licentiate: regime shifts in the anthropocene

Regime Shifts in the AnthropoceneJuan-Carlos Rocha

Sunday, September 1, 13

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 ShiftsRegime 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)



external forcing reverses, the response variable will flip back to the original equilibrium, but at a di!erentlevel. 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 di!erent types of regime shifts (smooth,abrupt, and discontinuous) can be generated from the same general models with di!erent parameters. Thus,the three types are, apparently, special cases of the same general models, corresponding to di!erent 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)



Science challenge: understand multi-causal phenomena where experimentation is rarely an option and time for action a constraint


1. A comparative framework: The database2. Global drivers of Regime Shifts3. 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 foodwebsMonsoon weakeningTermohaline circulation

EncroachmentFisheries collapse

Dryland degradationForest to savannaSteppe to tundra

Tundra to forest

Floating plantsGreenlandArctic sea ice

Bivalves collapseCoral transitionsEutrophicationHypoxiaKelps transitionsPeatlandsRiver channel changeSalt marshesSoil salinization



Ecosystem services

Drivers ...

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

Ecosystem Services

SupportingProvisioningRegulatingCulturalHuman well being



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


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


Challenges

We developed a framework to compare regime shifts

Issues of consistency:

DriversCLD

System boundaries

Uncertainty assessment: strength of feedbacks and the role of social dynamics

Methods to identify leverage points for management


3. 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: [email protected]

. 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: [email protected] or [email protected].

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

APP

LIED

PHYS

ICA

LSC

IEN

CES

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


1 3 5 7 11 16

Degree distribution

Degree

05

1015

20

●

●

●

●

●●

●●●

●

●●●●

●

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●

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●

●

●

●●●●●●

● ●●●

●

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● ●●●●

● ●● ●●● ●●●

●

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●

●

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●

●

●

●

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●

●

●

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●

5 10 15

0100

300

500

Degree

Betweenness

Co−occurrence Index DN

s−squaredDensity

1.4 1.6 1.8 2.0

01

23

45

6Average Degree DN

Degree

Density

20 22 24 26

0.0

0.2

0.4

0.6

Co−occurrence Index RN

s−squared

Density

8 9 10 11 12 13

0.0

0.2

0.4

0.6

0.8

Average Degree RN

Degree

Density

12 14 16 18

0.0

0.2

0.4

0.6


AgricultureAtmospheric CO2

DeforestationDemand

Droughts

Fishing

Global warming

Human population

Nutrients inputsUrbanization

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.


Encroachment

Mon

soon

wea

keni

ngS

oil s

alin

izat

ion

Dry

land

deg

rada

tion

Fore

st to

sav

anna

sFi

sher

ies

colla

pse

Mar

ine

food

web

sFl

oatin

g pl

ants

Peatlands

Sal

t mar

shes

Soi

l stru

ctur

eR

iver

cha

nnel

cha

nge

Tund

ra to

For

est

Greenland

Ther

moh

alin

e ci

rcul

atio

nC

oral

tran

sitio

nsB

ival

ves

colla

pse

Kel

ps tr

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 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.


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?


What does it mean for management?

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

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.


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


4. Future developments


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 ProgressCausal Networks: Cascading effects and regime shifts controllability


Degree centrality

Topological features of Causal Networks

Betweenness centrality Eigenvector centrality


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) !1"

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) !2"

has full rank, that is

rank(C)~N !3"

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.


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: [email protected] and papers on regime shifts: @juanrochaResearch blog: http://criticaltransitions.wordpress.com/


mailto:[email protected]

mailto:[email protected]

http://www.criticaltransitions.wordpress.com






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


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?


Data quality(time series)

Know

ledge

of t

he

syst

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Statistics: Autocorrelation and

variance

Bayesian networks - models

Models & Jacobians

Web crawlers &local knowledge

Research agenda on Regime Shifts

High

High

HighHigh

Low

Low


Data quality(time series)

Know

ledge

of t

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Statistics: Autocorrelation and

variance

Bayesian networks - models

Models & Jacobians

Web crawlers &local knowledge

Research agenda on Regime Shifts

?

High

High

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Tund

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For

est

Gre

enla

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Term

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circ

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ion

Salt

mar

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Mar

ine

food

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Fish

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Soil

stru

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Rive

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Floa

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plan

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Peat

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Cor

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Kelp

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Biva

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phic

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Hyp

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Fore

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Dry

land

deg

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Encr

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Mon

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Soil

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Soil salinizationMonsoon weakeningEncroachmentDry land degradationForest to savannasHypoxiaEutrophicationBivalves collapseKelps transitionsCoral transitionsPeatlandsFloating plantsRiver channel changeSoil structureFisheries collapseMarine foodwebsSalt marshesTermohaline circulationGreenlandTundra to Forest

Regime shifts

0 0.4 0.8Value

010

0Color Key

and HistogramC

ount

Average Degree in simulated Regime Shifts Networks

Mean Degree

Den

sity

12 13 14 15 16 17 18 19

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Regime Shifts Network Co−occurrence Index

s−squared

Density

8 9 10 11 12 13

0.0

0.2

0.4

0.6

0.8

Bivalvescollapse

Coral transitions

Dry land degradation

Encroachment

EutrophicationFisheries collapse

Forest to Savannas

Hypoxia

Kelps transitions

Marine foodwebs

Floating plantsRiver channel

change

Salt marshes

Soilsalinization

Soilstructure

Tundra toForest

Monsoonweakening

Peatlands

Greenland

Thermohalinecirculation

The co-occurrence of regime shifts is not random. Aquatic systems tend to share more drivers suggesting that their underlying processes are also similar


Turb

idity

Dis

ease

Pollu

tant

sSe

dim

ents

Ther

mal

ano

mal

ies

in s

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Sea surface temperatureDrainageDevelopment policiesGreen house gasesTemperatureSea level riseInvasive speciesFood supplyFishing technologyPrecipitationAtmospheric CO2Global warmingIrrigationFire frequencyDroughtsLoggingImmigrationInfrastructure developmentSubsidiesAccess to marketsTragedy of the commonsENSO like eventsUpwellingsWater availabilityAquifersWater infrastructureRanching (livestock)Labor availabilityFood pricesProduction intensificationSewageFertilizers useFloodsErosionAgricultureHuman populationDeforestationDemandFishingNutrients inputsUrbanizationUrban storm water runoffFlushingLandscape fragmentationRainfall variabilityImpoundmentsWater stratificationLow tidesHurricanesOcean acidificationThermal anomalies in summerSedimentsPollutantsDiseaseTurbidity

Drivers

0 0.4 0.8Value

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Color Keyand Histogram

Cou

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Average Degree in simulated Drivers Networks

Mean Degree

Den

sity

20 21 22 23 24 25 26

0.0

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Drivers Network Co−occurrence Index

s−squared

Density

1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1

01

23

45

6

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

DroughtsENSO like events

Erosion

Fertilizers use

Fishing

Floods

Global warming Human population

IrrigationNutrients inputs

Precipitation

Sewage

Upwellings

UrbanizationMarine General Terrestrial


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
