![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 marcvidal@
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](https://image.slidesharecdn.com/bascomptelab-talk131106-131107050849-phpapp02/85/Bascompte-lab-talk131106-23-320.jpg)
Bascompte lab talk131106
- 1. Regime Shifts in the Anthropocene Juan-Carlos Rocha
- 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 marcvidal@ 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/