Emergent Evolutionary Dynamics

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.