The document discusses two networks constructed from genetic disorder and disease gene data: the human disease network (HDN) and the disease gene network (DGN). The HDN connects disorders that share disease genes, revealing many connections between disorders. The DGN connects disease genes associated with the same disorders. Most disorders relate to a few genes, while a few disorders like cancers relate to dozens of genes. The networks provide an integrated framework to explore relationships between genetic disorders and disease genes.

1. The Network of Driving Forces of
Global Environmental Change
Juan-Carlos Rocha, Oonsie Biggs & Garry Peterson
Stockholm Resilience Centre
Stockholm University

2. The challenge
The Anthropocene: an era where
human impact on Earth is strong
enough to change global scale
dynamics.
Frequency and intensity of regime
shifts are likely to increase.
Society and economy could be
potentially affected through impacts
on ecosystem services.
Vulnerable areas?
Possible synergistic effects?
Cross-scale interactions?

3. Regime shifts:
Large, abrupt,
persistent change in
the structure and
function of a system.
Policy relevant:
Substantial change in
ecosystem services -
the goods people
receive from nature

4. Research agenda on Regime Shifts
High Bayesian networks - Web crawlers &
models local knowledge
Knowledge of the
Models & Jacobians
system
Statistics:
Autocorrelation and
variance
Low
Low Data quality High
(time series)

5. Research agenda on Regime Shifts
High Bayesian networks - Web crawlers &
models local knowledge
Knowledge of the
Models & Jacobians
system
Statistics:
Autocorrelation and
variance
Low
Low Data quality High
(time series)

6. Research agenda on Regime Shifts
High Bayesian networks - Web crawlers &
models local knowledge
Knowledge of the
Models & Jacobians
system
? Statistics:
Autocorrelation and
variance
Low
Low Data quality High
(time series)

7. Virtruvian Man, Leonardo Da Vinci

8. The human disease network Network Properties of Complex Human Disease Genes
Kwang-Il Goh*†‡§, Michael E. Cusick†‡¶, David Valleʈ, Barton Childsʈ, Marc Vidal†‡¶**, ´ ´
and Albert-Laszlo ´
Barabasi*†‡**
*Center for Complex Network Research and Department of Physics, University of Notre Dame, Notre Dame, IN 46556; †Center for Cancer Systems Biology
Identified through Genome-Wide Association Studies
(CCSB) and ¶Department of Cancer Biology, Dana–Farber Cancer Institute, 44 Binney Street, Boston, MA 02115; ‡Department of Genetics, Harvard Medical
School, 77 Avenue Louis Pasteur, Boston, MA 02115; §Department of Physics, Korea University, Seoul 136-713, Korea; and ʈDepartment of Pediatrics and the Fredrik Barrenas1.*, Sreenivas Chavali1., Petter Holme2,3, Reza Mobini1, Mikael Benson1
McKusick–Nathans Institute of Genetic Medicine, Johns Hopkins University School of Medicine, Baltimore, MD 21205
˚ ˚
1 The Unit for Clinical Systems Biology, University of Gothenburg, Gothenburg, Sweden, 2 Department of Physics, Umea University, Umea, Sweden, 3 Department of
Edited by H. Eugene Stanley, Boston University, Boston, MA, and approved April 3, 2007 (received for review February 14, 2007) Energy Science, Sungkyunkwan University, Suwon, Korea
A network of disorders and disease genes linked by known disorder– known genetic disorders, whereas the other set corresponds to all
gene associations offers a platform to explore in a single graph- known disease genes in the human genome (Fig. 1). A disorder and
theoretic framework all known phenotype and disease gene associ- a gene are then connected by a link if mutations in that gene are Abstract
ations, indicating the common genetic origin of many diseases. Genes implicated in that disorder. The list of disorders, disease genes, and
DISEASOME
associated with similar disorders show both higher likelihood of associations between them was obtained from the Online Mende- Background: Previous studies of network properties of human disease genes have mainly focused on monogenic diseases
physical interactions between their products and higher expression lian Inheritance in Man (OMIM; ref. 18), a compendium of human or cancers and have suffered from discovery bias. Here we investigated the network properties of complex disease genes
profiling similarity for their transcripts, supporting the existence of disease genes and phenotypes. As of December 2005, this list identified by genome-wide association studies (GWAs), thereby eliminating discovery bias.
distinct disease-specific functional modules. Wedisease phenome find that essential disease genome
contained 1,284 disorders and 1,777 disease genes. OMIM initially
Human Disease Network
human genes are likely to encode hub proteins and are expressed Disease Gene Network Principal findings: We derived a network of complex diseases (n = 54) and complex disease genes (n = 349) to explore the
Ataxia-telangiectasia
focused on AR monogenic disorders but in recent years has expanded
(HDN)
widely in most tissues. This suggests that disease genes hypospadias Perineal also would
Androgen insensitivity
(DGN)
to include complex traits and the associated genetic mutations that
ATM
shared genetic architecture of complex diseases. We evaluated the centrality measures of complex disease genes in
play a central role in the human interactome. In contrast, we find that confer susceptibility to these common disorders (18). Although this comparison with essential and monogenic disease genes in the human interactome. The complex disease network showed
T-cell lymphoblastic leukemia
the vast majority of disease genes are nonessential and show no
Charcot-Marie-Tooth disease
Papillary serous carcinoma
BRCA1
history introduces some biases, LMNA the disease gene record is far
and HEXB that diseases belonging to the same disease class do not always share common disease genes. A possible explanation could
tendency to encode hubLipodystrophy and their expression pattern indi-
proteins, BRCA2
from complete, OMIM represents the most complete and up-to-
ALS2
be that the variants with higher minor allele frequency and larger effect size identified using GWAs constitute disjoint parts
APPLIED PHYSICAL
Prostate cancer
cates that ataxia/paraplegia localized paraplegia syndrome
Spastic
they are Silver spastic in the functional periphery of the CDH1 BSCL2
date repository of all known VAPBdisease genes and the disorders they of the allelic spectra of similar complex diseases. The complex disease gene network showed high modularity with the size
SCIENCES
network. A selection-basedSandhoff disease model explains the observed difference
Ovarian cancer GARS
Amyotrophic lateral sclerosis confer. We manually classified each disorder into one of 22 disorder
GARS
of the largest component being smaller than expected from a randomized null-model. This is consistent with limited sharing
between essential and disease genes and also suggests that diseases
Lymphoma classes based on the physiological system affected [see supporting
HEXB
of genes between diseases. Complex disease genes are less central than the essential and monogenic disease genes in the
caused by somatic mutations should not be peripheral, a prediction
Spinal muscular atrophy
information (SI) Text, SI Fig. 5, and SI Table 1 for details].
KRAS AR
human interactome. Genes associated with the same disease, compared to genes associated with different diseases, more
we confirm for cancer genes. insensitivity
Androgen
Prostate cancer
Breast cancer Starting LMNA the diseasome bipartite graph we generated two
from ATM often tend to share a protein-protein interaction and a Gene Ontology Biological Process.
Perineal hypospadias
biological networks ͉ complex networks ͉ human genetics Pancreatic cancer
͉ systems
biologically relevant network projections (Fig. 1). In the ‘‘human
MSH2 BRIP1
BRCA2
biology ͉ diseasome Lymphoma
disease network’’ (HDN) nodes represent disorders, and two
PIK3CA BRCA1 Conclusions: This indicates that network neighbors of known disease genes form an important class of candidates for
Wilms tumor
Breast cancer
Wilms tumor
disorders are connected to each otherKRAS
TP53 RAD54L
if they share at least one gene identifying novel genes for the same disease.
Ovarian cancer
in which mutations are associated with both TP53 disorders (Figs. 1 and
D
Spinal muscular atrophy
ecades-long efforts to map human disease loci,Sandhoff disease
Pancreatic cancer at first genet- MAD1L1
2a). In the ‘‘disease gene network’’MAD1L1
(DGN) nodes represent disease
ically and later physically (1), followed by recent positional
Fanconi anemia
Papillary serous carcinoma
Lipodystrophy two
CHEK2
genes, andRAD54L genes are connected if they are associated with the Citation: Barrenas F, Chavali S, Holme P, Mobini R, Benson M (2009) Network Properties of Complex Human Disease Genes Identified through Genome-Wide
cloning of many disease T-cell lymphoblastic and genome-wide association
genes (2) leukemia Charcot-Marie-Tooth disease
PIK3CA
same disorder (Figs. 1 and 2b). Next, we discuss the potential of
VAPB Association Studies. PLoS ONE 4(11): e8090. doi:10.1371/journal.pone.0008090
studies (3), have generated an impressive list of disorder–gene
Ataxia-telangiectasia
these networks to help us understand and MSH2
CHEK2 CDH1
represent in a single Editor: Thomas Mailund, Aarhus University, Denmark
association pairs (4, 5). In addition, recent efforts to map the Amyotrophic lateral sclerosis
frameworkBSCL2 known disease gene and phenotype associations.
all Received September 15, 2009; Accepted November 3, 2009; Published November 30, 2009
protein–protein interactions in humans (6, 7), together paraplegia syndrome
Silver spastic
with efforts
ALS2
to curate an extensive map of human metabolism (8) and regulatory Spastic ataxia/paraplegia Copyright: ß 2009 Barrenas et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
Properties BRIP1the HDN. If each human disorder tends to have a
of
networks offer increasingly detailed maps of theFanconi anemia relationships unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
between different disease genes. Most of the successful studies distinct and unique genetic origin, then the HDN would be dis-
connected into many single nodes corresponding to specific disor- Funding: This work was supported by the Swedish Research Council, The European Commission, The Swedish Foundation for Strategic Research (PH), and the
building on these new approaches have focused, however, on a WCU (World Class University) program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology R31-R31-
single disease, using network-based tools to gain a better under- ders or grouped into small clusters of a few closely related disorders. 2008-000-10029-0 (PH). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
In contrast, the obtained HDN displays many connections between
Fig. 1. Construction of the diseasome bipartite network. (Center) A small subset of OMIM-based disorder– disease gene associations (18), where circles and rectangles
standing of the relationship between the genes implicated in a
correspond to disorders and disease genes, respectively. A link is placed between a disorder and aindividual disorders and disorder classes (Fig. 2a). Of 1,284
disease gene if mutations in that gene lead to the specific disorder. Competing Interests: The authors have declared that no competing interests exist.
selected circle is proportional to the number of genes participating in the corresponding both and the color corresponds to the disorder class to which the disease
The size of adisorder (9). disorder,
belongs. (Left) The HDN a conceptually different approach, which two disorders are connected there
Here we take projection of the diseasome bipartite graph, in exploring disorders, 867ifhave is a gene that is implicatedother disorders,ofand 516
at least one link to in both. The width * E-mail: fredrik.barrenas@gu.se
a link is proportional to the number of genes and are implicated in both diseases. For example, three genes area giant component, cancer and prostate cancer, genetic
whether human genetic disorders that the corresponding disease disorders form implicated in both breast suggesting that the . These authors contributed equally to this work.
resulting in a link ofrelated to each other at a higher level of cellular andtwo genes are connected if they are involved in the same disorder.shared with other
genes might be weight three between them. (Right) The DGN projection where origins of most diseases, to some extent, are The width of
a link is proportional to the number of diseases with which the two genes are commonly diseases. A full number of genes associated with Fig. 13.
associated. The diseasome bipartite map is provided as SI a disorder, s, has a
organismal organization. Support for the validity of this approach
is provided by examples of genetic disorders that arise from broad distribution (see SI Fig. 6a), indicating that most disorders
relate to a few disease genes, whereas a handful of phenotypes, such Introduction human interactome. A more recent report that evaluated the
a few otherin more than a singlefew phenotypes such as colon Formentary, gene-centered view of the diseasome. Given that the links
mutations disorders, whereas a gene (locus heterogeneity). network properties of disease genes showed that genes with
cancer (linked to k ϭ 50 other disorders) orby mutations (k ϭ 30) atsignify deafnessphenotypicleukemia (s ϭ 37), and colon cancer (s ϭ 34),
example, Zellweger syndrome is caused breast cancer in any of as related (s ϭ 41), association between two genes, they Systems Biology based approaches of studying human genetic intermediate degrees (numbers of neighbors) were more likely to
least 11 hubs that associated with peroxisome biogenesis (10).represent a to dozens of genes (Fig. 2a). The degree (k) distribution of
represent genes, all are connected to a large number of distinct relate measure of their phenotypic relatedness, which could be
diseases have brought in a shift in the paradigm of elucidating harbor germ-line disease mutations [12]. However, interpretation
disorders. The prominence of cancer among the most connected theusedHDN (SI Fig. 6b) in conjunction with protein–proteinlinked to only
Similarly, there are many examples of different mutations in in future studies, indicates that most disorders are inter- disease mechanisms from analyzing the effects of single genes to
disorders arises in part from the many clinically distinct cancercur-actions (6, 7, 19), transcription factor-promoter interactions (20),
same gene (allelic heterogeneity) giving rise to phenotypes of this dataset might not be applicable to complex disease genes
understanding the effect of molecular interaction networks. Such
subtypes tightly connected withdisorders. For example, mutations inand metabolic reactions (8), toM.V., and A.-L.B. designed research; K.-I.G. and M.E.C.
rently classified as different each other through common tumor
Author contributions: D.V., B.C.,
discover novel genetic interactions. since 97% of the disease genes were monogenic. Despite this
TP53 have been linked to 11 clinically distinguishable cancer-In the DGN, research;of 1,777 disease genes data; connected to other M.V., and
repressor genes such as TP53 and PTEN. performed 1,377 K.-I.G. and M.E.C. analyzed are and K.-I.G., M.E.C., D.V.,
networks have been exploited to find novel candidate genes, based reservation, both the latter studies found a functional clustering of
related disorders (11). Given the highly interlinked internal orga-disease genes, and paper.
Although the HDN layout was generated independently of any A.-L.B. wrote the 903 genes belong to a giant component (Fig. 2b). on the assumption that neighbors of a disease-causing gene in a disease genes. Another concern is that the above studies could be
knowledge on disorder classes,itthe resultingpossible to improve theWhereas the number of genesinterest.
nization of the cell (12–17), should be network is naturally The authors declare no conflict of involved in multiple diseases de- network are more likely to cause either the same or a similar confounded by discovery bias, in other words these disease genes
and visibly clustered accordingapproachdisorder classes. Yet, there
single gene–single disorder to major by developing a conceptualcreases article is a (SI Fig. 6d; light gray nodes in Fig. 2b), several
This rapidly PNAS Direct Submission. disease [1–14]. Initial studies investigating the network properties were identified based on previous knowledge. By contrast,
framework to link systematically all genetic disorders (the humandisease genes (e.g., TP53, PAX6) are involved in as many as 10 GO, Gene
are visible differences between different classes of disorders. Abbreviations: DGN, disease gene network; HDN, human disease network; of human disease genes were based on cancers and revealed that
Whereas the large cancer cluster is tightly interconnected due to the(thedisorders, representing major hubs in the network. Pearson correlation coeffi-
‘‘disease phenome’’) with the complete list of disease genes
Genome Wide Association studies (GWAs) do not suffer from
Ontology; OMIM, Online Mendelian Inheritance in Man; PCC, up-regulated genes in cancerous tissues were central in the
many genes associated with multiple global view of (TP53, KRAS,
‘‘disease genome’’), resulting in a types of cancer the ‘‘diseasome,’’ cient.
such bias [15].
ERBB2, NF1, etc.) of all known several diseases with strong pre- **To whom correspondence and DGN. To probe how the topology
the combined set and includes disorder/disease gene associations.Functional Clustering of HDN may be addressed. E-mail: alb@nd.edu or marc࿝vidal@ interactome and highly connected (often referred to as hubs) In this study, we have derived networks of complex diseases and
disposition to cancer, such as Fanconi anemia and ataxia telangi- of thedfci.harvard.edu. GDN deviates from random, we randomly
HDN and [1,2]. A subsequent study based on the human disease network complex disease genes to explore the shared genetic architecture of
Results
ectasia, metabolic disorders do not appear to form a single distinct shuffledarticle contains supporting information online at www.pnas.org/cgi/content/full/
This the associations between disorders and genes, while keep- and disease gene network derived from the Online Mendelian complex diseases studied using GWAs. Further, we have evaluated
cluster but are underrepresented in constructed a bipartite graphing the number of links per each disorder and disease gene in the
Construction of the Diseasome. We the giant component and 0701361104/DC1. Inheritance in Man (OMIM) demonstrated that the products of the topological and functional properties of complex disease genes
overrepresented in disjoint sets of nodes. One set corresponds to allbipartite network unchanged. Interestingly, the average size of the
consisting of two the small connected components (Fig. 2a). To © 2007 by The National Academy of Sciences of the USA disease genes tended (i) to have more interactions with each other in the human interactome by comparing them with essential,
quantify this difference, we measured the locus heterogeneity of giant component of 104 randomized disease networks is 643 Ϯ 16,
each disorder class and the fraction of disorders that are connected significantly larger than 516 (P Ͻ 10Ϫ4; for details of statistical than with non-disease genes, (ii) to be expressed in the same tissues monogenic and non-disease genes. We observed that diseases
www.pnas.org͞cgi͞doi͞10.1073͞pnas.0701361104
to each other in the HDN (see SI Text). We find that cancer and analyses of the results reported hereafter, ͉see SI104 ͉ no. 21 ͉ 8685– 8690
PNAS ͉ May 22, 2007 vol. Text), the actual and (iii) to share Gene Ontology (GO) terms [8]. Contradicting belonging to the same disease class do not always show a tendency
neurological disorders show high locus heterogeneity and also size of the HDN (SI Fig. 6c). Similarly, the average size of the giant earlier reports, this latter study demonstrated that the non-essential to share common disease genes; the complex disease gene net-
represent the most connected disease classes, in contrast with component from randomized gene networks is 1,087 Ϯ 20 genes, human disease genes showed no tendency to encode hubs in the work shows high modularity comparable to that of the human
metabolic, skeletal, and multiple disorders that have low genetic significantly larger than 903 (P Ͻ 10Ϫ4), the actual size of the DGN
heterogeneity and are the least connected (SI Fig. 7). (SI Fig. 6e). These differences suggest important pathophysiological
clustering of disorders and disease genes. Indeed, in the actual PLoS ONE | www.plosone.org 1 November 2009 | Volume 4 | Issue 11 | e8090
Properties of the DGN. In the DGN, two disease genes are connected networks disorders (genes) are more likely linked to disorders
if they are associated with the same disorder, providing a comple- (genes) of the same disorder class. For example, in the HDN there
8686 ͉ www.pnas.org͞cgi͞doi͞10.1073͞pnas.0701361104 Goh et al.

10. Regime shift database

11. Regime shift database

12. Regime shift database
Description of the alternative
regimes and reinforcing
feedbacks
The drivers that precipitate the
regime shift
Impacts on ecosystem services
and human well-being
Management options
www.regimeshifts.org

13. N Policy relevant regime shifts Mechanism Reversibility
1 Bivalves collapse Established H
2 Coral transitions Established H
3 Desertification Contested H, I
4 Encroachment Established H
5 Eutrophication Established H, I, R
Data: 6 Fisheries collapse
7 Marine foodwebs collapse
Contested
Contested
U
U
8 Forest - Savanna Established I
9 Hypoxia Established H, R
10 Kelp transitions Established H, R
20 policy relevant regime shifts: 11 Soil salinization Established H, I
12 Steppe - Tundra Established I
13 Tundra - Forest Established I
8 terrestrial
14 Monsoon circulation Established I
9 aquatic 15 Thermohaline circulation collapse Established I
2 global + 1 polar 16 Greenland ice sheet collapse Established I
17 Arctic salt marshes Established I
18 Peatlands Established I
19 River channel position Established I
20 Soil structure Established H, I
Reversibility: H = Hysteretic; I = Irreversible; R= Reversible;
U = Unknown

14. Methods
• Bipartite network and one-
mode projections: 20
Regime shifts + 55 Drivers
Drivers Regime shifts
• 104 random bipartite graphs
to explore significance of Regime Shift Database
couplings: mean degree and A 1 0 1 1 0 0 0 0 1 1 1 1 0 1 0 1
co-occurrence statistics on B
C
1 0 0 0 1 1 0 0 1 1 1 0 0 1 0 1
one-mode projections.
• ERGM models using Jaccard
Ecosystem services Spatial scale
similarity index on the RSDB Ecosystem processes Temporal scale
as edge covariates Ecosystem type Reversibility
Impact on human well being Evidence
Land use ...

15. 20
Number of vertex
5 10 0 15
1 3 5 7 10 12 16 19
Degree
Regime Shifts - Drivers
20 Regime shifts
Bipartite Network

16. Greenland
Monsoon
weakening
Tundra to Soil
Forest Coral transitions structure
Dry land
degradation
Thermohaline Kelps transitions
circulation Forest to Savannas
Soil
Eutrophication salinization
Fisheries collapse
Bivalves
Encroachment collapse
Salt marshes Peatlands
Marine foodwebs Hypoxia
Floating plants
River channel
change
Regime Shifts Network Top 5 occur in aquatic ecosystems

17. Color Key Greenland
Monsoon
weakening
and Histogram Tundra to
Forest Coral transitions
Soil
structure
Regime shifts
Count
Dry land
100
degradation
Thermohaline Kelps transitions
circulation Forest to Savannas
Soil
0
Eutrophication salinization
Fisheries collapse
Bivalves
0 0.4 0.8 Encroachment collapse
Value Salt marshes Peatlands
Marine foodwebs Hypoxia
Tundra to Forest Floating plants
River channel
Greenland change
Termohaline circulation
Average Degree in simulated
Salt marshes Regime Shifts Networks
0.7
Marine foodwebs
Fisheries collapse
0.6
Soil structure
0.5
River channel change
0.4
Density
Floating plants
0.3
Peatlands
Coral transitions
0.2
Kelps transitions
0.1
Bivalves collapse
0.0
Eutrophication
12 13 14 15 16 17 18 19
Hypoxia Mean Degree
Forest to savannas
Regime Shifts Network
Dry land degradation Co−occurrence Index
Encroachment
0.8
Monsoon weakening
Soil salinization
0.6
River channel change
Floating plants
Tundra to Forest
Soil structure
Greenland
Termohaline circulation
Salt marshes
Marine foodwebs
Fisheries collapse
Peatlands
Coral transitions
Kelps transitions
Bivalves collapse
Eutrophication
Hypoxia
Forest to savannas
Dry land degradation
Encroachment
Monsoon weakening
Soil salinization
Density
0.4
0.2
0.0
The co-occurrence of regime shifts is not random. Aquatic 8 9 10
s−squared
11 12 13
systems tend to share more drivers suggesting that their
underlying processes are also similar

18. ERGM models results
Parameters Base model Full model
Log-likelihood -84.6 -73.2
AIC 173.21 168.38 The likelihood of
Network structure
sharing
Edges -0.70 0.52
Edges covariates drivers increase
Regime Shift Database 6.95 **
when regime
Ecosystem services -1.54
Ecosystem processes -1.47 shifts happen in
Human well being -0.34 the same
ecosystem and
Ecosystem type 2.59 *
Land use 2.69 ·
Scale -0.54 under similar land
use practices.
Reversibility 2.63 **
Evidence 1.6 *
Mechanism 0.02
Existence 0.27

19. Upwellings Precipitation
Erosion
Fishing
300
Nutrients inputs
Irrigation
250
Atmospheric CO2 Agriculture
Number of links
Demand
200
Global warming
Human population
Fertilizers use
150
Urbanization
100
Deforestation
ENSO like events Sewage
50
Droughts
Floods
0
1 2 3 4 5 6 7 8 9 10
Number of Regime Shifts jointly caused
Drivers Network Agriculture and Climate change

20. Upwellings Precipitation
Erosion
Fishing
300
Nutrients inputs
Irrigation
250
Atmospheric CO2 Agriculture
Number of links
Demand
200
Global warming
Human population
Fertilizers use
150
Urbanization
100
Deforestation
ENSO like events Sewage
50
Droughts
Floods
0
1 2 3 4 5 6 7 8 9 10
Number of Regime Shifts jointly caused
Drivers Network Agriculture and Climate change

21. Color Key Upwellings
Erosion Precipitation
and Histogram
Count Drivers
0 1000
Fishing
Nutrients inputs
Irrigation
Atmospheric CO2 Agriculture
Demand
Global warming
Human population
Marine General Terrestrial
Fertilizers use
0 0.4 0.8
Value Urbanization
Deforestation
ENSO like events Sewage
Droughts
Turbidity
Floods
Disease
Pollutants
Sediments
Thermal anomalies in summer
Ocean acidification
Hurricanes
Average Degree in simulated
Low tides Drivers Networks
0.7
Water stratification
Impoundments
Rainfall variability
0.6
Landscape fragmentation
Flushing
Urban storm water runoff
0.5
Urbanization
Nutrients inputs
Fishing
0.4
Demand
Density
Deforestation
Human population
0.3
Agriculture
Erosion
Floods
0.2
Fertilizers use
Sewage
Production intensification
0.1
Food prices
Labor availability
Ranching (livestock)
0.0
Water infrastructure
Aquifers
Water availability 20 21 22 23 24 25 26
Upwellings Mean Degree
ENSO like events
Tragedy of the commons
Access to markets
Subsidies
Infrastructure development
Immigration Drivers Network
Logging Co−occurrence Index
Droughts
Fire frequency
6
Irrigation
Global warming
Atmospheric CO2
Precipitation
5
Fishing technology
Food supply
Invasive species
4
Sea level rise
Temperature
Density
Green house gases
Development policies
3
Drainage
Sea surface temperature
2
Turbidity
Disease
Pollutants
Sediments
Thermal anomalies in summer
Ocean acidification
Hurricanes
Low tides
Water stratification
Impoundments
Rainfall variability
Landscape fragmentation
Flushing
Urban storm water runoff
Urbanization
Nutrients inputs
Fishing
Demand
Deforestation
Labor availability
Ranching (livestock)
Human population
Agriculture
Erosion
Floods
Fertilizers use
Sewage
Production intensification
Food prices
Water infrastructure
Aquifers
Water availability
Upwellings
ENSO like events
Tragedy of the commons
Access to markets
Subsidies
Infrastructure development
Immigration
Logging
Droughts
Fire frequency
Irrigation
Global warming
Atmospheric CO2
Precipitation
Fishing technology
Food supply
Invasive species
Sea level rise
Temperature
Green house gases
Development policies
Drainage
Sea surface temperature
The co-occurrence of driver is not random. Drivers tend to
1
cluster according to the ecosystem type where the regime
0
1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1
shift takes place.
s−squared

22. Work in Progress
Causal Networks of Regime Shifts
Causal-loop diagrams is a
technique to map out the
feedback structure of a system
(Sterman 2000)

23. Topological features of Causal Networks
Degree centrality Betweenness centrality Eigenvector centrality

24. 1. What are the major global change
drivers of regime shifts?
80
60
Numbervertex vertex
Number vertexvertex
50
60
40
of
Number of of
Number of
40
30
20
20
10
0
0
1 2 3 4 5 6 7 8 9 11 12 14 15 17 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 19 22
Outgoing links
Outdegree
Incoming links
Indegree
Few nodes have a lot of links!

25. Marine Regime Shifts
Local centrality Global centrality
0.12
0.10
Nutrients input
10
Phytoplankton
Nutrients input
Fishing
0.08
Dissolved oxygenMid−predators
Noxious gases
Global warming
Betweenness
Algae Bivalves abundance
Outdegree
Agriculture Bivalves abundance
0.06
Floods Zooplankton
5
Top predators Space
GlobalUrban Macrophytes Phytoplankton
Planktivore fish
warminggrowth Dissolved oxygen
Turbidity
SST Erosion SST
ENSO−like Water temperature
events frequency
Canopy−forming algae algae
Turf−forming Biodiversity
Fishing
0.04
Greenhouse gasesand meso−predators
Disease outbreak Urchin barren
Lobsters Nekton Coral abundance
Unpalatability
AtmosphericDemand
Water vapor
CO2 Plankton and Macroalgae abundance
Human population Upwellings
ConsumptionFertilizers use runoff filamentous algae
Precipitation Flushing Coral abundance
Urban Sewage
Deforestation Sediments
preferences
Localstorm water Herbivores
Landscape fragmentation/conversion
water movements
Disease outbreak
Tragedy of thecolumn acidification
Impoundments densityLeakage
Water frequency
OceanIrrigation contrast
Thermal annomalies species
Invasive
Droughts
Perverse incentives mixing
TechnologyWater Zooxanthellae
Low tides commons
Sulfide stress
Wind release
Stratification relative cooling structural complexity
Mortality rate
Habitat
Density Thermal Fishmatter
Daily competitors
SubsidiesPollutants low pressurecolumn
Hurricanescontrast in the water
Noxious gases
Trade Other Organic Phosphorous in water Water vapor
0.02 Biodiversity Zooplankton
Nekton
Space Upwellings
0
Mid−predators
Turbidity Algae
Water temperature
Greenhouse gases Floods
Thermal low pressureErosion Macrophytes
Turf−forming algae
Macroalgae abundance Flushing
Lobsters and meso−predatorsTop predators
Wind stress
Water column density contrast
Urchin barren
Herbivores
Canopy−forming algae
Habitat structural complexity
Phosphorous in growth
Urban
Density contrast inOrganic matter and filamentous algae
Leakage Plankton
0.00
Zooxanthellae mixing water
ENSO−like events water column
Mortality the
Unpalatability frequency
Droughts
OceanHumanPerverseDemand
rate Agriculture Planktivore fish
AtmosphericWater Technology preferences
Landscape coolingwater incentives
fragmentation/conversion
acidification theuse
Other competitors Sediments
DailyInvasiveLocalSewage runoff
Low PollutantsFish Subsidies
population
HurricanesCO2 release
Consumption
relativePrecipitationTrade
Deforestation movements
Thermal annomalies of water
tidesUrban Stratificationcommons
storm
Fertilizers
Irrigation
frequency
Tragedy
Impoundments
species
Sulfide
0.00 0.02 0.04 0.06 0.08 0.10 0.12
0 5 10 15
Eigenvector
Indegree

26. Terrestrial Regime Shifts
Local centrality Global centrality
0.08
8
Fire frequency Precipitation
0.06
Global warming Precipitation Agriculture
Woody plants dominance
6
Fire frequency
Forest Grass dominance Deforestation
Cropland−Grassland area Deforestation
Betweenness
Outdegree
Agriculture Irrigation Albedo
0.04
Albedo Grass dominance
4
Irrigation
Rainfall variability
Soil productivity Forest
Droughts
DemandLand−Ocean temperature
Rainfall deficit
Savanna Native vegetation gradient
Woody plants dominance
Demand
Productivity
Land−Ocean temperature gradient
Atmospheric temperature
Erosion
Savanna
SST Atmospheric temperature
Floodsdemand
Grazing Water infrastructure Evapotranspiration
Water Erosion
Vegetation Space
Water availability
2
Atmospheric CO2
0.02
Human population Palatability
Soil moisture productivity
Soil Vegetation
Water infrastructure
Water availability
Advection
Carbon storage Global warming
Soil impermeability Solar radiation
Infrastructure developmentstress
WindTree release
maturity
Aquifers
LatentSoil quality
heatevents
Monsoon circulation
ENSO−likeDust frequency Vapor Soil salinity Soil salinity
Biomass
Logging industryShadow_rooting level
ImmigrationWater consumption
Land−Ocean pressure gradient concentration Productivity Aerosol concentration Soil moisture Rainfall deficit
use Moisture Carbon storage
Lifting Ranching
condensation Advection
FertilizersAbsorption of solar radiation
Aerosol Brown radiation
Solar clouds
Illegal logging
Sea tides Brown clouds Roughness
Temperature
Land conversion Ground water table
Grazers Absorption of solar radiation
Aquifers Evapotranspiration variability
Land conversion Rainfall Cropland−Grassland area
Vapor Droughts
Native vegetation
Ground Waterstress frequencyGrazers
ENSO−like events
SSTMonsoon
Land−Ocean water table
pressure gradient circulation
Wind demand
WaterTemperature
Shadow_rooting Moisture
Dust LiftingRoughnessTree maturity
Soil quality
consumptioncondensation level
Palatability
0
0.00
RanchingFloods
Grazing Space
Soil impermeabilityBiomass population
Human
Latent heat Logginglogging Atmospheric CO2
Fertilizers Illegal development
Immigration
Sea tides releaseindustry
Infrastructure
use
0 2 4 6 8 0.00 0.02 0.04 0.06 0.08
Indegree Eigenvector

27. Are regime shifts controllable?
To what extent can we manage them?
• Critics to Liu et al.:
ARTICLE doi:10.1038/nature10011
• Topology is not enough
Controllability of complex networks
Yang-Yu Liu1,2, Jean-Jacques Slotine3,4 & Albert-Laszlo Barabasi1,2,5
´ ´ ´
• Internal dynamics
The ultimate proof of our understanding of natural or technological systems is reflected in our ability to control them.
Although control theory offers mathematical tools for steering engineered and natural systems towards a desired state, a
framework to control complex self-organized systems is lacking. Here we develop analytical tools to study the
• Unmatched nodes change if
controllability of an arbitrary complex directed network, identifying the set of driver nodes with time-dependent
control that can guide the system’s entire dynamics. We apply these tools to several real networks, finding that the
number of driver nodes is determined mainly by the network’s degree distribution. We show that sparse
inhomogeneous networks, which emerge in many real complex systems, are the most difficult to control, but that
the periphery of the causal dense and homogeneous networks can be controlled using a few driver nodes. Counterintuitively, we find that in
both model and real systems the driver nodes tend to avoid the high-degree nodes.
networks change - The limits of According to control theory, a dynamical system is controllable if, with a
suitable choice of inputs, it can be driven from any initial state to any
of traffic that passes through a node i in a communication network24
or transcription factor concentration in a gene regulatory network25.
the system blur desired final state within finite time1–3. This definition agrees with our
intuitive notion of control, capturing an ability to guide a system’s
behaviour towards a desired state through the appropriate manipulation
The N 3 N matrix A describes the system’s wiring diagram and the
interaction strength between the components, for example the traffic
on individual communication links or the strength of a regulatory
of a few input variables, like a driver prompting a car to move with the interaction. Finally, B is the N 3 M input matrix (M # N) that iden-
desired speed and in the desired direction by manipulating the pedals tifies the nodes controlled by an outside controller. The system is
and the steering wheel. Although control theory is a mathematically controlled using the time-dependent input vector u(t) 5 (u1(t), …,
highly developed branch of engineering with applications to electric uM(t))T imposed by the controller (Fig. 1a), where in general the same
circuits, manufacturing processes, communication systems4–6, aircraft, signal ui(t) can drive multiple nodes. If we wish to control a system, we
• Unmatched nodes change
spacecraft and robots2,3, fundamental questions pertaining to the con- first need to identify the set of nodes that, if driven by different signals,
trollability of complex systems emerging in nature and engineering have can offer full control over the network. We will call these ‘driver
resisted advances. The difficulty is rooted in the fact that two independ- nodes’. We are particularly interested in identifying the minimum
when joining causal networks
ent factors contribute to controllability, each with its own layer of number of driver nodes, denoted by ND, whose control is sufficient
unknown: (1) the system’s architecture, represented by the network to fully control the system’s dynamics.
encapsulating which components interact with each other; and (2) the The system described by equation (1) is said to be controllable if it
dynamical rules that capture the time-dependent interactions between
to understand cascading
can be driven from any initial state to any desired final state in finite
the components. Thus, progress has been possible only in systems where time, which is possible if and only if the N 3 NM controllability matrix
both layers are well mapped, such as the control of synchronized net-
works7–10, small biological circuits11 and rate control for communica- C~(B, AB, A2 B, . . . , AN{1 B) ð2Þ
effects. tion networks4–6. Recent advances towards quantifying the topological
characteristics of complex networks12–16 have shed light on factor (1),
prompting us to wonder whether some networks are easier to control
has full rank, that is
rank(C)~N ð3Þ
than others and how network topology affects a system’s controllability.
Despite some pioneering conceptual work17–23 (Supplementary This represents the mathematical condition for controllability, and is
Information, section II), we continue to lack general answers to these called Kalman’s controllability rank condition1,2 (Fig. 1a). In practical
questions for large weighted and directed networks, which most com- terms, controllability can be also posed as follows. Identify the minimum
monly emerge in complex systems. number of driver nodes such that equation (3) is satisfied. For example,
equation (3) predicts that controlling node x1 in Fig. 1b with the input
Network controllability signal u1 offers full control over the system, as the states of nodes x1, x2, x3
Most real systems are driven by nonlinear processes, but the controll- and x4 are uniquely determined by the signal u1(t) (Fig. 1c). In contrast,

28. Conclusions
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.
Agricultural processes and global warming are the main causes of
regime shifts.
Marine regime shifts tend to share more drivers, while terrestrial
regime shifts are more context dependent.
Network analysis is an useful approach to study regime shifts
couplings when knowledge about system dynamics or time series of
key variables are limited. Network controllability opens a window of
opportunity to address causality relationships in systems with high
uncertainty.

29. Thanks!
Prof. Garry Peterson & Oonsie
Biggs for their supervision
RSDB folks for inspiring
discussion and writing examples
SRC for an inspiring research
place and Sweden FORMAS
and MISTRA funding!
Questions??
e-mail: juan.rocha@stockholmresilience.su.se
Twitter: @juanrocha
Blog: http://criticaltransitions.wordpress.com/