Emergent Evolutionary Dynamics

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1 Δεκ 2013 (πριν από 3 χρόνια και 8 μήνες)

40 εμφανίσεις

1

Emergent Evolutionary Dynamics

of Self
-
Reproducing Cellular Automata

Chris Salzberg

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

2

Credits


Research for this project fulfills requirements for the

Master of Science Degree
-

Computational Science

Universiteit van Amsterdam


Project work conducted jointly with
Antony Antony

(SCS)

Supervised by
Dr. Hiroki Sayama

(University of Electro
-
Communications, Japan)


Mentor: Prof. Dick van Albada

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

3

Lecture Plan

I.
Context & History

II.
Self
-
reproducing loops, the evoloop

III.
A closer look

a)
New method of analysis

b)
Genetic, phenotypic diversity

IV.
New discoveries

a)
Mutation
-
insensitive regions

b)
Emergent selection, cyclic genealogy

c)
The evoloop as quasi
-
species

V.
Conclusions

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

4

Context


Artificial Life:


Study of ”life
-
as
-
it
-
could
-
be” (Langton).


Emphasizes “bottom
-
up” approach:


synthesize using e.g. cellular automata (CA)


study collective behaviour emerging from local
interactions (complex systems)


Artificial self
-
reproduction:


“abstract from the natural self
-
reproduction
problem its logical form” (von Neumann)

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

5

A brief history

John von Neumann

Conway’s

Game of Life

1950s

1970

1984

Langton’s

SR Loop

First international

conference on

Artificial Life

1989

Chou & Reggia

(emergence of replicators)

Sayama

(SDSR Loop, Evoloop)

1996

Morita & Imai

(shape
-
encoding worms)

Suzuki & Ikegami

(interaction
-
based

evolution)

2003

Imai, Hori, Morita

(3D self
-
reproduction)

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

6

Self
-
reproduction in Biology


Traditionally (pre
-
1950):


Self
-
reproduction associated with biological systems
of carbon
-
based organisms.


Research limited by variety of natural self
-
replicators.


Problem of machine self
-
replication discussed purely
in philosophical terms.

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

7

Theory of self
-
reproduction


John von Neumann (1950s):


First attempt to
formalize

self
-
reproduction:


Theory of Self
-
Reproducing Automata


Universal Constructor (UC)


Cellular Automata (CA) introduced (with S.
Ulam).


This seminal work later spawns the field
of Artificial Life (late 1980s).

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

8

The Universal Constructor


Universal Constructor
(1950s):


29 state 5
-
neighbour cellular
automaton.


Capable of universal
construction.


Predicts separation between
genetic information and
translators/transcribers prior to
discovery of DNA/RNA.

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

9

Separation for evolution


Separation is necessary for evolution:


Self
-
description enables exact duplication.


Modified self
-
description (by noise, etc.)
introduces inexact duplication (mutation).

P =
r
-
b
-
r
-
y

C

= r
-
b
-
y
-
y

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

10

UC
-
based replication: Loops


Loop structure used to represent a cyclic
set of instructions.


Langton (SR Loop), Morita & Imai, Chou &
Reggia, Sayama, Sipper, Suzuki & Ikegami


Self
-
replication mechanism dependent on
structural configuration of self
-
replicator.

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

11

The self
-
reproducing loop


Sheath: Outer shell housing gene sequence.


Genes: 7s (straight growth) and 4s (turning).


Tube: core (1) states within sheath.


Arm: extensible loop structure for replication.

sheath

arm

tube

genes

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

12

The evolving SR loop
(evoloop)


A new self
-
reproducing loop by Sayama
(1999), based on SR Loop (Langton, 1984):


9
-
state cellular automaton.


5
-
state (von Neumann) neighbourhood.


Modifications to earlier models (SR, SDSR)
enable adaptivity leading to evolution.


Mutation mechanisms are
emergent
.

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

13

Evolutionary dynamics


Continuous reproduction leads to high
-
density
loop populations


Evolution ends with a homogeneous, single
-
species population


Evolutionary dynamics seem predictable.

8

7

6

5

4

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

14

Hidden complexity?


Emergent evolutionary dynamics demand
sophisticated analysis routines.


Original methods use size
-
based
identification only.


Missing structural detail:


gene arrangement and spacing


genealogical ancestry


Computational routines highly expensive.

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

15

A closer look


Loops composed of
phenotype
and

genotype
:


Phenotype
: inner and outer sheath of loop


Genotype
: gene sequence within loop


Define loop species by phenotype + genotype.


Sufficient information for loop reconstruction.

phenotype

w

l

genotype

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

16

Parallels to biology


The evoloop is a “messy” system:


replication is performed explicitly


mutation operator is emergent


interactions (collisions) produce “remnants” of inert
sheath states and anomalous dynamic structures


Birth and death must be externally defined.

remnants

dynamic

structures

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

17

Birth detection

Umbilical Cord

Dissolver (6)

phenotype

w

l

genotype

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

18

Scan
-
layer tracking

Loop Layer

Scan Layer

“footprint”

to parent loop

umbilical cord dissolver

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

19

Death detection

Dissolver state

Scan layer I.D.

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

20

Labeling scheme


G

T

C

growth

turning

core

G

G

G

G

C

G

C

G

T

T

G

C

C

C

C

G

GGGG
C
G
C
G
TT
G
CCCC
G

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

21

How many permutations?


Constraints for exact (stable) self
-
replicators:


2
T
-
genes,
n

G
-
genes, (
n
-
2)
C
-
genes.


T
-
genes must have no
G
-
genes between them.


Second
T
-
gene directly followed by
G
-
gene.

‘TG’

‘T’

n

(
n
-
2) free ‘C’s

(
n
-
1) free ‘G’s

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

22

Genetic state
-
space


For a loop of size
n
, there are

different
gene permutations resulting in exact self
-
replicators (stable species).


Do gene these permutations affect behaviour?

(2n
-
2)

n
-
2

( )

loop
size

# of
species

loop
size

# of species

loop
size

# of species

4

15

9

11,440

14

9,657,700

5

56

10

43,758

15

37,442,160

6

210

11

167,960

16

145,422,675

7

792

12

646,646

17

565,722,720

8

3,003

13

2,496,144

18

2,203,961,43
0

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

23

Phenotypic diversity

1000

2000

3000

4000

G
CCCC
GGG
TT
GG

GGG
C
G
TT
G
C
G
CC

GGGG
TT
G
CCCC
G

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

24

Population dynamics

G
CCCC
GGG
TT
GG

GGG
C
G
TT
G
C
G
CC

GGGG
TT
G
CCCC
G

size

Gene sequence

6

G
CCCC
GGG
TT
GG

7


G
CC
GGG
C
G
TT
G
CC
G

6


G
CC
GGG
TT
G
CC
G

5


GG
C
G
TT
G
CC
G

4


GG
TT
G
CC
G

4


GG
TT
G
C
G
C

size

Gene sequence

6


GGG
C
G
TT
G
C
G
CC

4


G
C
G
TT
G
C
G

5

G
C
G
C
G
TT
G
C
G

size

Gene sequence

6


GGGG
TT
G
CCCC
G

5


GGG
TT
G
CCC
G

4


GG
TT
G
C
G
C

5


GG
C
G
TT
G
C
G
C

4


GG
TT
G
CC
G

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

25

Emergent mutation


G
CCCC
GGG
TT
GG


G
CCCC
GGG
TT
GGG
CCCC
GGG
TT
GGG
CCCC




G
TT
GGG
CCCC
GGG
C


G
TT
GGG
CCCC
GGG
C
G
TT
GGG
CCCC
G…



GGG
C
G
TT
GGG
CC


GGG
C
G
TT
GGGCCGGG
C
G
TT
GGG
CC
GGG
C
G…


GG
CC
GGG
C
G
TT
G
CC

GG
CC
GGG
C
G
TT
G
CC
GG
CC
GGG
C
G
TT
G
CC
G…



G
CC
GGG
C
G
TT
G
CC
G

(a)

(b)

(c)

(d)

(a)

(b)

(c)

(d)

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

26

Fitness landscape


Evolution to both smaller
and

larger loops
occurs.


Smaller loops dominate:


higher reproductive rate


structurally robust


Fitness landscape balances size
-
based
fitness with genealogical connectivity.

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

27

Graph
-
based genealogy

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

28

Mutation insensitive regions


Certain gene subsequences are insensitive to
mutations:

G
{
C
}
T
{
C
}
T
G


These subsequences force a minimum loop
size.


Evolution confined to non
-
overlapping subsets of
genealogy state
-
space.

GGGG
C
G
C
G
CC
T
CC
T
G G

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

29

New discoveries


Long
-
term genetic diversity:


System continues to evolve over millions of
iterations.


Selection criteria not exclusively size
-
based
for species with long subsequences.


Complex evolutionary dynamics:


Strong graph
-
based genealogy.


Genealogical connectivity plays more
important role in selection.

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

30

Convergence to minimal loop

Size

Gene sequence

14


GGGG
C
GGGGGGG G
T
CCCCCCCCCCC
T
G G

15


GGGGG
C
GGGGGGG G
T
CCCCCCCCCCC
T
G
C
G

16


GGGGGG
C
GGGGGGG G
T
CCCCCCCCCCC
T
G
CC
G

17


GGGGGGG
C
GGGGGGG G
T
CCCCCCCCCCC
T
G
CCC
G

15

GGGG
C
GGGGGGGG
C
G
T
CCCCCCCCCCC
T
G G

14


GGGGGGGG
C
GGG G
T
CCCCCCCCCCC
T
G G

15

GGGGGGGG
C
GGGG
C
G
T
CCCCCCCCCCC
T
G G

13


GGGGGGGGGG G
T
CCCCCCCCCCC
T
G G

1

2

3

4

5

6

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

31

Cyclic genealogy

Size

Gene sequence

18


GGGGGGGGGGGGGGG G
CCC
T
CCCCCCCCCCCCC
T
G
G

19


GGGGGGGGGGGGGGGG
C

G
CCC
T
CCCCCCCCCCCCC
T
G G

19


GGGGGGGGGGGGGGGG
G
CCC
T
CCCCCCCCCCCCC
T
G
C
G

20


GGGGGGGGGGGGGGGGG
C

G
CCC
T
CCCCCCCCCCCCC
T
G
C
G

20


GGGGGGGGGGGGGGGGG
G
CCC
T
CCCCCCCCCCCCC
T
G
CC
G

20

GGGGGGGGGGGGGGGG
C
G
C

G
CCC
T
CCCCCCCCCCCCC
T
G G

20


GGGGGGGGGGGGGGGGG
G
CCC
T
CCCCCCCCCCCCC
T
G
C
G
C

19


GGGGGGGGGGGGGGGG
G
CCC
T
CCCCCCCCCCCCC
T
G G
C

20


GGGGGGGGGGGGGGGGG
C

G
CCC
T
CCCCCCCCCCCCC
T
G G
C

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

32

Observations


Fitness landscape:


fitness


reproduction rate


genealogical connectivity (cycles)


self
-
generated environments (remnants) ?


Stable state is reached with dominant
species + nearest relatives.


Similar to “quasi
-
species” model of Eigen,
McCaskill & Schuster (1988).

Section Computational Science, Universiteit van Amsterdam

University of Electro
-
Communications, Japan

33

Conclusions


Simple models may hide their complexity:


graph
-
based genealogy


mutation
-
insensitive regions


emergent selection (self
-
generated env.)


Sophisticated observation and
interpretation techniques play critical role.


Complex evolutionary phenomena need
not require a complex model.