evolution and ecology of the digital world

Kaj Kolja KLEINEBERG

Marián BOGUÑÁ

@KoljaKleineberg

Universitat de Barcelona

[email protected]

EVOLUTIONand

Digital world

Ecologyof the

all digital services need

Attentionbut our time is limited

The digital world forms a complexECOSYSTEM

with networks as competing species

Can we preservedigital diversity?

Evolution of isolated networks

Motivation Evolution Ecology 2.0 Summary & Outlook

The topological evolution of large quasi-isolated OSNexhibits a dynamical percolation transition

Dynamical percolation transition demands new classof growing network models.

The topological evolution of large quasi-isolated OSNexhibits a dynamical percolation transition

Dynamical percolation transition demands new classof growing network models.

The pre-existing underlying social structureforms the backbone of the evolution of the OSN

Online social network layer

Traditional contactnetwork layer

ActiveOnline & offline

PassiveOnline & offlineSusceptibleOnly offline

The pre-existing underlying social structureforms the backbone of the evolution of the OSN

Online social network layer

Traditional contactnetwork layer

ActiveOnline & offline

PassiveOnline & offlineSusceptibleOnly offline

Mass media activation Viral activation

Deactivation Viral reactivation

Final snapshot of empirical network as proxy forunderlying structure allows rigorous model validation

Finalsnapshot

Empiricalevolution

Extractsnapshots

Empiricaldata

Modelevolution

Compare

Finalsnapshot

Can we reproduce the entire topological evolutionof the empirical network?

Final snapshot of empirical network as proxy forunderlying structure allows rigorous model validation

Finalsnapshot

Empiricalevolution

Extractsnapshots

Empiricaldata

Modelevolution

Compare

Finalsnapshot

Can we reproduce the entire topological evolutionof the empirical network?

Model precisely reproduces the entire topological evolutionand reveals balance between virality and media influence

Model results ParametersGCC model

2nd comp. model

ASPL model x4

GCC Pokec

2nd comp. Pokec

ASPL Pokec x4

103 104 105 1060

Virality is about four timesstronger thanmass media

Interplay between virality andmass media dynamicsis the main underlying principle of the OSN evolution.

2nd comp. model

ASPL model x4

GCC Pokec

2nd comp. Pokec

ASPL Pokec x4

103 104 105 1060

2nd comp. model

ASPL model x4

GCC Pokec

2nd comp. Pokec

ASPL Pokec x4

103 104 105 1060

Below a critical value of the viral parameterthe network becomes entirely passive

0.00 0.02 0.04 0.06 0.08

Our model predicts the survival and death of onlinesocial networks.

Below a critical value of the viral parameterthe network becomes entirely passive

0.00 0.02 0.04 0.06 0.08

Our model predicts the survival and death of onlinesocial networks.

The microscopic picture revealsthe role of strong and weak ties

N103 104 105 1060.00

Clustering

Tie strength:

Transmissibility: λij ∝ λ [•+ 1]η

Individuals have a higher tendency to subscribe ifinvited byweaker social contacts.

The microscopic picture revealsthe role of strong and weak ties

N103 104 105 1060.00

Clustering

Tie strength:

Transmissibility: λij ∝ λ [•+ 1]η

Individuals have a higher tendency to subscribe ifinvited byweaker social contacts.

Evolution of the digital society revealsbalance between viral and mass media influence

Underlying social structuredetermines topological

evolution

Balanceof viral and mass media

influence

Survival and deathof networks

Weak tieshave higher transmissibility

PRX 4, 031046, 2014

Ecology 2.0

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

Gause's lawspecies competingfor same resourcecannot coexist

Rich-get-richereven slightestadvantage isamplified

Naturecommunities

contain handful ofcoexisting species

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

Underl.network

ActivePassiveSusceptible

Partial states}

Virality shareDistribution

between OSNsλi = ωi(ρ

Rich-get-richermore active

networks obtainhigher share

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

Underl.network

Partial states}

Underl.network

Partial states}

Underl.network

Partial states}

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

Meanfield:

ρ̇ai = ρai

[λ ⟨k⟩ωi(ρ

a) [1− ρai ]− 1

νωi(ρ

a)ρsi

ρ̇si = −λ

νωi(ρ

a)ρsi

[1 + ν ⟨k⟩ ρai

]Rich-get-richer: ωi = [ρai ]

σ/∑

j [ρaj ]

σ → σ activity affinity

Unstable FPStable FP

0.0 0.2 0.4 0.6 0.8 1.00.0

1.0Coexistence σ=0.8

0.0 0.2 0.4 0.6 0.8 1.00.0

1.0Domination σ=1.2

StableUnstable

0.50 0.75 1.00 1.25 1.500.00

Bifurcation diagram

0.0 0.5 1.0 1.5

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

Meanfield:

ρ̇ai = ρai

[λ ⟨k⟩ωi(ρ

a) [1− ρai ]− 1

νωi(ρ

a)ρsi

ρ̇si = −λ

νωi(ρ

a)ρsi

[1 + ν ⟨k⟩ ρai

]Rich-get-richer: ωi = [ρai ]

σ/∑

j [ρaj ]

σ → σ activity affinity

0.0 0.2 0.4 0.6 0.8 1.00.0

1.0Coexistence σ=0.8

0.0 0.2 0.4 0.6 0.8 1.00.0

1.0Domination σ=1.2

StableUnstable

0.50 0.75 1.00 1.25 1.500.00

Bifurcation diagram

0.0 0.5 1.0 1.5

Maximum number of coexisting networksis determined by total virality and activity affinity

Overall attention to OSNs

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

1 2 3 4 5 60.0

λ/λc1

How many networks can coexist

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

1 2 3 4 5 60.0

λ/λc1

3 networks

2 networks

1 network

Stable configurations

1 2 3 4 5 6 7 8 9 100.0

λ/λc1

3 networks

2 networks

1 network

1 2 3 4 5 6 7 8 9 100.0

λ/λc1

3 networks

2 networks

1 network

Noise and the shape of the basin of attraction limitobserved digital diversity starting from empty networks

Multi stabilityseveral stablefixed points

Noisein full dynamical

Dom.Coex.

2 4 6 8 100.0

λ/λc1

Reachability for 2 networks

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

Evenwithout precise knowledge of the empiricalparameters our theory predictsmoderate diversity.

Dom.Coex.

2 4 6 8 100.0

λ/λc1

Dom.Coex.

2 4 6 8 100.0

λ/λc1

Reachability of the coexistence solutiondepends on the influence of mass media

Reachabilityprobability to

coexist

Mass mediainfluences thereachability 0 4 8 12

Probability coex.

Recall: µi = λi/ν, small ν means high media influence

The influence ofmass media enhances the observeddigital diversity.

Reachability of the coexistence solutiondepends on the influence of mass media

Reachabilityprobability to

coexist

Mass mediainfluences thereachability 0 4 8 12

Probability coex.

Recall: µi = λi/ν, small ν means high media influence

The influence ofmass media enhances the observeddigital diversity.

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

Coexistencedespite

rich-get-richer

Moderateobserved diversity

Media effectscontrols observed

diversity

arxiv:1410.8865, 2014

Summary & Outlook

Multiscale theory of the digital world revealsconditions for sustaining digital diversity

Individuals Interacting Worldwide

el Strength ofsocial ties

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

101 - 102 105 - 106 106 - 109 >109

Isolatednetwork networks

PRX 4, 031046, 2014 arxiv:1410.8865, 2014 To appear23

ult Weak ties

101 - 102 105 - 106 106 - 109 >109

ult Weak ties

101 - 102 105 - 106 106 - 109 >109

ult Weak ties

101 - 102 105 - 106 106 - 109 >109

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.

IMAGE CREDITS

Oil field: http://www.rgvnewswire.com/wp-content/uploads/2014/12/energy-oil_rig-1.jpg

Cat attention: David CornejoHand icon: Irene HoffmanNetwork: Adam BeasleyBoxing gloves: Gabriele FumeroSummary icon: Stefan ParnarovLayer icon: MentaltoyBalance icon: Roman Kovbasyuk

Death symbol: Mila RedkoTeam icon: Joshua JonesMegaphone: Alex Auda SamoraSocial media chalk:mkhmarketing.wordpress.comflower: Nishanth Joiscables: jerry john

deer: Rob & Dawn ShrewsburyMoney sack: Lemon LiuNo: P.J. Onoridices: Drew Ellis3 arrows: Juan Pablo Bravo

evolution and ecology of the digital world

Science

osn evolution

summary outlookmodel

network models

entire topological evolutionof

modelaspl model x4gcc

pokecaspl pokec x4103

main underlying principle

new classof