Licentiate: Regime shifts in the Anthropocene

Regime Shifts in the Anthropocene
Juan-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 Shifts
Regime shifts are abrupt reorganization of a
system’s structure and function. A regime
correspond to characteristic behavior of the
system maintained by mutually reinforcing
processes or feedbacks. The shift occurs when
the strength of such feedbacks change, usually
driven by cumulative change in slow variables,
external disturbances or shocks.
collapse
collapse
recovery
Precipitation
Vegetation
Precipitation
Vegetation
PrecipitationVegetation
Precipitation
Vegetation
Precipitation Precipitation Precipitation Precipitation
low high low high low high low high
Vegetation
low
high
Gradual Threshold
Vegetation
low
high
Vegetation
low
high
Vegetation
low
high
Hystersis Irreversible
Stability
Landscape
Equilibria
(Gordon et al 2008)

Regime Shifts
external forcing reverses, the response variable will ﬂip back to the original equilibrium, but at a diﬀerent
Fig. 3. Catastrophe manifold illustrating that the three types of regime shifts are special cases along a continuum of internal ecosystem
structure. Adapted from Jones and Walters (1976).
J.S. Collie et al. / Progress in Oceanography 60 (2004) 281–302 287
(Collie 2004)

Regime Shifts
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
Existence
Well
established
Proposed
Contested
Contested
Proposed
Well established
Soil structure
Marine foodwebs
Monsoon weakening
Termohaline circulation
Encroachment
Fisheries collapse
Dryland degradation
Forest to savanna
Steppe to tundra
Tundra to forest
Floating plants
Greenland
Arctic sea ice
Bivalves collapse
Coral transitions
Eutrophication
Hypoxia
Kelps transitions
Peatlands
River channel change
Salt marshes
Soil salinization

Ecosystem services
Drivers ...
Biodiversity
Primary production
Nutrient cycling
Water cycling
Soil Formation
Fisheries
Wild animals and plants food
Freshwater
Foodcrops
Livestock
Timber
Woodfuel
Other crops
Hydropower
Water purification
Climate regulation
Regulation of soil erosion
Pest and disease regulation
Natural hazard regulation
Air quality regulation
Pollination
Recreation
Aesthetic values
Knowledge and educational values
Spiritual and religious
Livelihoods and economic activity
Food and nutrition
Cultural, aesthetic and recreational values
Security of housing and infrastructure
Health
Social confict
No direct impact
0 8 15 23 30
Ecosystem Services
Supporting
Provisioning
Regulating
Cultural
Human well being

Ecosystem services
Drivers ...
0.0 0.2 0.4 0.6 0.8 1.0
0.00.20.40.60.81.0
Proportion of Regime Shifts (n=20)
ProportionofDriverssharingcausalitytoRegimeShifts(n=55)
Agriculture
Atmospheric CO2
Deforestation
Demand
Droughts
Fishing
Global warming
Human population
Nutrients inputs
Urbanization

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

Challenges
We developed a framework to
compare regime shifts
Issues of consistency:
Drivers
CLD
System boundaries
Uncertainty assessment:
strength of feedbacks and the
role of social dynamics
Methods to identify leverage
points for management

3. Global drivers of Regime Shifts

Virtruvian Man, Leonardo Da Vinci

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

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
05101520
●
●
●
●
●
●
● ●●
●
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●
●
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●
●
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●
● ●●●
●
● ●
●
● ●●
●●
● ●
● ●●● ● ●●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
5 10 15
0100300500
Degree
Betweenness
Co−occurrence Index DN
s−squared
Density
1.4 1.6 1.8 2.0
0123456
Average Degree DN
Degree
Density
20 22 24 26
0.00.20.40.6
Co−occurrence Index RN
s−squared
Density
8 9 10 11 12 13
0.00.20.40.60.8
Average Degree RN
Degree
Density 12 14 16 18
0.00.20.40.6

Agriculture
Atmospheric CO2
Deforestation
Demand
Droughts
Fishing
Global warming
Human population
Nutrients inputs
Urbanization
Global drivers of Regime Shifts
Food production & climate change
are the most important drivers or
regime shifts globally
Only 5 out of 55 drivers cause
>50% of the 20 regime shifts
analyzed.
11 drivers interact with >50% of
other drivers when causing regime
shifts.

Encroachment
Monsoonweakening
Soilsalinization
Drylanddegradation
Foresttosavannas
Fisheriescollapse
Marinefoodwebs
Floatingplants
Peatlands
Saltmarshes
Soilstructure
Riverchannelchange
TundratoForest
Greenland
Thermohalinecirculation
Coraltransitions
Bivalvescollapse
Kelpstransitions
Eutrophication
Hypoxia
Human Indirect Activities
Climate
Water
Biodiversity Loss
Land Cover Change
Biogeochemical Cycle
Biophysical
0 2 4 6 8
Value
01530
Count
Global drivers of Regime Shifts
Food production & climate change
are the most important drivers or
regime shifts globally
Only 5 out of 55 drivers cause
>50% of the 20 regime shifts
analyzed.
11 drivers interact with >50% of
other drivers when causing regime
shifts.

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
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 plants
Bivalves collapse
Eutrophication
Fisheries collapse
Coral transitions
Hypoxia
Encroachment
Salt marshes
Soil salinization
Soil structure
Forest to savannas
Dry land degradation
Kelps transitions
Monsoon weakening
Peatlands
Marine foodwebs
Greenland
Thermohaline circulation
Tundra to Forest
Local
National
International
Drivers by Management Type
Proportion of RS Drivers
0.0 0.2 0.4 0.6 0.8 1.0
Half of the drivers of 75% of
the regime shifts require
international cooperation to
manage them.
Given the high diversity of
drivers, focusing on well
studied variables (e.g.
nutrients inputs) wont preclude
regime shifts from happening.
Avoiding regime shifts calls for
poly-centric institutions.

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 Progress
Causal Networks: Cascading effects and regime shifts controllability

Degree centrality
Topological features of Causal Networks
Betweenness centrality Eigenvector centrality

ARTICLE doi:10.1038/nature10011
Controllability of complex networks
Yang-Yu Liu1,2
, Jean-Jacques Slotine3,4
& Albert-La´szlo´ Baraba´si1,2,5
The ultimate proof of our understanding of natural or technological systems is reflected in our ability to control them.
Although control theory offers mathematical tools for steering engineered and natural systems towards a desired state, a
framework to control complex self-organized systems is lacking. Here we develop analytical tools to study the
controllability of an arbitrary complex directed network, identifying the set of driver nodes with time-dependent
control that can guide the system’s entire dynamics. We apply these tools to several real networks, finding that the
number of driver nodes is determined mainly by the network’s degree distribution. We show that sparse
inhomogeneous networks, which emerge in many real complex systems, are the most difficult to control, but that
dense and homogeneous networks can be controlled using a few driver nodes. Counterintuitively, we find that in
both model and real systems the driver nodes tend to avoid the high-degree nodes.
Accordingtocontroltheory,adynamicalsystemiscontrollableif,witha
suitable choice of inputs, it can be driven from any initial state to any
desired final state within finite time1–3
. This definition agrees with our
intuitive notion of control, capturing an ability to guide a system’s
behaviourtowardsadesiredstatethroughtheappropriatemanipulation
of a few input variables, like a driver prompting a car to move with the
desired speed and in the desired direction by manipulating the pedals
and the steering wheel. Although control theory is a mathematically
highly developed branch of engineering with applications to electric
circuits, manufacturing processes, communication systems4–6
, aircraft,
spacecraft and robots2,3
, fundamental questions pertaining to the con-
trollabilityofcomplex systemsemerging in nature andengineering have
resisted advances. The difficulty is rooted in the fact that two independ-
ent factors contribute to controllability, each with its own layer of
unknown: (1) the system’s architecture, represented by the network
encapsulating which components interact with each other; and (2) the
dynamical rules that capture the time-dependent interactions between
thecomponents.Thus,progresshasbeenpossibleonlyinsystemswhere
both layers are well mapped, such as the control of synchronized net-
works7–10
, small biological circuits11
and rate control for communica-
tion networks4–6
. Recent advances towards quantifying the topological
characteristics of complex networks12–16
have shed light on factor (1),
prompting us to wonder whether some networks are easier to control
than others and how network topology affects a system’s controllability.
Despite some pioneering conceptual work17–23
(Supplementary
Information, section II), we continue to lack general answers to these
questions for large weighted and directed networks, which most com-
monly emerge in complex systems.
Network controllability
Most real systems are driven by nonlinear processes, but the controll-
ability of nonlinear systems is in many aspects structurally similar to
that of linear systems3
, prompting us to start our study using the
of traffic that passes through a node i in a communication network24
or transcription factor concentration in a gene regulatory network25
.
The N 3 N matrix A describes the system’s wiring diagram and the
interaction strength between the components, for example the traffic
on individual communication links or the strength of a regulatory
interaction. Finally, B is the N 3 M input matrix (M # N) that iden-
tifies the nodes controlled by an outside controller. The system is
controlled using the time-dependent input vector u(t) 5 (u1(t), …,
uM(t))T
imposed by the controller (Fig. 1a), where in general the same
signal ui(t) can drive multiple nodes. If we wish to control a system, we
first need to identify the set of nodes that, if driven by different signals,
can offer full control over the network. We will call these ‘driver
nodes’. We are particularly interested in identifying the minimum
number of driver nodes, denoted by ND, whose control is sufficient
to fully control the system’s dynamics.
The system described by equation (1) is said to be controllable if it
can be driven from any initial state to any desired final state in finite
time, which is possible if and only if the N3 NM controllability matrix
C~(B, AB, A2
B, . . . , AN{1
B) ð2Þ
has full rank, that is
rank(C)~N ð3Þ
This represents the mathematical condition for controllability, and is
called Kalman’s controllability rank condition1,2
(Fig. 1a). In practical
terms,controllabilitycanbealsoposedasfollows.Identifytheminimum
number of driver nodes such that equation (3) is satisfied. For example,
equation (3) predicts that controlling node x1 in Fig. 1b with the input
signalu1 offersfullcontroloverthesystem,asthestatesofnodesx1,x2,x3
and x4 are uniquely determined by the signal u1(t) (Fig. 1c). In contrast,
controlling the top node in Fig. 1e is not sufficient for full control, as the
difference a31x2(t) 2 a21x3(t) (where aij are the elements of A) is not
Are regime shifts controllable?
To what extent can we manage them?
• Critics to Liu et al.:
• Topology is not enough
• Internal dynamics
• Unmatched nodes change if
the periphery of the causal
networks change - The limits of
the system blur
• Unmatched nodes change
when joining causal networks
to understand cascading
eﬀects.

Thanks!
Prof. Garry Peterson & Oonsie
Biggs for their supervision
RSDB folks for inspiring
discussion and writing
examples
Funding sources: FORMAS,
SSEESS, CSS.
Questions??
e-mail: juan.rocha@stockholmresilience.su.se
News and papers on regime shifts: @juanrocha
Research blog: http://criticaltransitions.wordpress.com/

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)
Knowledgeofthe
system
Statistics:
Autocorrelation and
variance
Bayesian networks -
models
Models & Jacobians
Web crawlers &
local knowledge
Research agenda on Regime Shifts
High
High
Low
Low

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

TundratoForest
Greenland
Termohalinecirculation
Saltmarshes
Marinefoodwebs
Fisheriescollapse
Soilstructure
Riverchannelchange
Floatingplants
Peatlands
Coraltransitions
Kelpstransitions
Bivalvescollapse
Eutrophication
Hypoxia
Foresttosavannas
Drylanddegradation
Encroachment
Monsoonweakening
Soilsalinization
Soil salinization
Monsoon weakening
Encroachment
Dry land degradation
Forest to savannas
Hypoxia
Eutrophication
Bivalves collapse
Kelps transitions
Coral transitions
Peatlands
Floating plants
Soil structure
Fisheries collapse
Marine foodwebs
Salt marshes
Termohaline circulation
Greenland
Tundra to Forest
Regime shifts
0 0.4 0.8
Value
0100
Color Key
and Histogram
Count
Average Degree in simulated
Regime Shifts Networks
Mean Degree
Density
12 13 14 15 16 17 18 19
0.00.10.20.30.40.50.60.7
Regime Shifts Network
Co−occurrence Index
s−squared
Density
8 9 10 11 12 13
0.00.20.40.60.8
Bivalves
collapse
Coral transitions
Dry land
degradation
Encroachment
Eutrophication
Fisheries collapse
Forest to Savannas
Hypoxia
Kelps transitions
Marine foodwebs
Floating plants
River channel
change
Salt marshes
Soil
salinization
Soil
structure
Tundra to
Forest
Monsoon
weakening
Peatlands
Greenland
Thermohaline
circulation
The co-occurrence of regime shifts is not random. Aquatic
systems tend to share more drivers suggesting that their
underlying processes are also similar

Turbidity
Disease
Pollutants
Sediments
Thermalanomaliesinsummer
Oceanacidification
Hurricanes
Lowtides
Waterstratification
Impoundments
Rainfallvariability
Landscapefragmentation
Flushing
Urbanstormwaterrunoff
Urbanization
Nutrientsinputs
Fishing
Demand
Deforestation
Humanpopulation
Agriculture
Erosion
Floods
Fertilizersuse
Sewage
Productionintensification
Foodprices
Laboravailability
Ranching(livestock)
Waterinfrastructure
Aquifers
Wateravailability
Upwellings
ENSOlikeevents
Tragedyofthecommons
Accesstomarkets
Subsidies
Infrastructuredevelopment
Immigration
Logging
Droughts
Firefrequency
Irrigation
Globalwarming
AtmosphericCO2
Precipitation
Fishingtechnology
Foodsupply
Invasivespecies
Sealevelrise
Temperature
Greenhousegases
Developmentpolicies
Drainage
Seasurfacetemperature
Sea surface temperature
Drainage
Development policies
Green house gases
Temperature
Sea level rise
Invasive species
Food supply
Fishing technology
Precipitation
Atmospheric CO2
Global warming
Irrigation
Fire frequency
Droughts
Logging
Immigration
Infrastructure development
Subsidies
Access to markets
Tragedy of the commons
ENSO like events
Upwellings
Water availability
Aquifers
Water infrastructure
Ranching (livestock)
Labor availability
Food prices
Production intensification
Sewage
Fertilizers use
Floods
Erosion
Agriculture
Human population
Deforestation
Demand
Fishing
Nutrients inputs
Urbanization
Urban storm water runoff
Flushing
Landscape fragmentation
Rainfall variability
Impoundments
Water stratification
Low tides
Hurricanes
Ocean acidification
Thermal anomalies in summer
Sediments
Pollutants
Disease
Turbidity
Drivers
0 0.4 0.8
Value
01000
Color Key
and Histogram
Count
Average Degree in simulated
Drivers Networks
Mean Degree
Density
20 21 22 23 24 25 26
0.00.10.20.30.40.50.60.7
Drivers Network
Co−occurrence Index
s−squared
Density
1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1
0123456
The co-occurrence of driver is not random. Drivers tend to
cluster according to the ecosystem type where the regime
shift takes place.
AgricultureAtmospheric CO2
Deforestation
Demand
Droughts
ENSO like events
Erosion
Fertilizers use
Fishing
Floods
Global warming
Human population
Irrigation
Nutrients inputs
Precipitation
Sewage
Upwellings
Urbanization
Marine General Terrestrial

Marine Regime Shifts
Local centrality Global centrality
0.00 0.02 0.04 0.06 0.08 0.10 0.12
0.000.020.040.060.080.100.12
Eigenvector
Betweenness
Agriculture
Algae
Atmospheric CO2
Biodiversity
Bivalves abundance
Canopy−forming algae
Consumption preferences
Coral abundance
Daily relative coolingDeforestation
DemandDensity contrast in the water column
Disease outbreak
Dissolved oxygen
DroughtsENSO−like events frequency
Erosion
Fertilizers useFish
Fishing
Floods
Flushing
Global warming
Greenhouse gases
Habitat structural complexity
Herbivores
Human populationHurricanesImpoundmentsInvasive speciesIrrigationLandscape fragmentation/conversion
Leakage
Lobsters and meso−predators
Local water movementsLow tides frequency
Macroalgae abundance Macrophytes
Mid−predators
Mortality rate
Nekton
Noxious gases
Nutrients input
Ocean acidification
Organic matter
Other competitorsPerverse incentives
Phosphorous in water
Phytoplankton
Planktivore fish
Plankton and filamentous algae
PollutantsPrecipitationSedimentsSewage
Space
SST
StratificationSubsidiesSulfide releaseTechnologyThermal annomalies
Thermal low pressure
Top predators
TradeTragedy of the commons
Turbidity
Turf−forming algae
Unpalatability
Upwellings
Urban growth
Urchin barrenWater column density contrast
Water mixing
Water temperature
Water vapor
Wind stress
Zooplankton
Zooxanthellae
0 5 10 15
0510
Indegree
Outdegree
Agriculture
Algae
Atmospheric CO2
Biodiversity
Bivalves abundance
Canopy−forming algae
Consumption preferences
Coral abundance
Daily relative cooling
Deforestation
Demand
Density contrast in the water column
Disease outbreak
Dissolved oxygen
Droughts
ENSO−like events frequency
Erosion
Fertilizers use
Fish
Fishing
Floods
Flushing
Global warming
Greenhouse gases
Habitat structural complexity
Herbivores
Human population
Hurricanes
ImpoundmentsInvasive species
Irrigation
Landscape fragmentation/conversion
Leakage
Lobsters and meso−predators
Local water movements
Low tides frequency
Macroalgae abundance
Macrophytes
Mid−predators
Mortality rate
Nekton
Noxious gases
Nutrients input
Ocean acidification
Organic matterOther competitors
Perverse incentives
Phosphorous in water
PhytoplanktonPlanktivore fish
Plankton and filamentous algae
Pollutants
Precipitation
SedimentsSewage
Space
SST
Stratification
Subsidies
Sulfide releaseTechnologyThermal annomalies
Thermal low pressure
Top predators
Trade
Tragedy of the commons
Turbidity
Turf−forming algae
Unpalatability
Upwellings
Urban growth
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
02468
Indegree
Outdegree
Absorption of solar radiationAdvectionAerosol concentration
Agriculture
Albedo
Aquifers
Atmospheric CO2
Atmospheric temperature
Biomass
Brown cloudsCarbon storage
Cropland−Grassland area Deforestation
Demand
Droughts
DustENSO−like events frequency
ErosionEvapotranspiration
Fertilizers use
Fire frequency
Floods
Forest
Global warming
Grass dominance
Grazers
Grazing
Ground water table
Human population
Illegal logging
Immigration
Infrastructure development
Irrigation
Land conversion
Land−Ocean pressure gradient
Land−Ocean temperature gradient
Latent heat release
Lifting condensation levelLogging industryMoisture
Monsoon circulation
Native vegetation
Palatability
Precipitation
Productivity
Rainfall deficit
Ranching
Roughness
Savanna
Sea tides
Shadow_rooting
Soil impermeability
Soil moistureSoil productivity
Soil quality Soil salinitySolar radiation
SpaceSST
Temperature
Tree maturity
Vapor
VegetationWater availability
Water consumption
Water demandWater infrastructure
Wind stress
Woody plants dominance
0.00 0.02 0.04 0.06 0.08
0.000.020.040.060.08
Eigenvector
Betweenness
Absorption of solar radiation
Advection
Aerosol concentration
Agriculture
Albedo
Aquifers
Atmospheric CO2
Atmospheric temperature
Biomass
Brown clouds
Carbon storage
Cropland−Grassland area
Deforestation
Demand
Droughts
Dust
ENSO−like events frequency
Erosion
Evapotranspiration
Fertilizers use
Fire frequency
Floods
Forest
Global warming
Grass dominance
Grazers
Grazing
Ground water table
Human populationIllegal loggingImmigrationInfrastructure development
Irrigation
Land conversion
Land−Ocean pressure gradient
Land−Ocean temperature gradient
Latent heat release
Lifting condensation level
Logging industry
Moisture
Monsoon circulation
Native vegetation
Palatability
Precipitation
Productivity
Rainfall deficit
Ranching
Roughness
Savanna
Sea tides
Shadow_rooting
Soil impermeability
Soil moisture
Soil productivity
Soil quality
Soil salinity
Solar radiation
Space
SST
Temperature Tree maturity
Vapor
Vegetation
Water availability
Water consumption
Water demand
Water infrastructure
Wind stress
Woody plants dominance

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