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Université du Québec à Montréal
Comment l'analyse comparée des réseaux biologiques, écologiques, sémantiques et sociaux permet-elle
d'évaluer l'universalité des propriétés structurelles et fonctionnelles des réseaux des systèmes vivants?
Rapport de synthèse environnementale présenté comme exigence partielle
du doctorat en sciences de l’environnement
Frédéric Mertens
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Structural and functional properties of networks
Introduction
Network measures and classification
Structural properties of networks
Functional properties of networks
On the universality of properties of networks
Small-World Framework as tool to answer important questions about networks: Two examples
Food websSocial networks
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Structural and functional properties of networks
Introduction
Network measures and classification
Structural properties of networks
Functional properties of networks
On the universality of properties of networks
Small-World Framework as tool to answer important questions about networks: Two examples
Food websSocial networks
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High number of elements, connected by a high number of relationships,analyzed at diferent hierachical levels.
Introduction
Complex living systems as networks
Exemple of networks
Amino-acids Proteins Individuals Populations
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Scholar-Google search : number of citations
2958: JC Venter et al. (2001) The Sequence of the Human Genome, Science.
2199: Granovetter M (1973) The strength of weak ties, American Journal of Sociology One of the most influential article in the social science
1350: Kohler G & Milstein C (1975) Continuous cultures of fused cells secreting specificity, Nature. (Nobel 1984)
709: Tonegawa S (1983) Somatic generation of antibody diversity, Nature. (Nobel 1987)
604: Petit et al. (1999) Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica, Nature. One of the most influential article in the environmental science
143: Wellman et al (1996) Computer networks as social networks, Annual Review of Sociology, 22: 213-238 One of the most cited article using “Social networks” as key word.
Introduction
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Scholar-Google search : number of citations
2958: JC Venter et al. (2001) The Sequence of the Human Genome, Science.
2199: Granovetter M (1973) The strength of weak ties, American Journal of Sociology One of the most influential article in the social science
1857: Watts DJ & Strogatz SH (1998) Collective dynamics of 'small-world' networks, Nature.
1490: Barabasi AL & Albert R (1999) Emergence of scaling in random networks, Science.
1350: Kohler G & Milstein C (1975) Continuous cultures of fused cells secreting specificity, Nature. (Nobel 1984)
709: Tonegawa S (1983) Somatic generation of antibody diversity, Nature. (Nobel 1987)
604: Petit et al. (1999) Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica, Nature. One of the most influential article in the environmental science
143: Wellman et al (1996) Computer networks as social networks, Annual Review of Sociology, 22: 213-238 One of the most cited article using “Social networks” as key word.
Introduction
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Structural and functional properties of networks
Introduction
Network measures and classification
Structural properties of networks
Functional properties of networks
On the universality of properties of networks
Small-World Framework as tool to answer important questions about networks: Two examples
Food websSocial networks
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Network measures and classification
N = total number of nodes = 14L = total number of links = 17
N, L
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Network measures and classification
d = distance between a pair of nodes = number of links on the shortest path between two nodes
d (A-B) = 1 d (J-M) = 4
D = average distance between every pairs of nodes
d and D
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Network measures and classification
ci = clustering coefficient of node i = number of links between node i’s neighbors / maximum possible number of links between them if the neighborhood was fully connected.C = average of ci over the network
ci and C
ci = 0 ci = 4 / 10 = 0,4 ci = 10 / 10 = 1
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Network measures and classification
k = degree = number of links of a nodeEX: k(A)=1 k(D)=5
<k> = mean degree = 2 (L/N) = 2 (17/14) = 2.4 Degree = number of links
Frequency
Degree distribution
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Network measures and classification
Reference network: Random network: nodes connected with probability p
D = D randomC = C random
Homogeneous degree distribution
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Network measures and classification
D >> D randomC >> C random
Regular network
Homogeneous degree distribution
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Network measures and classification
D D randomC >> C random
Small World Network: Ordered network with 20 shortcuts
Homogeneous degree distribution
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Network measures and classification
D D randomC >> C random
Heterogenous degree distribution
Small World Network: Ordered network with one highly connected node
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Structural and functional properties of networks
Introduction
Network measures and classification
Structural properties of networks
Functional properties of networks
On the universality of properties of networks
Small-World Framework as tool to answer important questions about networks: Two examples
Food websSocial networks
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Structural properties of networks
Summary of the data presented in table 3 of the text.
Network Number D D random C C random Hom. deg. dist.
Intra-molecular level Amino-acids in proteins 2 + + +
Molecular level Celular metabolism 2 + + -
Interactions between proteins 6 + + -Regulation of transcription 1 -
Celular level Neuronal network 1 + + +
Individual level Animal species 1 + + -Human species 11 + + -
2 - 1 + + + 1 - - + 2 + 1 + +
Population level Food-webs 5 + + -
2 + + + 13 + - + 3 + -
Animal and vegetal species - (majority)
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Structural and functional properties of networks
Introduction
Network measures and classification
Structural properties of networks
Functional properties of networks
On the universality of properties of networks
Small-World Framework as tool to answer important questions about networks: Two examples
Food websSocial networks
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Functional properties of networks
Network Short average distance
Amino-acids Stabilization of protein tertiary structure
High clustering
Transcription Information processing
Degree distribution
Molecular Network with homogeneous degree distributionSocial Vulnerability to node removal. Food webs
Network with heterogeneous degree distributionRobustness to random deletion and extreme vulnerability to targetted deletion ofthe most connected nodes.
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Structural and functional properties of networks
Introduction
Network measures and classification
Structural properties of networks
Functional properties of networks
On the universality of properties of networks
Small-World Framework as tool to answer important questions about networks: Two examples
Food websSocial networks
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On the universality of properties of networks
Small world properties: D D random
Short D is “easy” to achieve
Newman MEJ (2000) Models of the Small World: A Review, arXiv:cond-mat/0001118 v2 9
A small number of shortcuts A few hubs
Random networks
Weak links!
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On the universality of properties of networks
Small world properties: C >> C random
C >> C random for many kinds of networkswhen the reference random network has a Homogeneous Poisson Degree Distribution
Newman, M. E. J & Park, J. (2003). Why social networks are different from other types of networks. arXiv:cond-mat/0305612 v1 26.
Ex: Random network
N = 100 <k> 4,5
Homogeneous Poissondegree distribution
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On the universality of properties of networks
Small world properties: C >> C random
Newman, M. E. J & Park, J. (2003). Why social networks are different from other types of networks. arXiv:cond-mat/0305612 v1 26.
Ex: Random network
N = 100 <k> 4,5
Heterogeneousdegree distribution
C >> C random only for social networkswhen the reference random network has a degree distribution similar to the network being analyzed
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On the universality of properties of networks
High diversity in degree distributions
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On the universality of properties of networks
Positive feed-back loops associated to the emergence of hubs
Protein networksGene duplication
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On the universality of properties of networks
Information seeking networkEmegence of opinion leaders
Positive feed-back loops associated to the emergence of hubs
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On the universality of properties of networks
Friendship networkRegulation of the number of friends as a function of time and energy constrain
Negative feed-back loops regulating the number of links
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Structural and functional properties of networks
Introduction
Network measures and classification
Structural properties of networks
Functional properties of networks
On the universality of properties of networks
Small-World Framework as tool to answer important questions about networks: Two examples
Food websSocial networks
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The basic question:
To understand the links between food webs struture and dynamics
Sensibility to perturbationLoss of biodiversityEcosystem management
In structural analyses based on Small-World framework:
1. All nodes are considered as equivalent2. Links are bidirectional 3. Network is a snapshot in time and space
Small-World Framework as tool to answer important questions about networks
Food webs: The nodes characteristics
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To understand the links between food webs structure and dynamics
it is necessary to take into consideration:
1. The nodes characteristics
2. The links characteristics: intensity and directionality
3. Feed-back loops: positive and negative
4. The spatial and temporal variations in food web structure
5. The history of the system
Jordan F (2002) Comparability: the key to the applicability of food web research, Applied Ecology and Environmental Research, 1: 1-18. Borer et al. (2003). Topological approaches to food web analyses : a few modifications may improe our insights, Oikos, 99: 397-401. Berlow EL et al. (2004) Interaction strengths in food webs: issues and opportunities, Journal of Animal Ecology, 73: 585–598.
Small-World Framework as tool to answer important questions about networks
Food webs: The nodes characteristics
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Food webs: The nodes characteristics
Nodes can be:
Species
Different developmental stages When the trophic status of the species individuals change fundamentally trhough life cycle
Trophic functional groups
Small-World Framework as tool to answer important questions about networks
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Food webs: The links characteristics: directionality
Small-World Framework as tool to answer important questions about networks
Trophic relationship
Energy transfer
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Food webs: The links characteristics: intensity – energy tranfer
Small-World Framework as tool to answer important questions about networks
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The example of size-related predation
- -
++
Food webs: Positive feed-back loop: Amplification of perturbation in the network
Small-World Framework as tool to answer important questions about networks
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- -
++
Selective fishing, disease, etc.
Food webs: Positive feed-back loop: Amplification of perturbation in the network
The example of size-related predation
Small-World Framework as tool to answer important questions about networks
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- -
++
Food webs: Positive feed-back loop: Amplification of perturbation in the network
The example of size-related predation
Small-World Framework as tool to answer important questions about networks
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- -
++
Food webs: Positive feed-back loop: Amplification of perturbation in the network
The example of size-related predation
Small-World Framework as tool to answer important questions about networks
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- -
++
Size-related predation: example of positive feed-back loopFood webs: Positive feed-back loop: Amplification of perturbation in the network
The example of size-related predation
Small-World Framework as tool to answer important questions about networks
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- -
++
Food webs: Positive feed-back loop: Amplification of perturbation in the network
The example of size-related predation
Small-World Framework as tool to answer important questions about networks
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- -
++
Food webs: Positive feed-back loop: Amplification of perturbation in the network
The example of size-related predation
Small-World Framework as tool to answer important questions about networks
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- -
++
Food webs: Positive feed-back loop: Amplification of perturbation in the network
The example of size-related predation
Small-World Framework as tool to answer important questions about networks
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- -
++
Food webs: Positive feed-back loop: Amplification of perturbation in the network
The example of size-related predation
Small-World Framework as tool to answer important questions about networks
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- -
++
Food webs: Positive feed-back loop: Amplification of perturbation in the network
The example of size-related predation
Small-World Framework as tool to answer important questions about networks
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Food webs: Positive feed-back loop: Amplification of perturbation in the network
The example of size-related predation
Time
Density
Small-World Framework as tool to answer important questions about networks
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Food webs: Negative feed-back loop – Prey / Predator relationship
-
+
Small-World Framework as tool to answer important questions about networks
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Food webs: Negative feed-back loop – Prey / Predator relationship
Time
Density
Small-World Framework as tool to answer important questions about networks
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Food webs: The spatial and temporal variations in food web structure
Small-World Framework as tool to answer important questions about networks
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Basin of attraction 1 Basin of attraction 2
Jackson JBC et al. (2001) Historical OverÞshing and the Recent Collapse of Coastal Ecosystems, Science, 293: 629-638.
Food webs: Integrating network dynamics and the history of the system
Small-World Framework as tool to answer important questions about networks
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Food webs: The history of the system
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+
+
Selective fishing of carnivorous fish: human driven erosion of resilience
Food webs: The history of the system
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+
Selective fishing of herbivorous fish: human driven erosion of resilience
Food webs: The history of the system
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-
As the resilience of the system has been eroded by human intervention,
the system becomes very sensitive to a natural perturbation: a disease may
spread rapidly in the dense urchin population
Food webs: The history of the system
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-
The system shift to the second basin of attraction
Food webs: The history of the system
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Food webs: The history of the system
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Three examples:
Does the discussion network about mercury and health in an Amazonian community allow for an efficient circulation of information?Is this network robust in the context of a changing environment?
Do strong-ties social networks have small world properties?
How to promote horizontal communication in a research network?
Social networks
Small-World Framework as tool to answer important questions about networks
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Exemples 1 and 2
Brasilia Legal: 500 inhabitants
CARUSOMercury Exposure, Ecosystem
and Human Health in the Amazon
Small-World Framework as tool to answer important questions about networks
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Fishermen
Farmers
House wives
Health worker
School teacher
Ex 1: Robustness of mercury discussion network to promote the circulation of information in a changing environment
Small-World Framework as tool to answer important questions about networks
N=158Main component = 130<k>= 4.3D= 3.4D/Drand= 1.0C= 0.23C/Crand= 7.0
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Ex 1: Robustness of mercury discussion network to promote the circulation of information in a changing environment
Midwife
Small-World Framework as tool to answer important questions about networks
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Ex 1: Robustness of mercury discussion network to promote the circulation of information in a changing environment
Without the midwife
With the midwife
Small-World Framework as tool to answer important questions about networks
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Ex 1: Robustness of mercury discussion network to promote the circulation of information in a changing environment
Without the midwife
With the midwife
Small-World Framework as tool to answer important questions about networks
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Friendship – weak links Small World Network
N=336Main component = 336<k>= 6.4D= 5.4D/Drand=1.7C= 0.12C/Crand=6
Ex 2: Do strong-ties social networks have small world properties?
Small-World Framework as tool to answer important questions about networks
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Friendship – strong links (only reciprocal)NOT a Small World Network
N=336Only small components
Small-World Framework as tool to answer important questions about networks
Ex 2: Do strong-ties social networks have small world properties?
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Work – weak links Small World Network
N=336Main component = 287<k>= 5.7D= 5.0D/Drand= 1.5C= 0.23C/Crand= 11.5
Small-World Framework as tool to answer important questions about networks
Ex 2: Do strong-ties social networks have small world properties?
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Work – strong links (only reciprocal)NOT a Small World Network
N=336Main component = 130<k>= 3.0D= 6.7
Small-World Framework as tool to answer important questions about networks
Ex 2: Do strong-ties social networks have small world properties?
D/Drand= 1.5C= 0.23C/Crand= 11.5
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Bwetween spousesBetween brothers and/or sistersBetween parents and children
N=336Main component = 167<k>= 4.3
Family – strong linksNOT a Small World Network
Small-World Framework as tool to answer important questions about networks
Ex 2: Do strong-ties social networks have small world properties?
D= 7.5D/D rand= 2.1C= 0.68C/Crand= 25
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Small World network emerges from the multiple social relationships.
Dodds PS, Muhamad R and Watts DJ (2003) An Experimental Study of Search in Global Social Networks, Science, 301: 827-829.
A global social-search experiment: more than 60,000 e-mail users attempted to reach one of 18 target persons in 13 countries by forwarding messages to acquaintances. Mean chain lenght = 6
6
54
32
1 FriendRelative Co-worker
Friend
Friend
Small-World Framework as tool to answer important questions about networks
Ex 2: Do strong-ties social networks have small world properties?
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Build a strong tie social network using multiple social relationships
Friendship Family
Work
Small-World Framework as tool to answer important questions about networks
Ex 2: Do strong-ties social networks have small world properties?
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Friendship + Family + Work = emergence of a Small World Network
N=336Main component = 333<k>= 5.2D= 4.7D/Drand= 1.3C= 0.40C/Crand= 25
Small-World Framework as tool to answer important questions about networks
Ex 2: Do strong-ties social networks have small world properties?
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How to promote horizontal communication in a research network?
Research network Initiated by a Canadian professor and funded by a Canadian Agency
Heterogeneous degree distributionHigh degree of the canadian node= information overload
High average distance between nodes =Lack of horizontal communication
Small-World Framework as tool to answer important questions about networks
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How to promote horizontal communication in a research network?
Shortcuts between South-American nodes
Homogeneous degree distribution Short average distance between nodes
= efficient information flow= reduction of information overload= horizontal communication= new opportunities
Small-World Framework as tool to answer important questions about networks