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.
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