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Université du Québec à Montréal omment l'analyse comparée des réseaux biologiques, écologiques, sémantiques et sociaux permet-elle d'évaluer l'universalité des propriétés structurell et fonctionnelles des réseaux des systèmes vivants Rapport de synthèse environnementale présenté comme exigence partielle du doctorat en sciences de l’environnement Frédéric Mertens

Université du Québec à Montréal

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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? - PowerPoint PPT Presentation

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Page 1: Université du Québec à Montréal

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

Page 2: Université du Québec à Montréal

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

Page 3: Université du Québec à Montréal

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

Page 4: Université du Québec à Montréal

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

Page 5: Université du Québec à Montréal

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

Page 6: Université du Québec à Montréal

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

Page 7: Université du Québec à Montréal

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

Page 8: Université du Québec à Montréal

Network measures and classification

N = total number of nodes = 14L = total number of links = 17

N, L

Page 9: Université du Québec à Montréal

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

Page 10: Université du Québec à Montréal

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

Page 11: Université du Québec à Montréal

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

Page 12: Université du Québec à Montréal

Network measures and classification

Reference network: Random network: nodes connected with probability p

D = D randomC = C random

Homogeneous degree distribution

Page 13: Université du Québec à Montréal

Network measures and classification

D >> D randomC >> C random

Regular network

Homogeneous degree distribution

Page 14: Université du Québec à Montréal

Network measures and classification

D D randomC >> C random

Small World Network: Ordered network with 20 shortcuts

Homogeneous degree distribution

Page 15: Université du Québec à Montréal

Network measures and classification

D D randomC >> C random

Heterogenous degree distribution

Small World Network: Ordered network with one highly connected node

Page 16: Université du Québec à Montréal

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

Page 17: Université du Québec à Montréal

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)

Page 18: Université du Québec à Montréal

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

Page 19: Université du Québec à Montréal

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.

Page 20: Université du Québec à Montréal

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

Page 21: Université du Québec à Montréal

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!

Page 22: Université du Québec à Montréal

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

Page 23: Université du Québec à Montréal

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

Page 24: Université du Québec à Montréal

On the universality of properties of networks

High diversity in degree distributions

Page 25: Université du Québec à Montréal

On the universality of properties of networks

Positive feed-back loops associated to the emergence of hubs

Protein networksGene duplication

Page 26: Université du Québec à Montréal

On the universality of properties of networks

Information seeking networkEmegence of opinion leaders

Positive feed-back loops associated to the emergence of hubs

Page 27: Université du Québec à Montréal

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

Page 28: Université du Québec à Montréal

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

Page 29: Université du Québec à Montréal

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

Page 30: Université du Québec à Montréal

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

Page 31: Université du Québec à Montréal

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

Page 32: Université du Québec à Montréal

Food webs: The links characteristics: directionality

Small-World Framework as tool to answer important questions about networks

Trophic relationship

Energy transfer

Page 33: Université du Québec à Montréal

Food webs: The links characteristics: intensity – energy tranfer

Small-World Framework as tool to answer important questions about networks

Page 34: Université du Québec à Montréal

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

Page 35: Université du Québec à Montréal

- -

++

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

Page 36: Université du Québec à Montréal

- -

++

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

Page 37: Université du Québec à Montréal

- -

++

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

Page 38: Université du Québec à Montréal

- -

++

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

Page 39: Université du Québec à Montréal

- -

++

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

Page 40: Université du Québec à Montréal

- -

++

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

Page 41: Université du Québec à Montréal

- -

++

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

Page 42: Université du Québec à Montréal

- -

++

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

Page 43: Université du Québec à Montréal

- -

++

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

Page 44: Université du Québec à Montréal

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

Page 45: Université du Québec à Montréal

Food webs: Negative feed-back loop – Prey / Predator relationship

-

+

Small-World Framework as tool to answer important questions about networks

Page 46: Université du Québec à Montréal

Food webs: Negative feed-back loop – Prey / Predator relationship

Time

Density

Small-World Framework as tool to answer important questions about networks

Page 47: Université du Québec à Montréal

Food webs: The spatial and temporal variations in food web structure

Small-World Framework as tool to answer important questions about networks

Page 48: Université du Québec à Montréal

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

Page 49: Université du Québec à Montréal

Food webs: The history of the system

Page 50: Université du Québec à Montréal

+

+

Selective fishing of carnivorous fish: human driven erosion of resilience

Food webs: The history of the system

Page 51: Université du Québec à Montréal

+

Selective fishing of herbivorous fish: human driven erosion of resilience

Food webs: The history of the system

Page 52: Université du Québec à Montréal

-

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

Page 53: Université du Québec à Montréal

-

The system shift to the second basin of attraction

Food webs: The history of the system

Page 54: Université du Québec à Montréal

Food webs: The history of the system

Page 55: Université du Québec à Montréal

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

Page 56: Université du Québec à Montréal

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

Page 57: Université du Québec à Montréal

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

Page 58: Université du Québec à Montréal

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

Page 59: Université du Québec à Montréal

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

Page 60: Université du Québec à Montréal

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

Page 61: Université du Québec à Montréal

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

Page 62: Université du Québec à Montréal

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?

Page 63: Université du Québec à Montréal

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?

Page 64: Université du Québec à Montréal

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

Page 65: Université du Québec à Montréal

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

Page 66: Université du Québec à Montréal

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?

Page 67: Université du Québec à Montréal

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?

Page 68: Université du Québec à Montréal

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?

Page 69: Université du Québec à Montréal

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

Page 70: Université du Québec à Montréal

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