The overwhelming success of the web 2.0, with online social networks as key actors, has induced a paradigm shift in the nature of human interactions. The user-driven character of these services for the first time has allowed researchers to quantify large-scale social patterns. However, the mechanisms that determine the fate of networks at a system level are still poorly understood. For instance, the simultaneous existence of numerous digital services naturally raises the question under which conditions these services can coexist. In analogy to population dynamics, the digital world is forming a complex ecosystem of interacting networks whose fitnesses depend on their ability to attract and maintain users' attention, which constitutes a limited resource. In this paper, we introduce an ecological theory of the digital world which exhibits a stable coexistence of several networks as well as the domination of a single one, in contrast to the principle of competitive exclusion. Interestingly, our model also predicts that the most probable outcome is the coexistence of a moderate number of services, in agreement with empirical observations.

1. Kaj Kolja
KLEINEBERG
Marián
BOGUÑÁ
Universitat de Barcelona
@KoljaKleinebergkkl@ffn.ub.edu in Kaj Kolja Kleineberg
Coexistence and
domination
among interacting
networks
Ecology 2.0:

2. When I was 13 years old...

3. Digital revolution
We are the first generation of the

4. Information is the new oil

5. Information is the new oil
and
are the
oilfields
You

6. all digital services need
Attention
but our time is limited

7. The digital world forms a complex
ECOSYSTEM
with networks as competing species

8. Can we preserve
digital diversity?

9. Evolution of isolated networks

10. Motivation Evolution Ecology 2.0 Summary & outlook
Topological evolution of large quasi-isolated online
social network exhibits a dynamical percolation transition
10

11. Motivation Evolution Ecology 2.0 Summary & outlook
Topological evolution of large quasi-isolated online
social network exhibits a dynamical percolation transition
Dynamical percolation transition demands new class
of growing network models.
10

12. Motivation Evolution Ecology 2.0 Summary & outlook
Online social network emerges on top of pre-existing
underlying social structure via viral and mass media influence
Online social
network layer
Traditional contact
network layer
Active
Online & offline
Passive
Online & offline
Susceptible
Only offline
11

13. Motivation Evolution Ecology 2.0 Summary & outlook
Online social network emerges on top of pre-existing
underlying social structure via viral and mass media influence
Online social
network layer
Traditional contact
network layer
Active
Online & offline
Passive
Online & offline
Susceptible
Only offline
Mass media activation Viral activation
Deactivation Viral reactivation
11

14. Motivation Evolution Ecology 2.0 Summary & outlook
Below a critical value of the viral parameter
the network becomes entirely passive
Λc
0.00 0.02 0.04 0.06 0.08
0.00
0.05
0.10
0.15
0.20
0.25
Λ
ΡA
12

15. Motivation Evolution Ecology 2.0 Summary & outlook
Below a critical value of the viral parameter
the network becomes entirely passive
Λc
0.00 0.02 0.04 0.06 0.08
0.00
0.05
0.10
0.15
0.20
0.25
Λ
ΡA
Our model allows for the survival and death of online
social networks.
12

16. Motivation Evolution Ecology 2.0 Summary & outlook
Evolution of the digital society reveals balance
between viral and mass media influence
Underlying
social structure
PRX 4, 031046, 2014
13

17. Motivation Evolution Ecology 2.0 Summary & outlook
Evolution of the digital society reveals balance
between viral and mass media influence
Underlying
social structure
Balance between
viral & mass media
influence
PRX 4, 031046, 2014
13

18. Motivation Evolution Ecology 2.0 Summary & outlook
Evolution of the digital society reveals balance
between viral and mass media influence
Underlying
social structure
Balance between
viral & mass media
influence
Survival and death
of networks
PRX 4, 031046, 2014
13

19. Ecology 2.0

20. Motivation Evolution Ecology 2.0 Summary & outlook
Gause's law impedes the coexistence of species competing
for the same unique resource and is often violated in nature
Gause's law
species competing
for same resource
cannot coexist
15

21. Motivation Evolution Ecology 2.0 Summary & outlook
Gause's law impedes the coexistence of species competing
for the same unique resource and is often violated in nature
Gause's law
species competing
for same resource
cannot coexist
Rich-get-richer
even slightest
advantage is
amplified
15

22. Motivation Evolution Ecology 2.0 Summary & outlook
Gause's law impedes the coexistence of species competing
for the same unique resource and is often violated in nature
Gause's law
species competing
for same resource
cannot coexist
Rich-get-richer
even slightest
advantage is
amplified
Nature
communities
contain handful of
coexisting species
15

23. Motivation Evolution Ecology 2.0 Summary & outlook
Digital ecosystem is formed by multiple networks
competing for the attention of individuals
OSN 2
OSN 1
Underl.
network
Active
Passive
Susceptible
Partial
states}
16

24. Motivation Evolution Ecology 2.0 Summary & outlook
Digital ecosystem is formed by multiple networks
competing for the attention of individuals
OSN 2
OSN 1
Underl.
network
Active
Passive
Susceptible
Partial
states}
Virality share
Distribution
between OSNs
λi = ωi(ρa)λ
16

25. Motivation Evolution Ecology 2.0 Summary & outlook
Digital ecosystem is formed by multiple networks
competing for the attention of individuals
OSN 2
OSN 1
Underl.
network
Active
Passive
Susceptible
Partial
states}
Virality share
Distribution
between OSNs
λi = ωi(ρa)λ
Rich-get-richer
more active
networks obtain
higher share
16

26. Motivation Evolution Ecology 2.0 Summary & outlook
Digital ecosystem is formed by multiple networks
competing for the attention of individuals
OSN 2
OSN 1
Underl.
network
Active
Passive
Susceptible
Partial
states}
Virality share
Distribution
between OSNs
λi = ωi(ρa)λ
Rich-get-richer
more active
networks obtain
higher share
Here: ωi = [ρa
i ]σ/
∑
j[ρa
j ]σ
σ: activity affinity
16

27. Motivation Evolution Ecology 2.0 Summary & outlook
Digital ecosystem is formed by multiple networks
competing for the attention of individuals
OSN 2
OSN 1
Underl.
network
Active
Passive
Susceptible
Partial
states}
Virality share
Distribution
between OSNs
λi = ωi(ρa)λ
Rich-get-richer
more active
networks obtain
higher share
Here: ωi = [ρa
i ]σ/
∑
j[ρa
j ]σ
σ: activity affinity
Does rich-get-richer effect always lead to the
domination of a single network?
16

28. Motivation Evolution Ecology 2.0 Summary & outlook
Nonlinear dynamics of network evolution enable
coexistence despite rich-get-richer mechanism
Meanfield:
˙ρa
i = ρa
i
[
λ ⟨k⟩ ωi(ρa
) [1 − ρa
i ] − 1
]
+
λ
ν
ωi(ρa
)ρs
i
˙ρs
i = −
λ
ν
ωi(ρa
)ρs
i
[
1 + ν ⟨k⟩ ρa
i
]
Coexistence solution: ρa
i = 1 − 1
λ⟨k⟩ and ρs
i = 0
17

29. Motivation Evolution Ecology 2.0 Summary & outlook
Nonlinear dynamics of network evolution enable
coexistence despite rich-get-richer mechanism
Meanfield:
˙ρa
i = ρa
i
[
λ ⟨k⟩ ωi(ρa
) [1 − ρa
i ] − 1
]
+
λ
ν
ωi(ρa
)ρs
i
˙ρs
i = −
λ
ν
ωi(ρa
)ρs
i
[
1 + ν ⟨k⟩ ρa
i
]
Coexistence solution: ρa
i = 1 − 1
λ⟨k⟩ and ρs
i = 0
Unstable FP
Stable FP
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Coexistence σ=0.8
ρ1
a
ρ2
a
Unstable FP
Stable FP
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Domination σ=1.2
ρ1
a
ρ2
a
Stable
Unstable
0.50 0.75 1.00 1.25 1.50
0.00
0.25
0.50
0.75
Bifurcation diagram
ρ1
a
0.0 0.5 1.0 1.5
0.50
0.75
σ
σ
ρ1,2
a
17

30. Motivation Evolution Ecology 2.0 Summary & outlook
Nonlinear dynamics of network evolution enable
coexistence despite rich-get-richer mechanism
Meanfield:
˙ρa
i = ρa
i
[
λ ⟨k⟩ ωi(ρa
) [1 − ρa
i ] − 1
]
+
λ
ν
ωi(ρa
)ρs
i
˙ρs
i = −
λ
ν
ωi(ρa
)ρs
i
[
1 + ν ⟨k⟩ ρa
i
]
Coexistence solution: ρa
i = 1 − 1
λ⟨k⟩ and ρs
i = 0
Unstable FP
Stable FP
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Coexistence σ=0.8
ρ1
a
ρ2
a
Unstable FP
Stable FP
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Domination σ=1.2
ρ1
a
ρ2
a
Stable
Unstable
0.50 0.75 1.00 1.25 1.50
0.00
0.25
0.50
0.75
Bifurcation diagram
ρ1
a
0.0 0.5 1.0 1.5
0.50
0.75
σ
σ
ρ1,2
a
17

31. Motivation Evolution Ecology 2.0 Summary & outlook
Nonlinear dynamics of network evolution enable
coexistence despite rich-get-richer mechanism
Meanfield:
˙ρa
i = ρa
i
[
λ ⟨k⟩ ωi(ρa
) [1 − ρa
i ] − 1
]
+
λ
ν
ωi(ρa
)ρs
i
˙ρs
i = −
λ
ν
ωi(ρa
)ρs
i
[
1 + ν ⟨k⟩ ρa
i
]
Coexistence solution: ρa
i = 1 − 1
λ⟨k⟩ and ρs
i = 0
Unstable FP
Stable FP
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Coexistence σ=0.8
ρ1
a
ρ2
a
Unstable FP
Stable FP
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Domination σ=1.2
ρ1
a
ρ2
a
Stable
Unstable
0.50 0.75 1.00 1.25 1.50
0.00
0.25
0.50
0.75
Bifurcation diagram
ρ1
a
0.0 0.5 1.0 1.5
0.50
0.75
σ
σ
ρ1,2
a
17

32. Motivation Evolution Ecology 2.0 Summary & outlook
Nonlinear dynamics of network evolution enable
coexistence despite rich-get-richer mechanism
Meanfield:
˙ρa
i = ρa
i
[
λ ⟨k⟩ ωi(ρa
) [1 − ρa
i ] − 1
]
+
λ
ν
ωi(ρa
)ρs
i
˙ρs
i = −
λ
ν
ωi(ρa
)ρs
i
[
1 + ν ⟨k⟩ ρa
i
]
Coexistence solution: ρa
i = 1 − 1
λ⟨k⟩ and ρs
i = 0
Unstable FP
Stable FP
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Coexistence σ=0.8
ρ1
a
ρ2
a
Unstable FP
Stable FP
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Domination σ=1.2
ρ1
a
ρ2
a
Stable
Unstable
0.50 0.75 1.00 1.25 1.50
0.00
0.25
0.50
0.75
Bifurcation diagram
ρ1
a
0.0 0.5 1.0 1.5
0.50
0.75
σ
σ
ρ1,2
a
17

33. Motivation Evolution Ecology 2.0 Summary & outlook
Maximum number of coexisting networks
depends on total virality and activity affinity
Overall attention to OSNs
Morelikelytoengage
inmoreactiveOSNs
Dom.
2 coex.
3 coex.
4 coex.
5 coex.
1 2 3 4 5 6
0.0
0.5
1.0
1.5
λ/λc
1
σ
How many networks can coexist
18

34. Motivation Evolution Ecology 2.0 Summary & outlook
Maximum number of coexisting networks
depends on total virality and activity affinity
Overall attention to OSNs
Morelikelytoengage
inmoreactiveOSNs
Dom.
2 coex.
3 coex.
4 coex.
5 coex.
1 2 3 4 5 6
0.0
0.5
1.0
1.5
λ/λc
1
σ
How many networks can coexist
3 networks
2 networks
1 network
Stable configurations
18

35. Motivation Evolution Ecology 2.0 Summary & outlook
Maximum number of coexisting networks
depends on total virality and activity affinity
Overall attention to OSNs
Morelikelytoengage
inmoreactiveOSNs
How many networks can coexist
1 2 3 4 5 6 7 8 9 10
0.0
0.5
1.0
1.5
λ/λc
1
σ
Dom.
2 coex.
3 coex.
4 coex.
5 coex.
3 networks
2 networks
1 network
Stable configurations
18

36. Motivation Evolution Ecology 2.0 Summary & outlook
Maximum number of coexisting networks
depends on total virality and activity affinity
Overall attention to OSNs
Morelikelytoengage
inmoreactiveOSNs
How many networks can coexist
1 2 3 4 5 6 7 8 9 10
0.0
0.5
1.0
1.5
λ/λc
1
σ
Dom.
2 coex.
3 coex.
4 coex.
5 coex.
3 networks
2 networks
1 network
Stable configurations
Gause's law is violated as networks can coexist
despite rich-get-richer mechanism.
18

37. Motivation Evolution Ecology 2.0 Summary & outlook
Noise and the shape of the basin of attraction
limit observed digital diversity
Multi stability
several stable
fixed points
Noise
in full dynamical
model
Dom.
Coex.
2 4 6 8 10
0.0
0.4
0.8
1.2
λ/λc
1
σ
Reachability for 2 networks
19

38. Motivation Evolution Ecology 2.0 Summary & outlook
Noise and the shape of the basin of attraction
limit observed digital diversity
Multi stability
several stable
fixed points
Noise
in full dynamical
model
Dom.
Coex.
2 4 6 8 10
0.0
0.4
0.8
1.2
λ/λc
1
σ
Reachability for 2 networks
→ Effective critical lines for more networks saturate at
successively lower values σi,eff
c
19

39. Motivation Evolution Ecology 2.0 Summary & outlook
Noise and the shape of the basin of attraction
limit observed digital diversity
Multi stability
several stable
fixed points
Noise
in full dynamical
model
Dom.
Coex.
2 4 6 8 10
0.0
0.4
0.8
1.2
λ/λc
1
σ
Reachability for 2 networks
→ Effective critical lines for more networks saturate at
successively lower values σi,eff
c
Even without precise knowledge of the empirical
parameters our theory explains moderate diversity.
19

40. Motivation Evolution Ecology 2.0 Summary & outlook
Reachability of the coexistence solution
depends on the influence of mass media
Reachability
probability to
coexist
Mass media
influences the
reachability 0 4 8 12
0.0
0.2
0.4
0.6
0.8
1.0
ν
Probability coex.
Recall: µi = λi/ν, small ν means high media influence
20

41. Motivation Evolution Ecology 2.0 Summary & outlook
Reachability of the coexistence solution
depends on the influence of mass media
Reachability
probability to
coexist
Mass media
influences the
reachability 0 4 8 12
0.0
0.2
0.4
0.6
0.8
1.0
ν
Probability coex.
Recall: µi = λi/ν, small ν means high media influence
The influence of mass media enhances the observed
digital diversity.
20

42. Motivation Evolution Ecology 2.0 Summary & outlook
Ecological theory of the digital world explains why
we observe a moderate number of coexisting networks
Coexistence
despite rich-get-richer
Sci. Rep. 5, 10268, 2015
21

43. Motivation Evolution Ecology 2.0 Summary & outlook
Ecological theory of the digital world explains why
we observe a moderate number of coexisting networks
Coexistence
despite rich-get-richer
Damage
to diversity is irreversible
Sci. Rep. 5, 10268, 2015
21

44. Motivation Evolution Ecology 2.0 Summary & outlook
Ecological theory of the digital world explains why
we observe a moderate number of coexisting networks
Coexistence
despite rich-get-richer
Damage
to diversity is irreversible
Moderate
digital diversity observed
Sci. Rep. 5, 10268, 2015
21

45. Motivation Evolution Ecology 2.0 Summary & outlook
Ecological theory of the digital world explains why
we observe a moderate number of coexisting networks
Coexistence
despite rich-get-richer
Damage
to diversity is irreversible
Moderate
digital diversity observed
Media effects
controls observed diversity
Sci. Rep. 5, 10268, 2015
21

46. Summary & outlook

47. Motivation Evolution Ecology 2.0 Summary & outlook
Multiscale theory of the digital world: From individual ties
to globally interacting networks
Individuals Interacting Worldwide
Model
Strength of
social ties
Result
Weak ties
have higher
transmissibility
Viral + media
effect & under-
lying structure
Viral effect
is about four
times stronger
Rich-get-richer
& diminishing
returns
Coexistance of a
moderate number
of services
Network of net-
works & effective
activity
Local networks can
prevail under certain
conditions
Focus
12
3
101
- 102
105
- 106
106
- 109
>109
Order
Isolated
network networks
PRX 4, 031046 Sci. Rep. 5, 10268 arxiv:1504.01368 23

48. Motivation Evolution Ecology 2.0 Summary & outlook
Multiscale theory of the digital world: From individual ties
to globally interacting networks
Individuals Interacting Worldwide
Model
Strength of
social ties
Result
Weak ties
have higher
transmissibility
Viral + media
effect & under-
lying structure
Viral effect
is about four
times stronger
Rich-get-richer
& diminishing
returns
Coexistance of a
moderate number
of services
Network of net-
works & effective
activity
Local networks can
prevail under certain
conditions
Focus
12
3
101
- 102
105
- 106
106
- 109
>109
Order
Isolated
network networks
PRX 4, 031046 Sci. Rep. 5, 10268 arxiv:1504.01368 23

49. Motivation Evolution Ecology 2.0 Summary & outlook
Multiscale theory of the digital world: From individual ties
to globally interacting networks
Individuals Interacting Worldwide
Model
Strength of
social ties
Result
Weak ties
have higher
transmissibility
Viral + media
effect & under-
lying structure
Viral effect
is about four
times stronger
Rich-get-richer
& diminishing
returns
Coexistance of a
moderate number
of services
Network of net-
works & effective
activity
Local networks can
prevail under certain
conditions
Focus
12
3
101
- 102
105
- 106
106
- 109
>109
Order
Isolated
network networks
PRX 4, 031046 Sci. Rep. 5, 10268 arxiv:1504.01368 23

50. Motivation Evolution Ecology 2.0 Summary & outlook
Multiscale theory of the digital world: From individual ties
to globally interacting networks
Individuals Interacting Worldwide
Model
Strength of
social ties
Result
Weak ties
have higher
transmissibility
Viral + media
effect & under-
lying structure
Viral effect
is about four
times stronger
Rich-get-richer
& diminishing
returns
Coexistance of a
moderate number
of services
Network of net-
works & effective
activity
Local networks can
prevail under certain
conditions
Focus
12
3
101
- 102
105
- 106
106
- 109
>109
Order
Isolated
network networks
PRX 4, 031046 Sci. Rep. 5, 10268 arxiv:1504.01368 23

51. Just as a monopoly in economy
is a threat to free markets, the lack of
poses a threat to the
digital diversity
freedom of information.

52. Motivation Evolution Ecology 2.0 Summary & outlook
Digital diversity is important. So write down
the references and contact information now!
References:
K.-K. Kleineberg, M. Boguña.
PRX 4, 031046, 2014
K.-K. Kleineberg, M. Boguña.
Sci. Rep. 5, 10268, 2015
K.-K. Kleineberg, M. Boguña.
arxiv:1504.01368, 2015
Kaj Kolja Kleineberg:
• kkl@ffn.ub.edu
• @KoljaKleineberg
in • Kaj Kolja Kleineberg
25

53. Motivation Evolution Ecology 2.0 Summary & outlook
Digital diversity is important. So write down
the references and contact information now!
References:
K.-K. Kleineberg, M. Boguña.
PRX 4, 031046, 2014
K.-K. Kleineberg, M. Boguña.
Sci. Rep. 5, 10268, 2015
K.-K. Kleineberg, M. Boguña.
arxiv:1504.01368, 2015
Kaj Kolja Kleineberg:
• kkl@ffn.ub.edu
• @KoljaKleineberg ← Slides!
in • Kaj Kolja Kleineberg
25

54. Motivation Evolution Ecology 2.0 Summary & outlook
CREDITS
Vintage globe: jayneandd
Obsolete hardware David Hayward
oil field: Damian Gadal
Cat attention: David Cornejo
Cables: jerry john
Network "ring": Adam Beasley
Boxing gloves: Gabriele Fumero
World: Lorenzo Baldini
Megaphone: Alex Auda Samora
Biohazard: Shailendra Chouhan
Layer icon: Mentaltoy
Balance (scale) icon: Roman Kovbasyuk
Death symbol: Mila Redko
Pie Chart: P.J. Onori
Money sack: Lemon Liu
Team icon: Joshua Jones
Hand icon: irene hoffman
arm with muscle: Sergey Krivoy
Time: Richard de Vos
No: P.J. Onori
Local: Phil Goodwin
Summary (article) icon: Stefan Parnarov
flower: Nishanth Jois
Read magazine: Evan Travelstead
Globe 2: Ealancheliyan s
3 arrows: Juan Pablo Bravo
dices: Drew Ellis
Icons: thenounproject.com
Kaj Kolja Kleineberg:
• kkl@ffn.ub.edu
• @KoljaKleineberg
in • Kaj Kolja Kleineberg
26