Ecology 2.0: Coexistence and domination among interacting networks

Kaj Kolja KLEINEBERG

Marián BOGUÑÁ

Universitat de Barcelona

@[email protected] in Kaj Kolja Kleineberg

Coexistence and domination

among interacting networks

Ecology 2.0:

When I was 13 years old...

Digital revolutionWe are the first generation of the

Information is the new oil

Information is the new oil

and

are theoilfields

You

all digital services need

Attentionbut our time is limited

The digital world forms a complexECOSYSTEM

with networks as competing species

Can we preserve digital diversity?

Evolution of isolated networks

Motivation Evolution Ecology 2.0 Summary & outlook

Topological evolution of large quasi-isolated onlinesocial network exhibits a dynamical percolation transition

Dynamical percolation transition demands new classof growing network models.

10


Topological evolution of large quasi-isolated onlinesocial network exhibits a dynamical percolation transition

Dynamical percolation transition demands new classof growing network models.

10


Online social network emerges on top of pre-existingunderlying social structure via viral and mass media influence

Online social network layer

Traditional contactnetwork layer

ActiveOnline & offline

PassiveOnline & offlineSusceptibleOnly offline

11


Online social network emerges on top of pre-existingunderlying social structure via viral and mass media influence

Online social network layer

Traditional contactnetwork layer

ActiveOnline & offline

PassiveOnline & offlineSusceptibleOnly offline

Mass media activation Viral activation

Deactivation Viral reactivation

11


Below a critical value of the viral parameterthe 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 onlinesocial networks.

12


Below a critical value of the viral parameterthe 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 onlinesocial networks.

12


Evolution of the digital society reveals balancebetween viral and mass media influence

Underlyingsocial structure

Balance betweenviral & mass media

influence

Survival and deathof networks

PRX 4, 031046, 2014

13





influence


PRX 4, 031046, 2014

13





influence


PRX 4, 031046, 2014

13

Ecology 2.0


Gause's law impedes the coexistence of species competingfor the same unique resource and is often violated in nature

Gause's lawspecies competingfor same resourcecannot coexist

Rich-get-richereven slightestadvantage isamplified

Naturecommunities

contain handful ofcoexisting species

15





Naturecommunities


15





Naturecommunities


15


Digital ecosystem is formed by multiple networkscompeting for the attention of individuals

OSN 2

OSN 1

Underl.network

ActivePassiveSusceptible

Partial states}

Virality shareDistribution

between OSNsλi = ωi(ρ

a)λ

Rich-get-richermore active

networks obtainhigher share

Here: ωi = [ρai ]σ/

∑j [ρ

aj ]

σ

σ: activity affinity

Does rich-get-richer effect always lead to thedomination of a single network?

16



OSN 2

OSN 1

Underl.network


Partial states}



a)λ




∑j [ρ

aj ]

σ



16



OSN 2

OSN 1

Underl.network


Partial states}



a)λ




∑j [ρ

aj ]

σ



16



OSN 2

OSN 1

Underl.network


Partial states}



a)λ




∑j [ρ

aj ]

σ



16



OSN 2

OSN 1

Underl.network


Partial states}



a)λ




∑j [ρ

aj ]

σ



16


Nonlinear dynamics of network evolution enablecoexistence despite rich-get-richer mechanism

Meanfield:

ρ̇ai = ρai

[λ ⟨k⟩ωi(ρ

a) [1− ρai ]− 1

]+

λ

νωi(ρ

a)ρsi

ρ̇si = −λ

νωi(ρ

a)ρsi

[1 + ν ⟨k⟩ ρai

]Coexistence solution: ρai = 1− 1

λ⟨k⟩ and ρsi = 0

Unstable FPStable FP

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0Coexistence σ=0.8

ρ1a

ρ2a


0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0Domination σ=1.2

ρ1a

ρ2a

StableUnstable

0.50 0.75 1.00 1.25 1.500.00

0.25

0.50

0.75

Bifurcation diagram

ρ1a

0.0 0.5 1.0 1.5

0.50

0.75

σ

σ

ρ1,2

a

17



Meanfield:

ρ̇ai = ρai

[λ ⟨k⟩ωi(ρ

a) [1− ρai ]− 1

]+

λ

νωi(ρ

a)ρsi

ρ̇si = −λ

νωi(ρ

a)ρsi

[1 + ν ⟨k⟩ ρai




0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8


ρ1a

ρ2a


0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8


ρ1a

ρ2a

StableUnstable

0.50 0.75 1.00 1.25 1.500.00

0.25

0.50

0.75

Bifurcation diagram

ρ1a

0.0 0.5 1.0 1.5

0.50

0.75

σ

σ

ρ1,2

a


0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8


ρ1a

ρ2a


0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8


ρ1a

ρ2a

StableUnstable

0.50 0.75 1.00 1.25 1.500.00

0.25

0.50

0.75

Bifurcation diagram

ρ1a

0.0 0.5 1.0 1.5

0.50

0.75

σ

σ

ρ1,2

a

17



Meanfield:

ρ̇ai = ρai

[λ ⟨k⟩ωi(ρ

a) [1− ρai ]− 1

]+

λ

νωi(ρ

a)ρsi

ρ̇si = −λ

νωi(ρ

a)ρsi

[1 + ν ⟨k⟩ ρai




0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8


ρ1a

ρ2a


0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8


ρ1a

ρ2a

StableUnstable

0.50 0.75 1.00 1.25 1.500.00

0.25

0.50

0.75

Bifurcation diagram

ρ1a

0.0 0.5 1.0 1.5

0.50

0.75

σ

σ

ρ1,2

a


0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8


ρ1a

ρ2a


0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8


ρ1a

ρ2a

StableUnstable

0.50 0.75 1.00 1.25 1.500.00

0.25

0.50

0.75

Bifurcation diagram

ρ1a

0.0 0.5 1.0 1.5

0.50

0.75

σ

σ

ρ1,2

a

17



Meanfield:

ρ̇ai = ρai

[λ ⟨k⟩ωi(ρ

a) [1− ρai ]− 1

]+

λ

νωi(ρ

a)ρsi

ρ̇si = −λ

νωi(ρ

a)ρsi

[1 + ν ⟨k⟩ ρai




0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8


ρ1a

ρ2a


0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8


ρ1a

ρ2a

StableUnstable

0.50 0.75 1.00 1.25 1.500.00

0.25

0.50

0.75

Bifurcation diagram

ρ1a

0.0 0.5 1.0 1.5

0.50

0.75

σ

σ

ρ1,2

a


0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8


ρ1a

ρ2a


0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8


ρ1a

ρ2a

StableUnstable

0.50 0.75 1.00 1.25 1.500.00

0.25

0.50

0.75

Bifurcation diagram

ρ1a

0.0 0.5 1.0 1.5

0.50

0.75

σ

σ

ρ1,2

a

17



Meanfield:

ρ̇ai = ρai

[λ ⟨k⟩ωi(ρ

a) [1− ρai ]− 1

]+

λ

νωi(ρ

a)ρsi

ρ̇si = −λ

νωi(ρ

a)ρsi

[1 + ν ⟨k⟩ ρai




0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8


ρ1a

ρ2a


0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8


ρ1a

ρ2a

StableUnstable

0.50 0.75 1.00 1.25 1.500.00

0.25

0.50

0.75

Bifurcation diagram

ρ1a

0.0 0.5 1.0 1.5

0.50

0.75

σ

σ

ρ1,2

a

17


Maximum number of coexisting networksdepends on total virality and activity affinity

Overall attention to OSNs

Mor

e lik

ely

to e

ngag

ein

mor

e ac

tive

OS

Ns

Dom.2 coex.3 coex.4 coex.5 coex.

1 2 3 4 5 60.0

0.5

1.0

1.5

λ/λc1

σ

How many networks can coexist

Gause's law is violated as networks can coexistdespite rich-get-richer mechanism.

18




Mor

e lik

ely

to e

ngag

ein

mor

e ac

tive

OS

Ns


1 2 3 4 5 60.0

0.5

1.0

1.5

λ/λc1

σ


3 networks

2 networks

1 network

Stable configurations


18




Mor

e lik

ely

to e

ngag

ein

mor

e ac

tive

OS

Ns


1 2 3 4 5 6 7 8 9 100.0

0.5

1.0

1.5

λ/λc1

σ


3 networks

2 networks

1 network



18




Mor

e lik

ely

to e

ngag

ein

mor

e ac

tive

OS

Ns


1 2 3 4 5 6 7 8 9 100.0

0.5

1.0

1.5

λ/λc1

σ


3 networks

2 networks

1 network



18


Noise and the shape of the basin of attractionlimit observed digital diversity

Multi stabilityseveral stablefixed points

Noisein full dynamical

model

Dom.Coex.

2 4 6 8 100.0

0.4

0.8

1.2

λ/λc1

σ

Reachability for 2 networks

→ Effective critical lines for more networks saturate atsuccessively lower values σi,eff

c

Evenwithout precise knowledge of the empiricalparameters our theory explainsmoderate diversity.

19





model

Dom.Coex.

2 4 6 8 100.0

0.4

0.8

1.2

λ/λc1

σ



c


19





model

Dom.Coex.

2 4 6 8 100.0

0.4

0.8

1.2

λ/λc1

σ



c


19


Reachability of the coexistence solutiondepends on the influence of mass media

Reachabilityprobability to

coexist

Mass mediainfluences thereachability 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 ofmass media enhances the observeddigital diversity.

20


Reachability of the coexistence solutiondepends on the influence of mass media

Reachabilityprobability to

coexist

Mass mediainfluences thereachability 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 ofmass media enhances the observeddigital diversity.

20


Ecological theory of the digital world explains whywe observe a moderate number of coexisting networks

Coexistencedespite rich-get-richer

Damageto diversity is irreversible

Moderatedigital diversity observed

Media effectscontrols observed diversity

Sci. Rep. 5, 10268, 2015

21







Sci. Rep. 5, 10268, 2015

21







Sci. Rep. 5, 10268, 2015

21







Sci. Rep. 5, 10268, 2015

21

Summary & outlook


Multiscale theory of the digital world: From individual tiesto globally interacting networks

Individuals Interacting Worldwide

Mod

el Strength ofsocial ties

Res

ult Weak ties

have highertransmissibility

Viral + mediaeffect & under-lying structure

Viral effect is about fourtimes stronger

Rich-get-richer& diminishingreturns

Coexistance of amoderate numberof services

Network of net-works & effectiveactivity

Local networks canprevail under certainconditions

Focu

s

12

3

101 - 102 105 - 106 106 - 109 >109

Ord

er

Isolatednetwork networks

PRX 4, 031046 Sci. Rep. 5, 10268 arxiv:1504.01368 23




Mod


Res

ult Weak ties








Focu

s

12

3

101 - 102 105 - 106 106 - 109 >109

Ord

er


PRX 4, 031046 Sci. Rep. 5, 10268 arxiv:1504.01368 23




Mod


Res

ult Weak ties








Focu

s

12

3

101 - 102 105 - 106 106 - 109 >109

Ord

er


PRX 4, 031046 Sci. Rep. 5, 10268 arxiv:1504.01368 23




Mod


Res

ult Weak ties








Focu

s

12

3

101 - 102 105 - 106 106 - 109 >109

Ord

er


PRX 4, 031046 Sci. Rep. 5, 10268 arxiv:1504.01368 23

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.


Digital diversity is important. So write downthe 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:

• [email protected]

• @KoljaKleineberg

in • Kaj Kolja Kleineberg25


Digital diversity is important. So write downthe 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



• @KoljaKleineberg← Slides!



CREDITS

Vintage globe: jayneanddObsolete hardware David Haywardoil field: Damian GadalCat attention: David CornejoCables: jerry johnNetwork "ring": Adam BeasleyBoxing gloves: Gabriele FumeroWorld: Lorenzo BaldiniMegaphone: Alex Auda SamoraBiohazard: Shailendra ChouhanLayer icon: MentaltoyBalance (scale) icon: Roman KovbasyukDeath symbol: Mila RedkoPie Chart: P.J. Onori

Money sack: Lemon LiuTeam icon: Joshua JonesHand icon: irene hoffmanarm with muscle: Sergey KrivoyTime: Richard de VosNo: P.J. OnoriLocal: Phil GoodwinSummary (article) icon: Stefan Parnarovflower: Nishanth JoisRead magazine: Evan TravelsteadGlobe 2: Ealancheliyan s3 arrows: Juan Pablo Bravodices: Drew Ellis

Icons: thenounproject.com



• @KoljaKleineberg


Social Media

Ecology 2.0: Coexistence and domination among interacting networks