This document discusses regime shifts, which are abrupt reorganizations of a system's structure and function. A regime corresponds to characteristic behavior maintained by mutually reinforcing feedback processes. Regime shifts occur when these feedbacks change due to changes in slow variables, external disturbances, or shocks. The document presents examples of regime shifts including vegetation shifts driven by changes in precipitation. It notes that regime shifts are common in the Anthropocene due to human impacts and discusses the need to better understand their patterns, interactions, likelihood, impacts, and how to avoid them. The rest of the document outlines a framework for comparing regime shifts using a database and examines global drivers of regime shifts like climate change, deforestation and fishing.

1. Regime Shifts in the Anthropocene
Juan-Carlos Rocha

2. The Anthropocene

3. The Anthropocene

4. 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?

5. 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.
low
low
high
Vegetation
collapse
Vegetation
recovery
high
low
Precipitation
Irreversible
Pre
cip
ita
tio
n
Pre
cip
ita
tio
n
high
Vegetation
Vegetation
low
Precipitation
low
high
Vegetation
Equilibria
high
Vegetation
high
Vegetation
high
low
collapse
high
Vegetation
Hystersis
Pre
cip
it
low
Pre
cip
ita
t
ion
Stability
Landscape
Threshold
ati
on
Gradual
low
Precipitation
Precipitation
(Gordon et al 2008)

6. 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.
J.S. Collie et al. / Progress in Oceanography 60 (2004) 281–302
287
(Collie 2004)
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).

7. Regime Shifts
Regime shifts are abrupt reorganization of a
system’s structure and function. A regime
correspond to characteristic behavior of the
system maintained by mutually reinforcing
processes or feedbacks. The shift occurs when
the strength of such feedbacks change, usually
driven by cumulative change in slow variables,
external disturbances or shocks.
Science challenge: understand multicausal phenomena where experimentation
is rarely an option and time for action a
constraint

8. 1. A comparative framework: The database
2. Global drivers of Regime Shifts
3. Future developments

9. 1. A comparative framework: The database

10. 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

18. Existence
Well
established
Dryland degradation
Forest to savanna
Steppe to tundra
Mangroves collapse
Encroachment
Fisheries collapse
Marine Eutrophication
Proposed
Contested
Soil structure
Contested
Marine foodwebs
Monsoon weakening
Termohaline circulation
Proposed
Mechanism
Bivalves collapse
Coral transitions
Lake Eutrophication
Hypoxia
Kelps transitions
Sea grass
Peatlands
River channel change
Salt marshes
Soil salinization
Floating plants
Greenland
Arctic sea ice
West Antarctica Ice Sheet
Tundra to forest
Well established

19. Ecosystem Services
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
Regime Shifts DataBase
Ecosystem services
!
Drivers ...
Supporting
Provisioning
Regulating
Cultural
Human well being
0
8
15
23
30

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

21. 2. Global drivers of Regime Shifts

22. Virtruvian Man, Leonardo Da Vinci

23. The human disease network
Kwang-Il
Goh*†‡§,
Michael E.
Cusick†‡¶,
David
Valleʈ,
Barton
Childsʈ,
Marc
Vidal†‡¶**,
´
´
and Albert-Laszlo
Network Properties of Complex Human Disease Genes
Identified through Genome-Wide Association Studies
´
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 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
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
Edited by H. Eugene Stanley, Boston University, Boston, MA, and approved April 3, 2007 (received for review February 14, 2007)
Prostate cancer
Perineal hypospadias
biological networks ͉ complex networks ͉ human genetics Pancreatic cancer
͉ systems
Lymphoma
biology ͉ diseasome
Wilms tumor
Wilms tumor
D
Breast cancer
Ovarian cancer
Spinal muscular atrophy
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 Mendelian Inheritance in Man (OMIM; ref. 18), a compendium of human
disease genes and phenotypes. As of December 2005, this list
disease genome
contained 1,284 disorders and 1,777 disease genes. OMIM initially
Disease Gene Network
focused on AR
monogenic disorders but in recent years has expanded
(DGN)
to include complex traits and the associated genetic mutations that
ATM
confer susceptibility to these common disorders (18). Although this
BRCA1
history introduces some biases, LMNA the disease gene record is far
and HEXB
BRCA2
ALS2
from complete, OMIM represents the most complete and up-toBSCL2
CDH1
date repository of all known VAPB
disease genes and the disorders they
GARS
GARS
confer. We manually classified each disorder into one of 22 disorder
HEXB
classes based on the physiological system affected [see supporting
AR
KRAS
information (SI) Text, SI Fig. 5, and SI Table 1 for details].
StartingLMNA the diseasome bipartite graph we generated two
from
ATM
BRCA2
BRIP1
biologically relevant network projections (Fig. 1). In the ‘‘human
MSH2
disease network’’ (HDN) nodes represent disorders, and two
PIK3CA
BRCA1
disorders are connected to each otherKRAS
if they share at least one gene
TP53
RAD54L
TP53 disorders (Figs. 1 and
in which mutations are associated with both
MAD1L1
2a). In the ‘‘disease gene network’’ (DGN) nodes represent disease
MAD1L1
CHEK2
RAD54L
genes, and two genes are connected if they are associated with the
PIK3CA
VAPB
same disorder (Figs. 1 and 2b). Next, we discuss the potential of
MSH2
CDH1
CHEK2
these networks to help us understand and represent in a single
BSCL2
framework all known disease gene and phenotype associations.
ecades-long efforts to map human disease loci,Sandhoff disease
at first genetPancreatic cancer
ically and later anemiaPapillary serous carcinoma
Fanconi physically (1), followed by recent positional
Lipodystrophy
T-cell lymphoblastic leukemia
cloning of many disease genes (2) and genome-wide association
Charcot-Marie-Tooth disease
studies (3), have generated an impressive list of disorder–gene
Ataxia-telangiectasia
Amyotrophic lateral sclerosis
association pairs (4, 5). In addition, recent efforts to map the
Silver spastic
protein–protein interactions in humans (6, 7), together paraplegiaefforts
with syndrome
ALS2
Spastic ataxia/paraplegia
to curate an extensive map of human metabolism (8) and regulatory
Properties BRIP1 the HDN. If each human disorder tends to have a
of
networks offer increasingly detailed maps of theFanconi anemia
relationships
distinct and unique genetic origin, then the HDN would be disbetween different disease genes. Most of the successful studies
connected into many single nodes corresponding to specific disorbuilding on these new approaches have focused, however, on a
ders or grouped into small clusters of a few closely related disorders.
single disease, using network-based tools to gain a better underFig. 1. Construction of the diseasome bipartite network. (Center) A small subset of OMIM-based disorder– disease gene associations (18), where circles and rectangles
In contrast, the obtained HDN displays many connections between
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 a disease gene if mutations in that gene lead to the specific disorder.
both individual disorders and disorder classes (Fig. 2a). Of
selected circle is proportional to the number of genes participating in the corresponding disorder, and the color corresponds to the disorder class to which the disease 1,284
The size of adisorder (9).
disorders, 867 there at least one link to in both. The width of
Here we take a conceptually different approach, exploring
belongs. (Left) The HDN projection of the diseasome bipartite graph, in which two disorders are connected if have is a gene that is implicated other disorders, and 516
disorders form implicated in both breast suggesting that the
a link is proportional to the number of genes andare implicated in both diseases. For example, three genes are a giant component,cancer and prostate cancer, genetic
whether human genetic disorders that the corresponding disease
resulting in a link ofrelated to each other at a higher level projection where two genes are connected ifdiseases, to some extent, are shared with other
origins of most they are involved in the same disorder. The width of
genes might be weight three between them. (Right) The DGN of cellular and
a link is proportional to the number of diseases with which the two genes are commonly associated. A full diseasome bipartite map is providedwithFig.disorder, s, has a
diseases. The number of genes associated as SI a 13.
organismal organization. Support for the validity of this approach
broad distribution (see SI Fig. 6a), indicating that most disorders
is provided by examples of genetic disorders that arise from
relate to a few disease genes, diseasome. Given of phenotypes, such
mutations disorders, whereas a gene (locus heterogeneity).
a few otherin more than a singlefew phenotypes such as colon Formentary, gene-centered view of thewhereas a handfulthat the links
as related phenotypic association between two genes, they
example, Zellweger syndrome is caused breast cancer in any of
cancer (linked to k ϭ 50 other disorders) or by mutations (k ϭ 30) atsignify deafness (s ϭ 41), leukemia (s ϭ 37), and colon cancer (s ϭ 34),
relate to dozens their phenotypic relatedness, which could be
least 11 genes, all associated with peroxisome biogenesis (10).represent a measure ofof genes (Fig. 2a). The degree (k) distribution of
represent hubs that are connected to a large number of distinct
Similarly, there are many examples of different mutations in
in future Fig. 6b) indicates that most disorders are interdisorders. The prominence of cancer among the most connected theusedHDN (SI studies, in conjunction with protein–proteinlinked to only
same gene (allelic heterogeneity) giving rise distinct cancer
disorders arises in part from the many clinicallyto phenotypes cur-actions (6, 7, 19), transcription factor-promoter interactions (20),
rently classified as different each other through common tumor
discover novel genetic interactions.
subtypes tightly connected withdisorders. For example, mutations inand metabolic reactions (8), to M.V., and A.-L.B. designed research; K.-I.G. and M.E.C.
Author contributions: D.V., B.C.,
TP53 have been linked to 11 clinically distinguishable cancer-In the DGN, research; K.-I.G. and M.E.C. analyzed are connectedM.E.C., D.V., M.V., and
repressor genes such as TP53 and PTEN.
performed 1,377 of 1,777 disease genes data; and K.-I.G., to other
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).
nization of the cell (12–17), the resulting network is improve
knowledge on disorder classes,it should be possible to naturally theWhereas the number of genes interest. in multiple diseases deThe authors declare no conflict of involved
and visibly clustered accordingapproach by developing Yet, there
single gene–single disorder to major disorder classes. a conceptualcreases rapidly a(SI Fig. 6d; light gray nodes in Fig. 2b), several
This article is PNAS Direct Submission.
are visible differences between different classes of disorders.
framework to link systematically all genetic disorders (the humandisease genes (e.g., TP53, PAX6) are involved in as many as 10 GO, Gene
Abbreviations: DGN, disease gene network; HDN, human disease network;
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
Ontology; OMIM, Online Mendelian Inheritance in Man; PCC,
many genes associatedresulting in a global view of (TP53, KRAS,
‘‘disease genome’’), with multiple types of cancer the ‘‘diseasome,’’
cient.
ERBB2, NF1, etc.) of all known several diseases with strong preand includes disorder/disease gene associations.Functional Clustering of HDN and DGN. To probe how the topology
the combined set
**To whom correspondence may be addressed. E-mail: alb@nd.edu or marc࿝vidal@
of thedfci.harvard.edu. GDN deviates from random, we randomly
HDN and
disposition to cancer, such as Fanconi anemia and ataxia telangiResults
shuffled article contains supporting information online at www.pnas.org/cgi/content/full/
ectasia, metabolic disorders do not appear to form a single distinct
This the associations between disorders and genes, while keepcluster but are underrepresentedWe constructed a bipartite graphing the number of links per each disorder and disease gene in the
0701361104/DC1.
Construction of the Diseasome. in the giant component and
overrepresented in disjoint sets of nodes. One set corresponds to allbipartite network unchanged. Interestingly,the USA
© 2007 by The National Academy of Sciences of the average size of the
consisting of two the small connected components (Fig. 2a). To
giant component of 104 randomized disease networks is 643 Ϯ 16,
quantify this difference, we measured the locus heterogeneity of
significantly larger than 516 (P Ͻ 10Ϫ4; for details of statistical
each disorder class and the fraction of disorders that are connected
www.pnas.org͞cgi͞doi͞10.1073͞pnas.0701361104
PNAS ͉ May 22, 2007 see SI Text), the actual
analyses of the results reported hereafter, ͉ vol. 104 ͉ no. 21 ͉ 8685– 8690
to each other in the HDN (see SI Text). We find that cancer and
size of the HDN (SI Fig. 6c). Similarly, the average size of the giant
neurological disorders show high locus heterogeneity and also
component from randomized gene networks is 1,087 Ϯ 20 genes,
represent the most connected disease classes, in contrast with
significantly larger than 903 (P Ͻ 10Ϫ4), the actual size of the DGN
metabolic, skeletal, and multiple disorders that have low genetic
(SI Fig. 6e). These differences suggest important pathophysiological
heterogeneity and are the least connected (SI Fig. 7).
clustering of disorders and disease genes. Indeed, in the actual
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.
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.
APPLIED PHYSICAL
SCIENCES
A network of disorders and disease genes linked by known disorder–
gene associations offers a platform to explore in a single graphtheoretic framework all known phenotype and disease gene associations, indicating the common genetic origin of many diseases. Genes
associated with similar disorders show both higher likelihood of
DISEASOME
physical interactions between their products and higher expression
profiling similarity for their transcripts, supporting the existence of
distinct disease-specific functional modules. Wedisease phenome
find that essential
Human Disease Network
Ataxia-telangiectasia
human genes are likely to encode hub proteins and are expressed
Perineal also would
widely in most tissues. This suggests that disease genes hypospadias
(HDN)
Androgen insensitivity
play a central role in the human interactome. In contrast, we find that
T-cell lymphoblastic leukemia
the vast majority of disease genes are nonessential and show no
Charcot-Marie-Tooth disease
Papillary serous carcinoma
tendency to encode hubLipodystrophy and their expression pattern indiproteins,
Prostate cancer
Spastic
cates that ataxia/paraplegia localizedparaplegia syndrome
they are Silver spastic in the functional periphery of the
Ovarian cancer
network. A selection-based model explains the observed difference
Sandhoff disease
Amyotrophic lateral sclerosis
between essential and disease genes and also suggests that diseases
Lymphoma
Spinal muscular atrophy
caused by somatic mutations should not be peripheral, a prediction
we confirm for cancer genes. insensitivity
Androgen
Breast cancer
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-R312008-000-10029-0 (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
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 network shows high modularity comparable to that of the human
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
PLoS ONE | www.plosone.org
1
November 2009 | Volume 4 | Issue 11 | e8090

25. Methods
•Bipartite network and
one-mode projections:
20 Regime shifts + 55
Drivers
4
•10 random bipartite
graphs to explore
significance of couplings:
mean degree, cooccurrence & clustering
coefficient statistics on
one-mode projections.
Drivers
Regime shifts

26. Methods
•Bipartite network and
one-mode projections:
20 Regime shifts + 55
Drivers
4
•10 random bipartite
graphs to explore
significance of couplings:
mean degree, cooccurrence & clustering
coefficient statistics on
one-mode projections.
Drivers
Regime shifts

27. Simulation results for 25 Regime Shifts across the
globe
Demand
Drivers Network
Co−occurrence Index
6
5
Global warming
5
7
9
12 14 16 19
0.4
Density
0.2
Sewage
2.0
2.2
2.4
2.6
Agriculture
Sediments
Rainfall variability
Floods
Sea level rise
Landscape fragmentation
Upwellings
0.0
1.8
Fishing
Human population
Urbanization
Temperature
Sea surface temperature
1
0
3
Erosion
Nutrients inputs
22
23
24
25
26
27
28
Degree
s−squared
Regime Shifts Network
Co−occurrence Index
29
Mean Degree
Clustering Coefficient
Average Degree in simulated
Regime Shifts Networks
0.6
0.8
River channel change
Eutrophication
0.2
0.4
Mangroves collapse
Forest to savannas
Hypoxia
0.2
Density
0.6
Bivalves collapse
0.4
Density
30
20
5 10
Soil structure
Soil salinization
Dry land degradation
Peatlands
Marine Eutrophication
Floating plants
0.20
0.25
0.30
0.35
Clustering coefficient
0.40
Kelps transitions
0.0
0.0
Coral transitions
0
Density
Deforestation
4
3
2
Density
15
10
5
0
1
Atmospheric CO2
Droughts
0.6
30
20
25
Degree distribution
Average Degree in simulated
Drivers Networks
10
11
12
13
s−squared
14
15
16
Monsoon weakening
18
19
20
21
22
23
Encroachment
Sea grass
Mean Degree
Fisheries collapse
Thermohaline circulation
Greenland
Salt marshes
Arctic sea ice
Marine foodwebs
Tundra to Forest
Western Antarctic IceSheet Collapse

28. Global drivers of Regime Shifts
Fishing
Urbanization
Nutrients inputs
Demand
Global warming
Deforestation
Human population
Agriculture
Atmospheric CO2
Droughts
Food production & climate
change drive the most
frequent drivers of regime
shifts
Few frequent drivers: Only 5
out of 55 drivers influence
more than 1/2 of the regime
shifts analyzed.
More shared drivers: 11
drivers interact with >50% of
other drivers when causing
regime shifts.

29. Count
0 15 30
Global drivers of Regime Shifts
2
4 6
Value
8
Biophysical
Biogeochemical Cycle
Land Cover Change
Biodiversity Loss
Water
Climate
Human Indirect Activities
Encroachment
Monsoon weakening
Soil salinization
Dry land degradation
Forest to savannas
Fisheries collapse
Marine foodwebs
Floating plants
Peatlands
Salt marshes
Soil structure
River channel change
Tundra to Forest
Greenland
Thermohaline circulation
Coral transitions
Bivalves collapse
Kelps transitions
Eutrophication
Hypoxia
0
Food production & climate
change drive the most
frequent drivers of regime
shifts
Few frequent drivers: Only 5
out of 55 drivers influence
more than 1/2 of the regime
shifts analyzed.
More shared drivers: 11
drivers interact with >50% of
other drivers when causing
regime shifts.

30. How drivers tend to interact?
Tundra to Forest
Thermohaline circulation
Greenland
Fisheries collapse
Marine foodwebs
Salt marshes
Monsoon weakening
Dry land degradation
Coral transitions
Encroachment
Kelps transitions
Floating plants
Eutrophication
Forest to savannas
Bivalves collapse
Peatlands
Hypoxia
Soil structure
Soil salinization
River channel change
Marine regime shifts
share significantly more
drivers and have more
similar feedback
mechanisms, suggesting
they may synchronize in
space and time.
Terrestrial regime shifts
share fewer drivers.
Higher diversity of drivers
makes management
more context
dependent.

31. Impacts of Regime Shifts
on Ecosystem Services

32. Impacts of Regime Shifts
on Ecosystem Services
Encroachment
Bivalves collapse
Dry land degradation
Sea Grass
Eutrophication
Greenland
Peatlands
Hypoxia
Kelps transitions
Marine foodwebs
Mangroves collapse
Termohaline circulation
Western Antarctic IceSheet Collapse
Forest to savannas
Soil salinization
Arctic sea ice
Tundra to Forest
Floating plants
Monsoon weakening
River channel change
Marine eutrophication
Fisheries collapse
Soil structure
Coral transitions
Salt marshes

33. Impacts of Regime Shifts
on Ecosystem Services
Air quality regulation
Encroachment
Bivalves collapse
Dry land degradation
Sea Grass
Eutrophication
Greenland
Timber
Primary production
Water regulation
Peatlands
Hypoxia
Kelps transitions
Marine foodwebs
Biodiversity
Mangroves collapse
Termohaline circulation
Western Antarctic IceSheet Collapse
Forest to savannas
Soil salinization
Arctic sea ice
Knowledge and educational values
Wild animal and plant foods
Regulation of soil erosion
Freshwater
Water cycling
Floating plants
River channel change
Marine eutrophication
Water purification
Fisheries
Feed, fuel & fiber crops
Soil formation
Nutrient cycling
Pest and disease regulation
Fisheries collapse
Natural hazard regulation
Soil structure
Coral transitions
Salt marshes
Climate regulation
Livestock
Tundra to Forest
Monsoon weakening
Wood fuel
Foodcrops
Pollination
Recreation
Aesthetic values
Spiritual and religious

34. Impacts of Regime Shifts
on Ecosystem Services
Air quality regulation
Encroachment
Bivalves collapse
Dry land degradation
Sea Grass
Eutrophication
Greenland
Timber
Primary production
Water regulation
Peatlands
Hypoxia
Kelps transitions
Marine foodwebs
Biodiversity
Mangroves collapse
Termohaline circulation
Western Antarctic IceSheet Collapse
Forest to savannas
Soil salinization
Arctic sea ice
Knowledge and educational values
Wild animal and plant foods
Regulation of soil erosion
Freshwater
Water cycling
Floating plants
River channel change
Marine eutrophication
Fisheries
Soil formation
Nutrient cycling
Pest and disease regulation
Fisheries collapse
Natural hazard regulation
Pollination
Recreation
Spiritual and religious
Aesthetic values
Color Key
and Histogram
0
5
Value
10
15
Feed, fuel & fiber crops
Freshwater
Pest and disease regulation
Regulation of soil erosion
Soil formation
Natural hazard regulation
Wood fuel
Timber
Water regulation
Livestock
Foodcrops
Spiritual and religious
Knowledge and educational values
Pollination
Air quality regulation
Climate regulation
Water cycling
Wild animal and plant foods
Aesthetic values
Fisheries
Water purification
Nutrient cycling
Primary production
Recreation
Biodiversity
Green house gases
Sea surface temperature
Fire frequency
Low tides
Thermal anomalies in summer
Invasive species
Aquaculture
Irrigation infrastructure
Tides
Surface melting ponds
Surface melt water
Stratospheric ozone
Ocean temperature (deep water)
Ice surface melting
Glaciers growth
Climate variability (SAM)
Glaciers
Drainage
Water infrastructure
Aquifers
Water availability
Food supply
Water stratification
Tragedy of the commons
Access to markets
Subsidies
Development policies
Immigration
Logging
Ranching (livestock)
Production intensification
Food prices
Labor availability
Hurricanes
Ocean acidification
Pollutants
Disease
Turbidity
Flushing
Urban storm water runoff
Fishing technology
Impoundments
Fertilizers use
Precipitation
ENSO like events
Upwellings
Infrastructure development
Sea level rise
Sediments
Irrigation
Erosion
Landscape fragmentation
Rainfall variability
Atmospheric CO2
Temperature
Nutrients inputs
Floods
Sewage
Fishing
Urbanization
Global warming
Agriculture
Deforestation
Droughts
Demand
Human population
0 300 700
Count
Water purification
Feed, fuel & fiber crops
Soil structure
Coral transitions
Salt marshes
Climate regulation
Livestock
Tundra to Forest
Monsoon weakening
Wood fuel
Foodcrops

35. Impacts of Regime Shifts
on Ecosystem Services
Air quality regulation
Encroachment
Bivalves collapse
Dry land degradation
Sea Grass
Eutrophication
Greenland
Timber
Primary production
Water regulation
Peatlands
Hypoxia
Kelps transitions
Marine foodwebs
Biodiversity
Mangroves collapse
Termohaline circulation
Western Antarctic IceSheet Collapse
Forest to savannas
Soil salinization
Arctic sea ice
Knowledge and educational values
Wild animal and plant foods
Regulation of soil erosion
Freshwater
Water cycling
Floating plants
River channel change
Marine eutrophication
Fisheries
Soil formation
Nutrient cycling
Pest and disease regulation
Fisheries collapse
Natural hazard regulation
Pollination
Recreation
Spiritual and religious
Aesthetic values
Color Key
and Histogram
0
5
Value
10
15
Feed, fuel & fiber crops
Freshwater
Pest and disease regulation
Regulation of soil erosion
Soil formation
Natural hazard regulation
Wood fuel
Timber
Water regulation
Livestock
Foodcrops
Spiritual and religious
Knowledge and educational values
Pollination
Air quality regulation
Climate regulation
Water cycling
Wild animal and plant foods
Aesthetic values
Fisheries
Water purification
Nutrient cycling
Primary production
Recreation
Biodiversity
Green house gases
Sea surface temperature
Fire frequency
Low tides
Thermal anomalies in summer
Invasive species
Aquaculture
Irrigation infrastructure
Tides
Surface melting ponds
Surface melt water
Stratospheric ozone
Ocean temperature (deep water)
Ice surface melting
Glaciers growth
Climate variability (SAM)
Glaciers
Drainage
Water infrastructure
Aquifers
Water availability
Food supply
Water stratification
Tragedy of the commons
Access to markets
Subsidies
Development policies
Immigration
Logging
Ranching (livestock)
Production intensification
Food prices
Labor availability
Hurricanes
Ocean acidification
Pollutants
Disease
Turbidity
Flushing
Urban storm water runoff
Fishing technology
Impoundments
Fertilizers use
Precipitation
ENSO like events
Upwellings
Infrastructure development
Sea level rise
Sediments
Irrigation
Erosion
Landscape fragmentation
Rainfall variability
Atmospheric CO2
Temperature
Nutrients inputs
Floods
Sewage
Fishing
Urbanization
Global warming
Agriculture
Deforestation
Droughts
Demand
Human population
0 300 700
Count
Water purification
Feed, fuel & fiber crops
Soil structure
Coral transitions
Salt marshes
Climate regulation
Livestock
Tundra to Forest
Monsoon weakening
Wood fuel
Foodcrops
• Ecosystem services
frequently affected by
regime shifts are:
biodiversity, food production
(fisheries, primary
production, nutrient cycling),
recreation and aesthetic
values.

36. Managing regime shift drivers
Drivers by Management Type
Tundra to Forest
River channel change
Thermohaline circulation
Greenland
Marine foodwebs
Peatlands
Monsoon weakening
Kelps transitions
Dry land degradation
Forest to savannas
Soil structure
Soil salinization
Salt marshes
Encroachment
Hypoxia
Coral transitions
Fisheries collapse
Eutrophication
Bivalves collapse
Floating plants
International cooperation
to manage most drivers
of 75% of regime shifts.
Local
National
International
Regulating single drivers,
such as Climate change,
won’t prevent regime
shifts.
Regulating local drivers
can build resilience to
global drivers
0.0
0.2
0.4
0.6
Proportion of RS Drivers
0.8
1.0
Avoiding regime shifts
requires poly-centric
institutions.

37. 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.
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.

38. 3. Future developments
1. Theoretical stuff:
• ERGMs **
• Causal Networks *
• Cascading effects **
• Controllability of Regime Shifts.
!
2. Empirical stuff:
• Trade Networks
• Ecosystem Services Text Mining **

39. Methods
•Bipartite network and onemode projections: 20
Regime shifts + 55 Drivers
Drivers
Regime shifts
4
•10 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 Shift Database
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
Ecosystem services
Spatial scale
Ecosystem processes
Temporal scale
Ecosystem type
Reversibility
Impact on human well being
Evidence
Land use
...

40. Work in Progress
Causal Networks: Cascading effects and regime shifts controllability
Causal-loop diagrams is a
technique to map out the
feedback structure of a system
(Sterman 2000)

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

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

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

44. Cascading effects
D1
RS1
RS2
RS3
Floating plants
Kelp transitions
Arctic salt marsh
Eutrophication
Fisheries collapse
River channel change
Bivalves collapse
Foodwebs
Soil structure
Hypoxia
Forks: when sharing a driver
synchronize two regime shifts
Coral bleaching
Coral transitions
Encroachment
Forest to savanna
!RS1
...
D1
RS2
Causal chains: the domino effect
Soil salinization
!
Desertification
Forest to cropland
Monsoon
RS1
!
Peatlands
Thermohaline
Tundra to forest
Greenland icesheet collapse
Arctic Icesheet collapse
!
D2
D1
RS2
Inconvenient feedbacks: when two
shifts reinforce or dampen each
other

45. 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.
ARTICLE
doi:10.1038/nature10011
Controllability of complex networks
´ ´
´
Yang-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 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.
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
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
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 controllability of complex systems emerging in nature and engineering have
resisted advances. The difficulty is rooted in the fact that two independent 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
the components. Thus, progress has been possible only in systems where
both layers are well mapped, such as the control of synchronized networks7–10, small biological circuits11 and rate control for communication 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 commonly emerge in complex systems.
Network controllability
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 identifies 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 N 3 NM controllability matrix
C~(B, AB, A2 B, . . . , AN{1 B)
has full rank, that is
rank(C)~N
ð2Þ
ð3Þ
This represents the mathematical condition for controllability, and is
called Kalman’s controllability rank condition1,2 (Fig. 1a). In practical
terms, controllability can be also posed as follows. Identify the minimum
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
signal u1 offers full control over the system, as the states of nodes x1, x2, x3
and x4 are uniquely determined by the signal u1(t) (Fig. 1c). In contrast,

46. 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.
ARTICLE
doi:10.1038/nature10011
Controllability of complex networks
´ ´
´
Yang-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 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.
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
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
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 controllability of complex systems emerging in nature and engineering have
resisted advances. The difficulty is rooted in the fact that two independent 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
the components. Thus, progress has been possible only in systems where
both layers are well mapped, such as the control of synchronized networks7–10, small biological circuits11 and rate control for communication 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 commonly emerge in complex systems.
Network controllability
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 identifies 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 N 3 NM controllability matrix
C~(B, AB, A2 B, . . . , AN{1 B)
has full rank, that is
rank(C)~N
ð2Þ
ð3Þ
This represents the mathematical condition for controllability, and is
called Kalman’s controllability rank condition1,2 (Fig. 1a). In practical
terms, controllability can be also posed as follows. Identify the minimum
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
signal u1 offers full control over the system, as the states of nodes x1, x2, x3
and x4 are uniquely determined by the signal u1(t) (Fig. 1c). In contrast,

47. Trade Networks
• Test empirically cascading
effects by using trade networks
• Which countries are driving the
resource collapse of others
• Where trade matters?
1. Fisheries collapse
2. Land transitions

48. Using language to detect potential change in
ecosystem services in the light of ecological
surprises
Juan Carlos Rocha & Robin Wikström

49. Foley et al. 2005. Science
Ecosystem services are the benefits humans receive from nature (MEA 2005)

50. Foley et al. 2005. Science
Ecosystem services are the benefits humans receive from nature (MEA 2005)

51. LDA (illustrative example by Blei)

52. Model selection & number of topics
VEM5
VEM4
VEM4
VEM3
VEM3
VEM2
VEM2
VEM1
• We test Variational
Estimation Methods
(VEM), correlated topic
models (CTM) & Gibbs
sampling.
VEM5
VEM1
0.010
0.015
0.020
1600
alpha
1800
2000
2200
Perplexity
VEM5
VEM5
VEM4
VEM4
VEM3
VEM3
VEM2
VEM2
VEM1
VEM1
-3050000 -3000000 -2950000
logLik
• We tested 5 models with
different topic numbers
(10:100)
• VEM algorithm with 80
topics fit the best the
MEA training dataset
0.2
0.4
0.6
Entropy
0.8

53. 1500
0
0.2
0.4
0.6
Value
0.8
Chapter 27 Urban Systems.pdf.txt
Chapter 19 Coastal Systems.pdf.txt
Chapter 13 Climate and Air Quality.pdf.txt
Chapter 11 Biodiversity Regulation of Ecosystem Services.pdf.txt
Chapter 20 Inland Water Systems-2.pdf.txt
Chapter 23 Island Systems.pdf.txt
Chapter 2 Analytical Approaches for Assessing Ecosystem Condition and Human Well-being.
Chapter 24 Mountain Systems.pdf.txt
Chapter 18 Marine Fisheries Systems.pdf.txt
Chapter 26 Cultivated Systems.pdf.txt
Chapter 4 Biodiversity.pdf.txt
Chapter 9 Timber Fuel and Fiber.pdf.txt
Chapter 7 Fresh Water.pdf.txt
Chapter 21 Forest and Woodland Systems.pdf.txt
Chapter 1 MA Conceptual Framework.pdf.txt
Chapter 5 Ecosystem Conditions and Human Well-being.pdf.txt
Chapter 6 Vulnerable Peoples and Places.pdf.txt
Chapter 17 Cultural and Amenity Services.pdf.txt
Chapter 12 Nutrient Cycling.pdf.txt
Chapter 8 Food.pdf.txt
Chapter 25 Polar Systems.pdf.txt
Nelson-2005-Chapter 3 Drivers of ecosystem change summary chapter.pdf.txt
Chapter 16 Regulation of Natural Hazards Floods and Fires.pdf.txt
Chapter 22 Dryland Systems.pdf.txt
Chapter 15 Waste Processing and Detoxification.pdf.txt
Chapter 28 Synthesis Condition and Trends in Systems and Services Trade-offs for Human W
Chapter 10 New Products and Industries from Biodiversity.pdf.txt
Chapter 14 Human Health Ecosystem Regulation of Infectious Diseases.pdf.txt
29
79
27
55
46
15
57
12
9
53
62
47
34
66
69
59
1
73
5
60
4
11
19
44
31
14
68
50
67
8
37
22
65
24
76
56
26
39
18
23
16
38
2
78
74
30
40
3
75
61
43
20
17
45
72
64
48
49
25
21
36
70
52
28
58
41
80
32
35
51
77
6
10
7
33
54
13
63
71
42
Count
Color Key
and Histogram
Topics detection
Topics = 80
Millenium Ecosystem Assessment

54. Topics detection
Topics = 80
Millenium Ecosystem Assessment

55. Topics matching
Ecosystem Services
Ecosystem Processes
Soil formation
Primary production
Nutrient cycling
Water cycling
Biodiversity
Provisioning services
Freshwater
Food crops
Livestock
Fisheries
Wild animals and plants products
Timber
Wood fuel
Feed, fuel and fiber crops
Hydropower
Regulating services
Air quality regulation
Climate regulation
Water purification
Regulation of soil erosion
Pest and disease
Pollination
Natural hazards
Cultural services
Recreation
Aesthetic values
Knowledge and educational values
Spiritual and religious
Topics
Words
59, 69
nutrient, ecosystem, soil, global, ocean, cycling
39, 60, 26, 5 species, plant, richness, biodiversity, services
62, 68
12, 66, 3
water, world, human, supply, freshwater, river
food, production, countries, growth, health
44, 19
marine, fisheries, fish, species, coastal, system
34, 43
47
47
forest, countries, world, global, tropical, fao
production, forest, wood, products, timber, fao
production, forest, wood, products, timber, fao
2, 38 16
2, 38, 16
55
46
29
carbon, atmospheric, ecosystem, land, air
global, climate, emissions, change, atmospheric
waste, water, environment, human, nitrogen
dryland, land, soil, degradation, water
disease, human, health, infectious, malaria
15
11, 4
fire, events, floods, natural, regulation, impact
cultural, human, ecosystems, landscapes,
heritage

56. Topics detection
Topics = 80
Corpus = 381 papers

57. 0 8000
Count
Color Key
and Histogram
0.1 0.4
Value
46
55
68
59
44
2
11
12
4
60
3
47
43
34
15
66
69
62
29
26
5
16
38
39
19
Topics detection
Topics = 80
Corpus = 381 papers

58. 250
4
8
Value
Bivalves collapse (2)
Coral transitions (27)
Dry land degradation (18)
Encroachment (7)
Eutrophication (13)
Fisheries collapse (52)
Floating plants (1)
Forest to savannas (29)
Greenland (1)
Hypoxia (4)
Kelps transitions (6)
Marine foodwebs (40)
Monsoon weakening (5)
Peatlands (3)
River channel change (5)
Salt marshes (0)
Soil salinization (1)
Soil structure (0)
Thermohaline circulation (1)
Tundra to forest (2)
Theory (97)
Other cases (132)
Topics detection
Cultural services
Natural hazards
Pest and disease
Regulation of soil erosion
Water purification
Climate regulation
Air quality regulation
Feed, fuel & timber crops
Woodfuel
Timber
Fisheries
Food crops
Freshwater
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
Termohaline circulation
Tundra to Forest
Biodiversity
Value
0
1
Nutrient cycling
0.4
Soil formation
Primary production
Nutrient cycling
Water cycling
Biodiversity
Freshwater
Foodcrops
Livestock
Fisheries
Wild animal and plant foods
Timber
Wood fuel
Feed, fuel & fiber crops
Hydropower
Air quality regulation
Climate regulation
Water purification
Regulation of soil erosion
Pest and disease regulation
Pollination
Natural hazard regulation
Recreation
Aesthetic values
Knowledge and educational values
Spiritual and religious
0
Color Key
and Histogram
0
Count
180
Count
Color Key
and Histogram
Topics = 80
Corpus = 381 papers

59. 1
250
0
4
8
Value
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
Termohaline circulation
Tundra to Forest
Topics detection
Nutrient cycling
Cultural services
Freshwater
Pest and disease
Regulation of soil erosion
Water purification
Natural hazards
Feed, fuel & timber crops
Woodfuel
Timber
Climate regulation
Air quality regulation
Food crops
Fisheries
Other cases (132)
Theory (97)
Fisheries collapse (52)
Marine foodwebs (40)
Dry land degradation (18)
Eutrophication (13)
Monsoon weakening (5)
Coral transitions (27)
Peatlands (3)
Tundra to forest (2)
Thermohaline circulation (1)
Greenland (1)
Bivalves collapse (2)
Floating plants (1)
Soil salinization (1)
Soil structure (0)
Salt marshes (0)
River channel change (5)
Encroachment (7)
Kelps transitions (6)
Hypoxia (4)
Forest to savannas (29)
Biodiversity
0.4
Value
Soil formation
Primary production
Nutrient cycling
Water cycling
Biodiversity
Freshwater
Foodcrops
Livestock
Fisheries
Wild animal and plant foods
Timber
Wood fuel
Feed, fuel & fiber crops
Hydropower
Air quality regulation
Climate regulation
Water purification
Regulation of soil erosion
Pest and disease regulation
Pollination
Natural hazard regulation
Recreation
Aesthetic values
Knowledge and educational values
Spiritual and religious
0
Color Key
and Histogram
0
Count
180
Count
Color Key
and Histogram
Topics = 80
Corpus = 381 papers

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