Emergent Evolutionary Dynamics of Self-Reproducing Cellular Automata

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Emergent Evolutionary Dynamics of
Self-Reproducing Cellular Automata

• Chris Salzberg

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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

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Lecture Plan

• Context History
• Self-reproducing loops, the evoloop
• A closer look
• New method of analysis
• Genetic, phenotypic diversity
• New discoveries
• Mutation-insensitive regions
• Emergent selection, cyclic genealogy
• The evoloop as quasi-species
• Conclusions

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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)

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A brief history
Chou Reggia (emergence of replicators)
Morita Imai (shape-encoding worms)
John von Neumann
Imai, Hori, Morita (3D self-reproduction)
2003
1970
1984
1989
1950s
1996
First international conference on Artificial Life
Suzuki Ikegami (interaction-based evolution)
Conways Game of Life
Langtons SR Loop
Sayama (SDSR Loop, Evoloop)
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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.

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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).

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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.

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Separation for evolution
P r-b-r-y
C r-b-y-y

• Separation is necessary for evolution
• Self-description enables exact duplication.
• Modified self-description (by noise, etc.)
  introduces inexact duplication (mutation).

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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.

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The self-reproducing loop
genes
sheath
arm
tube

• 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.

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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.

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Evolutionary dynamics
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• Continuous reproduction leads to high-density
  loop populations
• Evolution ends with a homogeneous, single-species
  population
• Evolutionary dynamics seem predictable.

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6
5
4
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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.

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A closer look
w
phenotype
l
genotype

• 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.

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Parallels to biology
remnants
dynamic structures

• 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.

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Birth detection
Umbilical Cord Dissolver (6)
phenotype
w
l
genotype
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Scan-layer tracking
umbilical cord dissolver
Loop Layer
to parent loop
Scan Layer
footprint
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Death detection
Dissolver state
Scan layer I.D.
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Labeling scheme
growth
turning
core
G
T
C
G
C
C
C
C
G
G
G
G
G
C
G
C
G
T
T
GGGGCGCGTTGCCCCG
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How many permutations?
(n-1) free Gs
TG
T
n
(n-2) free Cs

• 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.

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Genetic state-space
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 2,203,961,430

• For a loop of size n, there are different
  gene permutations resulting in exact
  self-replicators (stable species).
• Do gene these permutations affect behaviour?

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Phenotypic diversity
1000
2000
3000
4000
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Population dynamics
size Gene sequence
6 GCCCCGGGTTGG
7 GCCGGGCGTTGCCG
6 GCCGGGTTGCCG
5 GGCGTTGCCG
4 GGTTGCCG
4 GGTTGCGC
size Gene sequence
6 GGGCGTTGCGCC
4 GCGTTGCG
5 GCGCGTTGCG
size Gene sequence
6 GGGGTTGCCCCG
5 GGGTTGCCCG
4 GGTTGCGC
5 GGCGTTGCGC
4 GGTTGCCG
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Emergent mutation
GCCCCGGGTTGG GCCCCGGGTTGGGCCCCGGGTTGGGCCCC
GTTGGGCCCCGGGC GTTGGGCCCCGGGCGTTGGGCC
CCG GGGCGTTGGGCC GGGCGTTGGGCCGGGCGTTGGGC
CGGGCG GGCCGGGCGTTGCC GGCCGGGCGTTGCCGGCCGGGCGTTG
CCG GCCGGGCGTTGCCG
(a)
(a)
(b)
(b)
(c)
(c)
(d)
(d)
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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.

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Graph-based genealogy
Loop Size
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Mutation insensitive regions
GGGGCGC GCCTCCTG G

• Certain gene subsequences are insensitive to
  mutations
• GCTCTG
• These subsequences force a minimum loop size.
• Evolution confined to non-overlapping subsets of
  genealogy state-space.

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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.

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Convergence to minimal loop
1
2
3
4
5
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Size Gene sequence
14 GGGGCGGGGGGG GTCCCCCCCCCCCTG G
15 GGGGGCGGGGGGG GTCCCCCCCCCCCTG CG
16 GGGGGGCGGGGGGG GTCCCCCCCCCCCTG CCG
17 GGGGGGGCGGGGGGG GTCCCCCCCCCCCTG CCCG
15 GGGGCGGGGGGGGC GTCCCCCCCCCCCTG G
14 GGGGGGGGCGGG GTCCCCCCCCCCCTG G
15 GGGGGGGGCGGGGC GTCCCCCCCCCCCTG G
13 GGGGGGGGGG GTCCCCCCCCCCCTG G
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Cyclic genealogy
Size Gene sequence
18 GGGGGGGGGGGGGGG GCCCTCCCCCCCCCCCCCTG G
19 GGGGGGGGGGGGGGGGC GCCCTCCCCCCCCCCCCCTG G
19 GGGGGGGGGGGGGGGG GCCCTCCCCCCCCCCCCCTG CG
20 GGGGGGGGGGGGGGGGGC GCCCTCCCCCCCCCCCCCTG CG
20 GGGGGGGGGGGGGGGGG GCCCTCCCCCCCCCCCCCTG CCG
20 GGGGGGGGGGGGGGGGCGC GCCCTCCCCCCCCCCCCCTG G
20 GGGGGGGGGGGGGGGGG GCCCTCCCCCCCCCCCCCTG CGC
19 GGGGGGGGGGGGGGGG GCCCTCCCCCCCCCCCCCTG GC
20 GGGGGGGGGGGGGGGGGC GCCCTCCCCCCCCCCCCCTG GC
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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).

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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.