Université du Québec à Montréal

1. 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

2. 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 webs Social networks

3. 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 webs Social networks

4. Introduction Complex living systems as networks High number of elements, connected by a high number of relationships, analyzed at diferent hierachical levels. Exemple of networks Amino-acids Proteins Individuals Populations

5. Introduction 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.

6. Introduction 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.

7. 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 webs Social networks

8. Network measures and classification N, L N = total number of nodes = 14 L = total number of links = 17

9. Network measures and classification d and D 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

10. Network measures and classification ci and C ci = 0 ci = 4 / 10 = 0,4 ci = 10 / 10 = 1 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

11. Network measures and classification Degree distribution Frequency k = degree = number of links of a node EX: k(A)=1 k(D)=5 <k> = mean degree = 2 (L/N) = 2 (17/14) = 2.4 Degree = number of links

12. Network measures and classification Reference network: Random network: nodes connected with probability p D = D random C = C random Homogeneous degree distribution

13. Network measures and classification Regular network D >> D random C >> C random Homogeneous degree distribution

14. Network measures and classification Small World Network: Ordered network with 20 shortcuts D D random C >> C random Homogeneous degree distribution

15. Network measures and classification Small World Network: Ordered network with one highly connected node D D random C >> C random Heterogenous degree distribution

16. 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 webs Social networks

17. Structural properties of networks 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) Summary of the data presented in table 3 of the text.

18. 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 webs Social networks

19. Functional properties of networks NetworkShort average distance Amino-acids Stabilization of protein tertiary structure High clustering Transcription Information processing Degree distribution Molecular Network with homogeneous degree distribution Social Vulnerability to node removal. Food webs Network with heterogeneous degree distribution Robustness to random deletion and extreme vulnerability to targetted deletion of the most connected nodes.

20. 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 webs Social networks

21. On the universality of properties of networks Small world properties: D D random Short D is “easy” to achieve Random networks Weak links! A small number of shortcuts A few hubs Newman MEJ (2000) Models of the Small World: A Review, arXiv:cond-mat/0001118 v2 9

22. On the universality of properties of networks Small world properties: C >> C random C >> C random for many kinds of networks when the reference random network has a Homogeneous Poisson Degree Distribution Ex: Random network N = 100 <k> 4,5 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.

23. On the universality of properties of networks Small world properties: C >> C random C >> C random only for social networks when the reference random network has a degree distribution similar to the network being analyzed Ex: Random network N = 100 <k> 4,5 Heterogeneous 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.

24. On the universality of properties of networks High diversity in degree distributions

25. On the universality of properties of networks Positive feed-back loops associated to the emergence of hubs Protein networks Gene duplication

26. On the universality of properties of networks Positive feed-back loops associated to the emergence of hubs Information seeking network Emegence of opinion leaders

27. On the universality of properties of networks Negative feed-back loops regulating the number of links Friendship network Regulation of the number of friends as a function of time and energy constrain

28. 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 webs Social networks

29. Small-World Framework as tool to answer important questions about networks Food webs: The nodes characteristics • The basic question: • To understand the links between food webs struture and dynamics • Sensibility to perturbation • Loss of biodiversity • Ecosystem management • In structural analyses based on Small-World framework: • All nodes are considered as equivalent • Links are bidirectional • Network is a snapshot in time and space

30. Small-World Framework as tool to answer important questions about networks Food webs: The nodes characteristics • To understand the links between food webs structure and dynamics • it is necessary to take into consideration: • The nodes characteristics • The links characteristics: intensity and directionality • Feed-back loops: positive and negative • The spatial and temporal variations in food web structure • 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 AnimalEcology, 73: 585–598.

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

32. Small-World Framework as tool to answer important questions about networks Food webs: The links characteristics: directionality Energy transfer Trophic relationship

33. Small-World Framework as tool to answer important questions about networks Food webs: The links characteristics: intensity – energy tranfer

34. Small-World Framework as tool to answer important questions about networks + + - - Food webs: Positive feed-back loop: Amplification of perturbation in the network The example of size-related predation

35. Small-World Framework as tool to answer important questions about networks + + - - Food webs: Positive feed-back loop: Amplification of perturbation in the network Selective fishing, disease, etc. The example of size-related predation

36. Small-World Framework as tool to answer important questions about networks + + - - Food webs: Positive feed-back loop: Amplification of perturbation in the network The example of size-related predation

37. Small-World Framework as tool to answer important questions about networks + + - - Food webs: Positive feed-back loop: Amplification of perturbation in the network The example of size-related predation

38. Small-World Framework as tool to answer important questions about networks + + - - Size-related predation: example of positive feed-back loop Food webs: Positive feed-back loop: Amplification of perturbation in the network The example of size-related predation

39. Small-World Framework as tool to answer important questions about networks + + - - Food webs: Positive feed-back loop: Amplification of perturbation in the network The example of size-related predation

40. Small-World Framework as tool to answer important questions about networks + + - - Food webs: Positive feed-back loop: Amplification of perturbation in the network The example of size-related predation

41. Small-World Framework as tool to answer important questions about networks + + - - Food webs: Positive feed-back loop: Amplification of perturbation in the network The example of size-related predation

42. Small-World Framework as tool to answer important questions about networks + + - - Food webs: Positive feed-back loop: Amplification of perturbation in the network The example of size-related predation

43. Small-World Framework as tool to answer important questions about networks + + - - Food webs: Positive feed-back loop: Amplification of perturbation in the network The example of size-related predation

44. Small-World Framework as tool to answer important questions about networks Food webs: Positive feed-back loop: Amplification of perturbation in the network Density Time The example of size-related predation

45. Small-World Framework as tool to answer important questions about networks + - Food webs: Negative feed-back loop – Prey / Predator relationship

46. Small-World Framework as tool to answer important questions about networks Food webs: Negative feed-back loop – Prey / Predator relationship Density Time

47. Small-World Framework as tool to answer important questions about networks Food webs: The spatial and temporal variations in food web structure

48. Small-World Framework as tool to answer important questions about networks Food webs: Integrating network dynamics and the history of the system Basin of attraction 2 Basin of attraction 1 Jackson JBC et al. (2001) Historical OverÞshing and the RecentCollapse of Coastal Ecosystems, Science, 293: 629-638.

49. Food webs: The history of the system

50. Food webs: The history of the system + + Selective fishing of carnivorous fish: human driven erosion of resilience