regime shifts analyzed.
More shared drivers: 11 drivers interact with >50% of other drivers when causing regime shifts.
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 share significantly more drivers and have more similar feedback mechanisms, suggesting they may synchronize in space and time.
Terrestrial regime shifts share fewer drivers. Higher diversity of drivers makes management more context dependent.
How drivers tend to interact?
Impacts of Regime Shifts on Ecosystem Services
Impacts of Regime Shifts on Ecosystem Services
Arctic sea ice
Bivalves collapse
Coral transitions
Dry land degradationEncroachment
Eutrophication
Fisheries collapse
Floating plants
Forest to savannas
Greenland
HypoxiaKelps transitions
Mangroves collapse
Marine eutrophication
Marine foodwebs
Monsoon weakening
Peatlands
River channel change
Salt marshes
Sea Grass
Soil salinization
Soil structure
Termohaline circulation
Tundra to Forest
Western Antarctic IceSheet Collapse
Impacts of Regime Shifts on Ecosystem Services
Arctic sea ice
Bivalves collapse
Coral transitions
Dry land degradationEncroachment
Eutrophication
Fisheries collapse
Floating plants
Forest to savannas
Greenland
HypoxiaKelps transitions
Mangroves collapse
Marine eutrophication
Marine foodwebs
Monsoon weakening
Peatlands
River channel change
Salt marshes
Sea Grass
Soil salinization
Soil structure
Termohaline circulation
Tundra to Forest
Western Antarctic IceSheet Collapse
Soil formation
Primary production
Nutrient cycling
Water cycling
Biodiversity
Freshwater
Foodcrops
Livestock
Fisheries
Wild animal and plant foods
Timber
Wood fuel
Feed, fuel & fiber crops
Air quality regulation
Climate regulation
Water purification
Water regulation
Regulation of soil erosion
Pest and disease regulation
Pollination
Natural hazard regulation
Recreation Aesthetic values
Knowledge and educational values
Spiritual and religious
Impacts of Regime Shifts on Ecosystem Services
Arctic sea ice
Bivalves collapse
Coral transitions
Dry land degradationEncroachment
Eutrophication
Fisheries collapse
Floating plants
Forest to savannas
Greenland
HypoxiaKelps transitions
Mangroves collapse
Marine eutrophication
Marine foodwebs
Monsoon weakening
Peatlands
River channel change
Salt marshes
Sea Grass
Soil salinization
Soil structure
Termohaline circulation
Tundra to Forest
Western Antarctic IceSheet Collapse
Soil formation
Primary production
Nutrient cycling
Water cycling
Biodiversity
Freshwater
Foodcrops
Livestock
Fisheries
Wild animal and plant foods
Timber
Wood fuel
Feed, fuel & fiber crops
Air quality regulation
Climate regulation
Water purification
Water regulation
Regulation of soil erosion
Pest and disease regulation
Pollination
Natural hazard regulation
Recreation Aesthetic values
Knowledge and educational values
Spiritual and religious
Gre
en h
ouse
gas
esSe
a su
rface
tem
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ture
Fire
freq
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Ther
mal
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ies
in s
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ve s
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esAq
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lture
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n in
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eep
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r)Ic
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owth
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ate
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fers
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y of
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mon
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to m
arke
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bsid
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elop
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t pol
icie
sIm
mig
ratio
nLo
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(live
stoc
k)Pr
oduc
tion
inte
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catio
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od p
rices
Labo
r ava
ilabi
lity
Hur
rican
esO
cean
aci
dific
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nPo
lluta
nts
Dis
ease
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idity
Flus
hing
Urb
an s
torm
wat
er ru
noff
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ing
tech
nolo
gyIm
poun
dmen
tsFe
rtiliz
ers
use
Prec
ipita
tion
ENSO
like
eve
nts
Upw
ellin
gsIn
frast
ruct
ure
deve
lopm
ent
Sea
leve
l ris
eSe
dim
ents
Irrig
atio
nEr
osio
nLa
ndsc
ape
fragm
enta
tion
Rai
nfal
l var
iabi
lity
Atm
osph
eric
CO
2Te
mpe
ratu
reN
utrie
nts
inpu
tsFl
oods
Sewa
geFi
shin
gU
rban
izat
ion
Glo
bal w
arm
ing
Agric
ultu
reD
efor
esta
tion
Dro
ught
sD
eman
dH
uman
pop
ulat
ion
BiodiversityRecreationPrimary productionNutrient cyclingWater purificationFisheriesAesthetic valuesWild animal and plant foodsWater cyclingClimate regulationAir quality regulationPollinationKnowledge and educational valuesSpiritual and religiousFoodcropsLivestockWater regulationTimberWood fuelNatural hazard regulationSoil formationRegulation of soil erosionPest and disease regulationFreshwaterFeed, fuel & fiber crops
0 5 10 15Value
030
070
0
Color Keyand Histogram
Cou
nt
Impacts of Regime Shifts on Ecosystem Services
Arctic sea ice
Bivalves collapse
Coral transitions
Dry land degradationEncroachment
Eutrophication
Fisheries collapse
Floating plants
Forest to savannas
Greenland
HypoxiaKelps transitions
Mangroves collapse
Marine eutrophication
Marine foodwebs
Monsoon weakening
Peatlands
River channel change
Salt marshes
Sea Grass
Soil salinization
Soil structure
Termohaline circulation
Tundra to Forest
Western Antarctic IceSheet Collapse
Soil formation
Primary production
Nutrient cycling
Water cycling
Biodiversity
Freshwater
Foodcrops
Livestock
Fisheries
Wild animal and plant foods
Timber
Wood fuel
Feed, fuel & fiber crops
Air quality regulation
Climate regulation
Water purification
Water regulation
Regulation of soil erosion
Pest and disease regulation
Pollination
Natural hazard regulation
Recreation Aesthetic values
Knowledge and educational values
Spiritual and religious
• Ecosystem services frequently affected by regime shifts are: biodiversity, food production (fisheries, primary production, nutrient cycling), recreation and aesthetic values.
Gre
en h
ouse
gas
esSe
a su
rface
tem
pera
ture
Fire
freq
uenc
yLo
w ti
des
Ther
mal
ano
mal
ies
in s
umm
erIn
vasi
ve s
peci
esAq
uacu
lture
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frast
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sSu
rface
mel
t wat
erSt
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ric o
zone
Oce
an te
mpe
ratu
re (d
eep
wate
r)Ic
e su
rface
mel
ting
Gla
cier
s gr
owth
Clim
ate
varia
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y (S
AM)
Gla
cier
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rain
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er in
frast
ruct
ure
Aqui
fers
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er a
vaila
bilit
yFo
od s
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ater
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tific
atio
nTr
aged
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the
com
mon
sAc
cess
to m
arke
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bsid
ies
Dev
elop
men
t pol
icie
sIm
mig
ratio
nLo
ggin
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k)Pr
oduc
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inte
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catio
nFo
od p
rices
Labo
r ava
ilabi
lity
Hur
rican
esO
cean
aci
dific
atio
nPo
lluta
nts
Dis
ease
Turb
idity
Flus
hing
Urb
an s
torm
wat
er ru
noff
Fish
ing
tech
nolo
gyIm
poun
dmen
tsFe
rtiliz
ers
use
Prec
ipita
tion
ENSO
like
eve
nts
Upw
ellin
gsIn
frast
ruct
ure
deve
lopm
ent
Sea
leve
l ris
eSe
dim
ents
Irrig
atio
nEr
osio
nLa
ndsc
ape
fragm
enta
tion
Rai
nfal
l var
iabi
lity
Atm
osph
eric
CO
2Te
mpe
ratu
reN
utrie
nts
inpu
tsFl
oods
Sewa
geFi
shin
gU
rban
izat
ion
Glo
bal w
arm
ing
Agric
ultu
reD
efor
esta
tion
Dro
ught
sD
eman
dH
uman
pop
ulat
ion
BiodiversityRecreationPrimary productionNutrient cyclingWater purificationFisheriesAesthetic valuesWild animal and plant foodsWater cyclingClimate regulationAir quality regulationPollinationKnowledge and educational valuesSpiritual and religiousFoodcropsLivestockWater regulationTimberWood fuelNatural hazard regulationSoil formationRegulation of soil erosionPest and disease regulationFreshwaterFeed, fuel & fiber crops
0 5 10 15Value
030
070
0
Color Keyand Histogram
Cou
nt
Managing regime shift drivers
Floating plantsBivalves collapseEutrophication
Fisheries collapseCoral transitions
HypoxiaEncroachment
Salt marshesSoil salinization
Soil structureForest to savannas
Dry land degradationKelps transitions
Monsoon weakeningPeatlands
Marine foodwebsGreenland
Thermohaline circulationRiver channel change
Tundra to ForestLocalNationalInternational
Drivers by Management Type
Proportion of RS Drivers
0.0 0.2 0.4 0.6 0.8 1.0
International cooperation to manage most drivers of 75% of regime shifts.
Regulating single drivers, such as Climate change, won’t prevent regime shifts.
Regulating local drivers can build resilience to global drivers
Avoiding regime shifts requires poly-centric institutions.
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
3. Future developments
1. Theoretical stuff: • ERGMs **• Causal Networks *• Cascading effects **• Controllability of Regime Shifts.!
2. Empirical stuff: • Trade Networks• Ecosystem Services Text Mining **
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
...
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
Degree centrality
Topological features of Causal Networks
Betweenness centrality Eigenvector centrality
Marine Regime Shifts
Local centrality Global centrality
0.00 0.02 0.04 0.06 0.08 0.10 0.12
0.00
0.02
0.04
0.06
0.08
0.10
0.12
Eigenvector
Betw
eenn
ess
Agriculture
Algae
Atmospheric CO2
Biodiversity
Bivalves abundance
Canopy−forming algae
Consumption preferences
Coral abundance
Daily relative coolingDeforestationDemandDensity contrast in the water column
Disease outbreak
Dissolved oxygen
DroughtsENSO−like events frequency
Erosion
Fertilizers useFish
Fishing
FloodsFlushing
Global warming
Greenhouse gases
Habitat structural complexityHerbivores
Human populationHurricanesImpoundmentsInvasive speciesIrrigationLandscape fragmentation/conversionLeakage
Lobsters and meso−predators
Local water movementsLow tides frequency
Macroalgae abundance Macrophytes
Mid−predators
Mortality rate
Nekton
Noxious gases
Nutrients input
Ocean acidificationOrganic matter
Other competitorsPerverse incentivesPhosphorous in water
Phytoplankton
Planktivore fishPlankton and filamentous algae
PollutantsPrecipitationSedimentsSewage
Space
SST
StratificationSubsidiesSulfide releaseTechnologyThermal annomalies
Thermal low pressureTop predators
TradeTragedy of the commons
TurbidityTurf−forming algae
Unpalatability
Upwellings
Urban growthUrban storm water runoff
Urchin barrenWater column density contrast
Water mixing
Water temperature
Water vapor
Wind stress
Zooplankton
Zooxanthellae
0 5 10 15
05
10
Indegree
Out
degr
ee Agriculture Algae
Atmospheric CO2
Biodiversity
Bivalves abundance
Canopy−forming algae
Consumption preferences
Coral abundance
Daily relative cooling
DeforestationDemand
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
HerbivoresHuman population
HurricanesImpoundmentsInvasive speciesIrrigation
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 acidificationOrganic matterOther competitors
Perverse incentivesPhosphorous in water
PhytoplanktonPlanktivore fish
Plankton and filamentous algae
Pollutants
Precipitation SedimentsSewage
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 barren
Water column density contrastWater mixing
Water temperature
Water vapor
Wind stress
Zooplankton
Zooxanthellae
Terrestrial Regime Shifts
Local centrality Global centrality
0 2 4 6 8
02
46
8
Indegree
Out
degr
ee
Absorption of solar radiationAdvectionAerosol concentration
AgricultureAlbedo
Aquifers
Atmospheric CO2Atmospheric temperature
BiomassBrown cloudsCarbon storage
Cropland−Grassland area Deforestation
DemandDroughts
DustENSO−like events frequency
ErosionEvapotranspiration
Fertilizers use
Fire frequency
Floods
Forest
Global warming
Grass dominance
Grazers
Grazing
Ground water table
Human population
Illegal loggingImmigration
Infrastructure development
Irrigation
Land conversionLand−Ocean pressure gradient
Land−Ocean temperature gradient
Latent heat releaseLifting condensation levelLogging industryMoisture
Monsoon circulation
Native vegetation
Palatability
Precipitation
Productivity
Rainfall deficit
Rainfall variability
Ranching Roughness
Savanna
Sea tidesShadow_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
0.00
0.02
0.04
0.06
0.08
Eigenvector
Betw
eenn
ess
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
DustENSO−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
MoistureMonsoon circulation
Native vegetation
Palatability
Precipitation
Productivity
Rainfall deficitRainfall variability
RanchingRoughness
Savanna
Sea tides
Shadow_rooting
Soil impermeability
Soil moisture
Soil productivity
Soil quality
Soil salinitySolar radiation
Space
SSTTemperature Tree maturity
Vapor
VegetationWater availability
Water consumptionWater demand
Water infrastructure
Wind stress
Woody plants dominance
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
ARTICLEdoi:10.1038/nature10011
Controllability of complex networksYang-Yu Liu1,2, Jean-Jacques Slotine3,4 & Albert-Laszlo Barabasi1,2,5
The ultimate proof of our understanding of natural or technological systems is reflected in our ability to control them.Although control theory offersmathematical tools for steering engineered and natural systems towards a desired state, aframework to control complex self-organized systems is lacking. Here we develop analytical tools to study thecontrollability of an arbitrary complex directed network, identifying the set of driver nodes with time-dependentcontrol that can guide the system’s entire dynamics. We apply these tools to several real networks, finding that thenumber of driver nodes is determined mainly by the network’s degree distribution. We show that sparseinhomogeneous networks, which emerge in many real complex systems, are the most difficult to control, but thatdense and homogeneous networks can be controlled using a few driver nodes. Counterintuitively, we find that inboth model and real systems the driver nodes tend to avoid the high-degree nodes.
According to control theory, a dynamical system is controllable if, with asuitable choice of inputs, it can be driven from any initial state to anydesired final state within finite time1–3. This definition agrees with ourintuitive notion of control, capturing an ability to guide a system’sbehaviour towards adesired state through the appropriatemanipulationof a few input variables, like a driver prompting a car to move with thedesired speed and in the desired direction by manipulating the pedalsand the steering wheel. Although control theory is a mathematicallyhighly developed branch of engineering with applications to electriccircuits, 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 haveresisted advances. The difficulty is rooted in the fact that two independ-ent factors contribute to controllability, each with its own layer ofunknown: (1) the system’s architecture, represented by the networkencapsulating which components interact with each other; and (2) thedynamical rules that capture the time-dependent interactions betweenthe components. Thus, progress has beenpossible only in systemswhereboth 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 topologicalcharacteristics of complex networks12–16 have shed light on factor (1),prompting us to wonder whether some networks are easier to controlthan others and how network topology affects a system’s controllability.Despite some pioneering conceptual work17–23 (SupplementaryInformation, section II), we continue to lack general answers to thesequestions for large weighted and directed networks, which most com-monly emerge in complex systems.
Network controllabilityMost real systems are driven by nonlinear processes, but the controll-ability of nonlinear systems is in many aspects structurally similar tothat of linear systems3, prompting us to start our study using thecanonical linear, time-invariant dynamics
dx(t)dt
~Ax(t)zBu(t) ð1Þ
where the vector x(t)5 (x1(t), …, xN(t))T captures the state of a
system ofN nodes at time t. For example, xi(t) can denote the amount
of traffic that passes through a node i in a communication network24
or transcription factor concentration in a gene regulatory network25.The N3N matrix A describes the system’s wiring diagram and theinteraction strength between the components, for example the trafficon individual communication links or the strength of a regulatoryinteraction. Finally, B is the N3M input matrix (M#N) that iden-tifies the nodes controlled by an outside controller. The system iscontrolled using the time-dependent input vector u(t)5 (u1(t), …,uM(t))
T imposed by the controller (Fig. 1a), where in general the samesignal ui(t) can drivemultiple nodes. If wewish to control a system, wefirst need to identify the set of nodes that, if driven by different signals,can offer full control over the network. We will call these ‘drivernodes’. We are particularly interested in identifying the minimumnumber of driver nodes, denoted by ND, whose control is sufficientto 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 finitetime, which is possible if and only if theN3NM controllability matrix
C~(B,AB,A2B, . . . ,AN{1B) ð2Þ
has full rank, that is
rank(C)~N ð3Þ
This represents the mathematical condition for controllability, and iscalled Kalman’s controllability rank condition1,2 (Fig. 1a). In practicalterms, controllability canbe alsoposed as follows. Identify theminimumnumber of driver nodes such that equation (3) is satisfied. For example,equation (3) predicts that controlling node x1 in Fig. 1b with the inputsignalu1 offers full controlover the system, as the states of nodesx1,x2,x3and 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 thedifference a31x2(t)2 a21x3(t) (where aij are the elements of A) is notuniquely determined by u1(t) (see Fig. 1f and SupplementaryInformation section III.A). To gain full control, wemust simultaneouslycontrol node x1 and any two nodes among {x2, x3, x4} (see Fig. 1h, i for amore complex example).To apply equations (2) and (3) to an arbitrary network, we need to
know the weight of each link (that is, the aij), which for most real
1Center for Complex Network Research and Departments of Physics, Computer Science and Biology, Northeastern University, Boston, Massachusetts 02115, USA. 2Center for Cancer Systems Biology,Dana-Farber Cancer Institute, Boston, Massachusetts 02115, USA. 3Nonlinear Systems Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. 4Department ofMechanical EngineeringandDepartmentofBrain andCognitiveSciences,Massachusetts Institute of Technology, Cambridge,Massachusetts02139,USA. 5DepartmentofMedicine,BrighamandWomen’sHospital, Harvard Medical School, Boston, Massachusetts 02115, USA.
1 2 M A Y 2 0 1 1 | V O L 4 7 3 | N A T U R E | 1 6 7
Macmillan Publishers Limited. All rights reserved©2011
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.
ARTICLEdoi:10.1038/nature10011
Controllability of complex networksYang-Yu Liu1,2, Jean-Jacques Slotine3,4 & Albert-Laszlo Barabasi1,2,5
The ultimate proof of our understanding of natural or technological systems is reflected in our ability to control them.Although control theory offersmathematical tools for steering engineered and natural systems towards a desired state, aframework to control complex self-organized systems is lacking. Here we develop analytical tools to study thecontrollability of an arbitrary complex directed network, identifying the set of driver nodes with time-dependentcontrol that can guide the system’s entire dynamics. We apply these tools to several real networks, finding that thenumber of driver nodes is determined mainly by the network’s degree distribution. We show that sparseinhomogeneous networks, which emerge in many real complex systems, are the most difficult to control, but thatdense and homogeneous networks can be controlled using a few driver nodes. Counterintuitively, we find that inboth model and real systems the driver nodes tend to avoid the high-degree nodes.
According to control theory, a dynamical system is controllable if, with asuitable choice of inputs, it can be driven from any initial state to anydesired final state within finite time1–3. This definition agrees with ourintuitive notion of control, capturing an ability to guide a system’sbehaviour towards adesired state through the appropriatemanipulationof a few input variables, like a driver prompting a car to move with thedesired speed and in the desired direction by manipulating the pedalsand the steering wheel. Although control theory is a mathematicallyhighly developed branch of engineering with applications to electriccircuits, 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 haveresisted advances. The difficulty is rooted in the fact that two independ-ent factors contribute to controllability, each with its own layer ofunknown: (1) the system’s architecture, represented by the networkencapsulating which components interact with each other; and (2) thedynamical rules that capture the time-dependent interactions betweenthe components. Thus, progress has beenpossible only in systemswhereboth 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 topologicalcharacteristics of complex networks12–16 have shed light on factor (1),prompting us to wonder whether some networks are easier to controlthan others and how network topology affects a system’s controllability.Despite some pioneering conceptual work17–23 (SupplementaryInformation, section II), we continue to lack general answers to thesequestions for large weighted and directed networks, which most com-monly emerge in complex systems.
Network controllabilityMost real systems are driven by nonlinear processes, but the controll-ability of nonlinear systems is in many aspects structurally similar tothat of linear systems3, prompting us to start our study using thecanonical linear, time-invariant dynamics
dx(t)dt
~Ax(t)zBu(t) ð1Þ
where the vector x(t)5 (x1(t), …, xN(t))T captures the state of a
system ofN nodes at time t. For example, xi(t) can denote the amount
of traffic that passes through a node i in a communication network24
or transcription factor concentration in a gene regulatory network25.The N3N matrix A describes the system’s wiring diagram and theinteraction strength between the components, for example the trafficon individual communication links or the strength of a regulatoryinteraction. Finally, B is the N3M input matrix (M#N) that iden-tifies the nodes controlled by an outside controller. The system iscontrolled using the time-dependent input vector u(t)5 (u1(t), …,uM(t))
T imposed by the controller (Fig. 1a), where in general the samesignal ui(t) can drivemultiple nodes. If wewish to control a system, wefirst need to identify the set of nodes that, if driven by different signals,can offer full control over the network. We will call these ‘drivernodes’. We are particularly interested in identifying the minimumnumber of driver nodes, denoted by ND, whose control is sufficientto 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 finitetime, which is possible if and only if theN3NM controllability matrix
C~(B,AB,A2B, . . . ,AN{1B) ð2Þ
has full rank, that is
rank(C)~N ð3Þ
This represents the mathematical condition for controllability, and iscalled Kalman’s controllability rank condition1,2 (Fig. 1a). In practicalterms, controllability canbe alsoposed as follows. Identify theminimumnumber of driver nodes such that equation (3) is satisfied. For example,equation (3) predicts that controlling node x1 in Fig. 1b with the inputsignalu1 offers full controlover the system, as the states of nodesx1,x2,x3and 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 thedifference a31x2(t)2 a21x3(t) (where aij are the elements of A) is notuniquely determined by u1(t) (see Fig. 1f and SupplementaryInformation section III.A). To gain full control, wemust simultaneouslycontrol node x1 and any two nodes among {x2, x3, x4} (see Fig. 1h, i for amore complex example).To apply equations (2) and (3) to an arbitrary network, we need to
know the weight of each link (that is, the aij), which for most real
1Center for Complex Network Research and Departments of Physics, Computer Science and Biology, Northeastern University, Boston, Massachusetts 02115, USA. 2Center for Cancer Systems Biology,Dana-Farber Cancer Institute, Boston, Massachusetts 02115, USA. 3Nonlinear Systems Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. 4Department ofMechanical EngineeringandDepartmentofBrain andCognitiveSciences,Massachusetts Institute of Technology, Cambridge,Massachusetts02139,USA. 5DepartmentofMedicine,BrighamandWomen’sHospital, Harvard Medical School, Boston, Massachusetts 02115, USA.
1 2 M A Y 2 0 1 1 | V O L 4 7 3 | N A T U R E | 1 6 7
Macmillan Publishers Limited. All rights reserved©2011
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.
Trade Networks
• Test empirically cascading effects by using trade networks
• Which countries are driving the resource collapse of others
• Where trade matters?
1. Fisheries collapse
2. Land transitions
Using language to detect potential change in ecosystem services in the light of ecological surprises
Juan Carlos Rocha & Robin Wikström
Ecosystem services are the benefits humans receive from nature (MEA 2005)
Foley et al. 2005. Science
Ecosystem services are the benefits humans receive from nature (MEA 2005)
Foley et al. 2005. Science
LDA (illustrative example by Blei)
Model selection & number of topics
Entropy
VEM1
VEM2
VEM3
VEM4
VEM5
0.2 0.4 0.6 0.8
Perplexity
VEM1
VEM2
VEM3
VEM4
VEM5
1600 1800 2000 2200
logLik
VEM1
VEM2
VEM3
VEM4
VEM5
-3050000 -3000000 -2950000
alpha
VEM1
VEM2
VEM3
VEM4
VEM5
0.010 0.015 0.020
• We test Variational Estimation Methods (VEM), correlated topic models (CTM) & Gibbs sampling.
• We tested 5 models with different topic numbers (10:100)
• VEM algorithm with 80 topics fit the best the MEA training dataset
29 79 27 55 46 15 57 12 9 53 62 47 34 66 69 59 1 73 5 60 4 11 19 44 31 14 68 50 67 8 37 22 65 24 76 56 26 39 18 23 16 38 2 78 74 30 40 3 75 61 43 20 17 45 72 64 48 49 25 21 36 70 52 28 58 41 80 32 35 51 77 6 10 7 33 54 13 63 71 42
Chapter 14 Human Health Ecosystem Regulation of Infectious Diseases.pdf.txtChapter 10 New Products and Industries from Biodiversity.pdf.txtChapter 28 Synthesis Condition and Trends in Systems and Services Trade-offs for Human Well-being and Implications for the Future.pdf.txtChapter 15 Waste Processing and Detoxification.pdf.txtChapter 22 Dryland Systems.pdf.txtChapter 16 Regulation of Natural Hazards Floods and Fires.pdf.txtNelson-2005-Chapter 3 Drivers of ecosystem change summary chapter.pdf.txtChapter 25 Polar Systems.pdf.txtChapter 8 Food.pdf.txtChapter 12 Nutrient Cycling.pdf.txtChapter 17 Cultural and Amenity Services.pdf.txtChapter 6 Vulnerable Peoples and Places.pdf.txtChapter 5 Ecosystem Conditions and Human Well-being.pdf.txtChapter 1 MA Conceptual Framework.pdf.txtChapter 21 Forest and Woodland Systems.pdf.txtChapter 7 Fresh Water.pdf.txtChapter 9 Timber Fuel and Fiber.pdf.txtChapter 4 Biodiversity.pdf.txtChapter 26 Cultivated Systems.pdf.txtChapter 18 Marine Fisheries Systems.pdf.txtChapter 24 Mountain Systems.pdf.txtChapter 2 Analytical Approaches for Assessing Ecosystem Condition and Human Well-being.pdf.txtChapter 23 Island Systems.pdf.txtChapter 20 Inland Water Systems-2.pdf.txtChapter 11 Biodiversity Regulation of Ecosystem Services.pdf.txtChapter 13 Climate and Air Quality.pdf.txtChapter 19 Coastal Systems.pdf.txtChapter 27 Urban Systems.pdf.txt
0.2 0.4 0.6 0.8Value
01500
Color Keyand Histogram
Count
Topics = 80Millenium Ecosystem AssessmentTopics detection
Topics = 80Millenium Ecosystem AssessmentTopics detection
Topics matchingEcosystem Services Topics WordsEcosystem Processes
Soil formationPrimary productionNutrient cycling 59, 69 nutrient, ecosystem, soil, global, ocean, cyclingWater cyclingBiodiversity 39, 60, 26, 5 species, plant, richness, biodiversity, services
Provisioning servicesFreshwater 62, 68 water, world, human, supply, freshwater, riverFood crops 12, 66, 3 food, production, countries, growth, healthLivestockFisheries 44, 19 marine, fisheries, fish, species, coastal, systemWild animals and plants productsTimber 34, 43 forest, countries, world, global, tropical, faoWood fuel 47 production, forest, wood, products, timber, faoFeed, fuel and fiber crops 47 production, forest, wood, products, timber, faoHydropower
Regulating servicesAir quality regulation 2, 38 16 carbon, atmospheric, ecosystem, land, airClimate regulation 2, 38, 16 global, climate, emissions, change, atmosphericWater purification 55 waste, water, environment, human, nitrogenRegulation of soil erosion 46 dryland, land, soil, degradation, waterPest and disease 29 disease, human, health, infectious, malariaPollinationNatural hazards 15 fire, events, floods, natural, regulation, impact
Cultural services 11, 4 cultural, human, ecosystems, landscapes, Recreation heritageAesthetic valuesKnowledge and educational valuesSpiritual and religious
Topics = 80Corpus = 381 papersTopics detection
Topics = 80Corpus = 381 papersTopics detection
1939381652629626966153443473604121124459685546
0.1 0.4Value
08000
Color Keyand Histogram
Count
Topics = 80Corpus = 381 papersTopics detection
Soi
l for
mat
ion
Prim
ary
prod
uctio
nN
utrie
nt c
yclin
gW
ater
cyc
ling
Biodiversity
Freshwater
Foodcrops
Livestock
Fisheries
Wild
ani
mal
and
pla
nt fo
ods
Timber
Woo
d fu
elFe
ed, f
uel &
fibe
r cro
psHydropower
Air
qual
ity re
gula
tion
Clim
ate
regu
latio
nW
ater
pur
ifica
tion
Reg
ulat
ion
of s
oil e
rosi
onP
est a
nd d
isea
se re
gula
tion
Pollination
Nat
ural
haz
ard
regu
latio
nRecreation
Aes
thet
ic v
alue
sK
now
ledg
e an
d ed
ucat
iona
l val
ues
Spi
ritua
l and
relig
ious
Tundra to ForestTermohaline circulationSoil structureSoil salinizationSalt marshesRiver channel changePeatlandsMonsoon weakeningMarine foodwebsKelps transitionsHypoxiaGreenlandForest to savannasFloating plantsFisheries collapseEutrophicationEncroachmentDry land degradationCoral transitionsBivalves collapse
0 0.4 1Value
180
Color Keyand Histogram
Count
Nut
rient
cyc
ling
Biodiversity
Freshwater
Food
cro
ps
Fisheries
Timber
Woodfuel
Feed
, fue
l & ti
mbe
r cro
ps
Air
qual
ity re
gula
tion
Clim
ate
regu
latio
n
Wat
er p
urifi
catio
n
Reg
ulat
ion
of s
oil e
rosi
on
Pes
t and
dis
ease
Nat
ural
haz
ards
Cul
tura
l ser
vice
s
Other cases (132)Theory (97)Tundra to forest (2)Thermohaline circulation (1)Soil structure (0)Soil salinization (1)Salt marshes (0)River channel change (5)Peatlands (3)Monsoon weakening (5)Marine foodwebs (40)Kelps transitions (6)Hypoxia (4)Greenland (1)Forest to savannas (29)Floating plants (1)Fisheries collapse (52)Eutrophication (13)Encroachment (7)Dry land degradation (18)Coral transitions (27)Bivalves collapse (2)
0 4 8Value
0250
Color Keyand Histogram
Count
Topics = 80Corpus = 381 papersTopics detection
Soi
l for
mat
ion
Prim
ary
prod
uctio
nN
utrie
nt c
yclin
gW
ater
cyc
ling
Biodiversity
Freshwater
Foodcrops
Livestock
Fisheries
Wild
ani
mal
and
pla
nt fo
ods
Timber
Woo
d fu
elFe
ed, f
uel &
fibe
r cro
psHydropower
Air
qual
ity re
gula
tion
Clim
ate
regu
latio
nW
ater
pur
ifica
tion
Reg
ulat
ion
of s
oil e
rosi
onP
est a
nd d
isea
se re
gula
tion
Pollination
Nat
ural
haz
ard
regu
latio
nRecreation
Aes
thet
ic v
alue
sK
now
ledg
e an
d ed
ucat
iona
l val
ues
Spi
ritua
l and
relig
ious
Tundra to ForestTermohaline circulationSoil structureSoil salinizationSalt marshesRiver channel changePeatlandsMonsoon weakeningMarine foodwebsKelps transitionsHypoxiaGreenlandForest to savannasFloating plantsFisheries collapseEutrophicationEncroachmentDry land degradationCoral transitionsBivalves collapse
0 0.4 1Value
180
Color Keyand Histogram
Count
Biodiversity
Fisheries
Food
cro
ps
Air
qual
ity re
gula
tion
Clim
ate
regu
latio
n
Timber
Woodfuel
Feed
, fue
l & ti
mbe
r cro
ps
Nat
ural
haz
ards
Wat
er p
urifi
catio
n
Reg
ulat
ion
of s
oil e
rosi
on
Pes
t and
dis
ease
Freshwater
Cul
tura
l ser
vice
sN
utrie
nt c
yclin
g
Forest to savannas (29)Hypoxia (4)Kelps transitions (6)Encroachment (7)River channel change (5)Salt marshes (0)Soil structure (0)Soil salinization (1)Floating plants (1)Bivalves collapse (2)Greenland (1)Thermohaline circulation (1)Tundra to forest (2)Peatlands (3)Coral transitions (27)Monsoon weakening (5)Eutrophication (13)Dry land degradation (18)Marine foodwebs (40)Fisheries collapse (52)Theory (97)Other cases (132)
0 4 8Value
0250
Color Keyand Histogram
Count
Thanks! Garry Peterson, Oonsie Biggs & Örjan Bodin 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/