Evolution and Ecology of the Digital World

Kaj Kolja
KLEINEBERG
Marián
BOGUÑÁ
@KoljaKleineberg
Universitat de Barcelona
kkl@ffn.ub.edu
EVOLUTION
and
Digital world
Ecology
of the

all digital services need
Attention
but our time is limited

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

Can we preserve
digital diversity?

Evolution of isolated networks

Motivation Evolution Ecology 2.0 Summary & Outlook
The topological evolution of large quasi-isolated OSN
exhibits a dynamical percolation transition
7

The topological evolution of large quasi-isolated OSN
exhibits a dynamical percolation transition
Dynamical percolation transition demands new class
of growing network models.
7

The pre-existing underlying social structure
forms the backbone of the evolution of the OSN
Online social
network layer
Traditional contact
network layer
Active
Online & offline
Passive
Online & offline
Susceptible
Only offline
8

The pre-existing underlying social structure
forms the backbone of the evolution of the OSN
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
8

Final snapshot of empirical network as proxy for
underlying structure allows rigorous model validation
Final
snapshot
Empirical
evolution
Extract
snapshots
Empirical
data
Model
evolution
Compare
Final
snapshot
9

Final snapshot of empirical network as proxy for
underlying structure allows rigorous model validation
Final
snapshot
Empirical
evolution
Extract
snapshots
Empirical
data
Model
evolution
Compare
Final
snapshot
Can we reproduce the entire topological evolution
of the empirical network?
9

Model precisely reproduces the entire topological evolution
and reveals balance between virality and media influence
Model results Parameters
GCC model
2nd comp. model
ASPL model x4
GCC Pokec
2nd comp. Pokec
ASPL Pokec x4
103
104
105
106
0
20
40
60
80
100
120
140
N
10

GCC model
2nd comp. model
ASPL model x4
GCC Pokec
2nd comp. Pokec
ASPL Pokec x4
103
104
105
106
0
20
40
60
80
100
120
140
N
Virality is about four times
stronger than mass media
10

GCC model
2nd comp. model
ASPL model x4
GCC Pokec
2nd comp. Pokec
ASPL Pokec x4
103
104
105
106
0
20
40
60
80
100
120
140
N
Virality is about four times
stronger than mass media
Interplay between virality and mass media dynamics
is the main underlying principle of the OSN evolution.
10

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
11

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 predicts the survival and death of online
social networks.
11

The microscopic picture reveals
the role of strong and weak ties
N
103
104 105
106
0.00
0.05
0.10
0.15
0.20
Clustering
Data
Tie strength:
i j
Transmissibility: λij ∝ λ [• + 1]η
12

The microscopic picture reveals
the role of strong and weak ties
N
103
104 105
106
0.00
0.05
0.10
0.15
0.20
Clustering
Data
Tie strength:
i j
Transmissibility: λij ∝ λ [• + 1]η
Individuals have a higher tendency to subscribe if
invited by weaker social contacts.
12

Evolution of the digital society reveals
balance between viral and mass media influence
Underlying social structure
determines topological
evolution
Balance
of viral and mass media
influence
Survival and death
of networks
Weak ties
have higher transmissibility
PRX 4, 031046, 2014
13

Gause's law impeding the coexistence of species competing
for the same unique resource 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

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

OSN 2
OSN 1
Underl.
network
Active
Passive
Susceptible
Partial
states}
Virality share
Distribution
between OSNs
λi = ωi(ρa)λ
16

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

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
Does rich-get-richer effect always lead to the
domination of a single network?
16

Nonlinear dynamics of network evolution can 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
]
Rich-get-richer: ωi = [ρa
i ]σ/
∑
j[ρa
j ]σ → σ activity affinity
17

Nonlinear dynamics of network evolution can 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
]
Rich-get-richer: ωi = [ρa
i ]σ/
∑
j[ρa
j ]σ → σ activity affinity
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

Maximum number of coexisting networks
is determined by 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

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
3 networks
2 networks
1 network
Stable configurations
18

Morelikelytoengage
inmoreactiveOSNs
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
18

Morelikelytoengage
inmoreactiveOSNs
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
Gause's law is violated as networks can coexist
despite rich-get-richer mechanism.
18

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

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
→ Effective critical lines for more networks saturate at
successively lower values σi,eff
c
19

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
→ Effective critical lines for more networks saturate at
successively lower values σi,eff
c
Even without precise knowledge of the empirical
parameters our theory predicts moderate diversity.
19

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

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

Ecological theory of the digital world explains why
we observe a moderate number of coexisting networks
Coexistence
despite
rich-get-richer
Moderate
observed diversity
Media effects
controls observed
diversity
arxiv:1410.8865, 2014
21

Multiscale theory of the digital world reveals
conditions for sustaining digital diversity
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, 2014 arxiv:1410.8865, 2014 To appear
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.

IMAGE CREDITS
Oil field: http://www.rgvnewswire.com/wp-content/uploads/2014/12/energy-oil_rig-1.jpg
Cat attention: David Cornejo
Hand icon: Irene Hoffman
Network: Adam Beasley
Boxing gloves: Gabriele Fumero
Summary icon: Stefan Parnarov
Layer icon: Mentaltoy
Balance icon: Roman Kovbasyuk
Death symbol: Mila Redko
Team icon: Joshua Jones
Megaphone: Alex Auda Samora
Social media chalk:
mkhmarketing.wordpress.com
flower: Nishanth Jois
cables: jerry john
deer: Rob & Dawn Shrewsbury
Money sack: Lemon Liu
No: P.J. Onori
dices: Drew Ellis
3 arrows: Juan Pablo Bravo
26

Evolution and Ecology of the Digital World

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