1. I. Introduction II. Motivation III. Model IV. Results V. Summary
Extremal dynamics on dynamically changing networks with power-law weights
I. Introduction
II. Motivation
III. Model
IV. Results
V. Summary
Sungmin Lee, Yup Kim
Kyung Hee Univ.
이 연구는 학술진흥재단 기초과학 연구지원사업
(KRF C00185)의 지원을 받아 수행되었습니다.

2. I. Introduction The "punctuated equilibrium" theory
Instead of a slow, continuous movement, evolution
tends to be characterized by long periods of virtual
standstill ("equilibrium"), "punctuated" by episodes
of very fast development of new forms
S.J.Gould (1972)
Self-organized critical steady state

3. The Bak-Sneppen evolution model
P.Bak and K.sneppen
PRL 71,4083 (1993)
Fitness
- An entire species is represented by a single fitness
- The ability of species to survive
- The fitness of each species is affected by other
species to which it is coupled in the ecosystem.
Lowest fitness
PBC
0.2
0.3
0.15
0.4
0.45
0.7
0.9
0.35
0.1
0.55
0.75
0.5
0.8
0.65
0.6
0.25
At each time step, the
ecology is updated by
(i) locating the site with the
lowest fitness and mutating
it by assigning a new random
number to that site, and
(ii) changing the
landscapes of the two
neighbors by assigning
new random numbers to
those sites
0.2
0.3
0.15
0.4
0.45
0.7
0.9
0.95
0.47
0.22
0.75
0.5
0.8
0.65
0.6
0.25
New lowest fitness
Snapshot of
the stationary state
M.Paczuski, S.Maslov, P.Bak
PRE 53,414 (1996)

4. Gap, Critical fitness and avalanche
: The lowest fitness at step s
Avalanche
- subsequent sequences of mutations
through fitness below a certain threshold
Distribution of avalanche
sizes in the critical state 1d 2d
1.07(1)
1.245(10)

5. Summary of previous work
◆ Mean Field
◆ Random Network
◆ Scale-free Network

6. II. Motivation (1) Study for a characteristic
of evolution when the influence
strength or interacting structures
of biospecies are dynamically
changed with power-law weights.
(2) Are the structures changed
dynamically with power-law
weights still Scale-free network
in steady state?

7. III. Models lowest fitness remove links Choose update size
0.2
0.3
0.11
0.4
0.45
0.7
0.9
0.01
0.1
0.55
0.75
0.5
remove links
0.2
0.3
0.11
0.4
0.45
0.7
0.9
0.01
0.1
0.55
0.75
0.5
Choose update size
(number of links) from
0.2
0.3
0.11
0.4
0.15
0.47
0.29
0.21
0.8
0.51
0.28
0.5
reassign new links and new fitness
- 1d lattice with N sites (PBC)
- A random fitness equally distributed between 0 and 1, is assigned to each site.
- At each time step, the ecology is updated by
(i) locating the site i with the lowest fitness
(ii) removing its links
(ii) choosing the update size from power-law distritubion
(iii) connecting the site i with sites within the update size
(iv) reassign new random numbers to those sites and i.

8. IV. Results

12. V. Summary ◆ We study punctuated equilibrium
properties of Bak-Sneppen (BS)
model on two different one
dimensional geometric structures,
regular lattice and random network.
◆ We measure the critical fitness and avalanche size distribution.