1 Emergent Evolutionary Dynamics of Self-Reproducing Cellular Automata Chris Salzberg

1

Emergent Evolutionary Dynamics Emergent Evolutionary Dynamics of Self-Reproducing Cellular of Self-Reproducing Cellular

AutomataAutomata

Chris SalzbergChris Salzberg

Section Computational Science, Universiteit van AmsterdamSection Computational Science, Universiteit van Amsterdam

University of Electro-Communications, JapanUniversity of Electro-Communications, Japan 2

CreditsCredits

Research for this project fulfills requirements for theResearch for this project fulfills requirements for the

Master of Science Degree - Computational ScienceMaster of Science Degree - Computational Science

Universiteit van AmsterdamUniversiteit van Amsterdam

Project work conducted jointly with Project work conducted jointly with Antony AntonyAntony Antony (SCS)(SCS)

Supervised by Supervised by Dr. Hiroki SayamaDr. Hiroki Sayama

(University of Electro-Communications, Japan)(University of Electro-Communications, Japan)

Mentor: Prof. Dick van AlbadaMentor: Prof. Dick van Albada



Lecture PlanLecture Plan

I.I. Context & HistoryContext & HistoryII.II. Self-reproducing loops, the evoloopSelf-reproducing loops, the evoloopIII.III. A closer lookA closer look

a)a) New method of analysisNew method of analysisb)b) Genetic, phenotypic diversityGenetic, phenotypic diversity

IV.IV. New discoveriesNew discoveriesa)a) Mutation-insensitive regionsMutation-insensitive regionsb)b) Emergent selection, cyclic genealogyEmergent selection, cyclic genealogyc)c) The evoloop as quasi-speciesThe evoloop as quasi-species

V.V. ConclusionsConclusions



ContextContext

Artificial Life:Artificial Life: Study of ”life-as-it-could-be” (Langton).Study of ”life-as-it-could-be” (Langton). Emphasizes “bottom-up” approach:Emphasizes “bottom-up” approach:

synthesize using e.g. cellular automata (CA)synthesize using e.g. cellular automata (CA) study collective behaviour emerging from study collective behaviour emerging from

local interactions (complex systems)local interactions (complex systems)

Artificial self-reproduction:Artificial self-reproduction: ““abstract from the natural self-abstract from the natural self-

reproduction problem its logical form” reproduction problem its logical form” (von Neumann)(von Neumann)



A brief historyA brief history

John von NeumannJohn von Neumann

Conway’sConway’sGame of LifeGame of Life

1950s1950s

19701970 19841984

Langton’sLangton’sSR LoopSR Loop

First international First international conference onconference onArtificial LifeArtificial Life

19891989

Chou & ReggiaChou & Reggia(emergence of replicators)(emergence of replicators)

SayamaSayama(SDSR Loop, Evoloop)(SDSR Loop, Evoloop)

19961996

Morita & ImaiMorita & Imai(shape-encoding worms)(shape-encoding worms)

Suzuki & IkegamiSuzuki & Ikegami(interaction-based(interaction-based

evolution)evolution)

20032003

Imai, Hori, MoritaImai, Hori, Morita(3D self-reproduction)(3D self-reproduction)



Self-reproduction in BiologySelf-reproduction in Biology

Traditionally (pre-1950):Traditionally (pre-1950): Self-reproduction associated with biological Self-reproduction associated with biological

systems of carbon-based organisms.systems of carbon-based organisms. Research limited by variety of natural self-Research limited by variety of natural self-

replicators.replicators. Problem of machine self-replication discussed Problem of machine self-replication discussed

purely in philosophical terms.purely in philosophical terms.



Theory of self-reproductionTheory of self-reproduction

John von Neumann (1950s):John von Neumann (1950s): First attempt to First attempt to formalizeformalize self- self-

reproduction:reproduction: Theory of Self-Reproducing AutomataTheory of Self-Reproducing Automata Universal Constructor (UC)Universal Constructor (UC)

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

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



The Universal The Universal ConstructorConstructor

Universal Constructor Universal Constructor (1950s):(1950s): 29 state 5-neighbour 29 state 5-neighbour

cellular automaton.cellular automaton. Capable of universal Capable of universal

construction.construction. Predicts separation between Predicts separation between

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



Separation for evolutionSeparation for evolution

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

introduces inexact duplication (mutation).introduces inexact duplication (mutation).

P = P = r-b-r-yr-b-r-y

CC = r-b-y-y = r-b-y-y



UC-based replication: UC-based replication: LoopsLoops

Loop structure used to represent a Loop structure used to represent a cyclic set of instructions.cyclic set of instructions. Langton (SR Loop), Morita & Imai, Chou & Langton (SR Loop), Morita & Imai, Chou &

Reggia, Sayama, Sipper, Suzuki & IkegamiReggia, Sayama, Sipper, Suzuki & Ikegami Self-replication mechanism dependent Self-replication mechanism dependent

on structural configuration of self-on structural configuration of self-replicator.replicator.



The self-reproducing The self-reproducing looploop

Sheath: Outer shell housing gene sequence.Sheath: Outer shell housing gene sequence. Genes: 7s (straight growth) and 4s (turning).Genes: 7s (straight growth) and 4s (turning). Tube: core (1) states within sheath.Tube: core (1) states within sheath. Arm: extensible loop structure for Arm: extensible loop structure for

replication.replication.

sheathsheatharmarm

tubetube

genesgenes



The evolving SR loop The evolving SR loop (evoloop)(evoloop)

A new self-reproducing loop by Sayama A new self-reproducing loop by Sayama (1999), based on SR Loop (Langton, 1984):(1999), based on SR Loop (Langton, 1984): 9-state cellular automaton.9-state cellular automaton. 5-state (von Neumann) neighbourhood.5-state (von Neumann) neighbourhood.

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

Mutation mechanisms are Mutation mechanisms are emergentemergent..



Evolutionary dynamicsEvolutionary dynamics

Continuous reproduction leads to high-Continuous reproduction leads to high-density loop populationsdensity loop populations

Evolution ends with a homogeneous, Evolution ends with a homogeneous, single-species populationsingle-species population

Evolutionary dynamics seem predictable.Evolutionary dynamics seem predictable.

8

7

6

5

4



Hidden complexity?Hidden complexity?

Emergent evolutionary dynamics Emergent evolutionary dynamics demand sophisticated analysis routines.demand sophisticated analysis routines.

Original methods use size-based Original methods use size-based identification only.identification only.

Missing structural detail:Missing structural detail: gene arrangement and spacinggene arrangement and spacing genealogical ancestrygenealogical ancestry

Computational routines highly Computational routines highly expensive.expensive.



A closer lookA closer look

Loops composed of Loops composed of phenotype phenotype andand genotypegenotype:: PhenotypePhenotype: inner and outer sheath of loop: inner and outer sheath of loop GenotypeGenotype: gene sequence within loop: gene sequence within loop

Define loop species by phenotype + genotype.Define loop species by phenotype + genotype. Sufficient information for loop reconstruction.Sufficient information for loop reconstruction.

phenotypephenotypew

l

genotypegenotype



Parallels to biologyParallels to biology

The evoloop is a “messy” system:The evoloop is a “messy” system: replication is performed explicitlyreplication is performed explicitly mutation operator is emergentmutation operator is emergent interactions (collisions) produce “remnants” of inert interactions (collisions) produce “remnants” of inert

sheath states and anomalous dynamic structuressheath states and anomalous dynamic structures Birth and death must be externally defined.Birth and death must be externally defined.

remnantsremnantsdynamicdynamic

structuresstructures



Birth detectionBirth detection

Umbilical CordUmbilical CordDissolver (6)Dissolver (6)

phenotypephenotypew

l

genotypegenotype



Scan-layer trackingScan-layer tracking

Loop LayerLoop Layer

Scan LayerScan Layer

“footprint”

to parent loopto parent loop

umbilical cord dissolverumbilical cord dissolver



Death detectionDeath detection

Dissolver state

Scan layer I.D.



Labeling schemeLabeling scheme

G T C

growth turning core

G G G G C G C G T T G CC CC G

GGGGCGCGTTGCCCCG



How many permutations?How many permutations?

Constraints for exact (stable) self-replicators:Constraints for exact (stable) self-replicators: 2 2 TT-genes, -genes, nn GG-genes, (-genes, (nn-2) -2) CC-genes.-genes. TT-genes must have no -genes must have no GG-genes between them.-genes between them. Second Second TT-gene directly followed by -gene directly followed by G-G-gene.gene.

‘‘TG’TG’‘‘T’T’

n((nn-2) free ‘C’s-2) free ‘C’s

((nn-1) free ‘G’s-1) free ‘G’s



Genetic state-spaceGenetic state-space

For a loop of size For a loop of size nn, there are, there are different gene permutations resulting in exact different gene permutations resulting in exact self-replicators (stable species). self-replicators (stable species).

Do gene these permutations affect behaviour?Do gene these permutations affect behaviour?

(2n-2)(2n-2)n-2n-2( )

loop loop sizesize

# of # of speciesspecies

loop loop sizesize


loop loop sizesize


44 1515 99 11,44011,440 1414 9,657,7009,657,70055 5656 1010 43,75843,758 1515 37,442,16037,442,16066 210210 1111 167,960167,960 1616 145,422,67145,422,67

5577 792792 1212 646,646646,646 1717 565,722,72565,722,72

0088 3,0033,003 1313 2,496,1442,496,144 1818 2,203,961,42,203,961,4

3030



Phenotypic diversityPhenotypic diversity1000 2000 3000 4000

GCCCCGGGTTGG

GGGCGTTGCGCC

GGGGTTGCCCCG



Population dynamicsPopulation dynamics

GCCCCGGGTTGG

GGGCGTTGCGCC

GGGGTTGCCCCG

sizesize Gene sequenceGene sequence66 GGCCCCCCCCGGGGGGTTTTGGGG

77 GGCCCCGGGGGGCCGGTTTTGGCCCCGG

66 GGCCCCGGGGGGTTTTGGCCCCGG

55 GGGGCCGGTTTTGGCCCCGG

44 GGGGTTTTGGCCCCGG

44 GGGGTTTTGGCCGGCC

sizesize Gene sequenceGene sequence66 GGGGGGCCGGTTTTGGCCGGCCCC

44 GGCCGGTTTTGGCCGG

55 GGCCGGCCGGTTTTGGCCG G

sizesize Gene sequenceGene sequence66 GGGGGGGGTTTTGGCCCCCCCCGG55 GGGGGGTTTTGGCCCCCCGG44 GGGGTTTTGGCCGGCC55 GGGGCCGGTTTTGGCCGGCC44 GGGGTTTTGGCCCCG G



Emergent mutationEmergent mutation

GCCCCGGGTTGG GCCCCGGGTTGGGCCCCGGGTTGGGCCCC…

GTTGGGCCCCGGGCC GTTGGGCCCCGGGCGTTGGGCCCCG…

GGGCGTTGGGCC GGGCGTTGGGCCGGGCGTTGGGCCGGGCG…

GGCCGGGCGTTGCCCCGGCCGGGCGTTGCCGGCCGGGCGTTGCCG…

GCCGGGCGTTGCCG

(a)

(b)

(c)

(d)

(a)

(b)

(c)

(d)



Fitness landscapeFitness landscape

Evolution to both smaller Evolution to both smaller andand larger larger loops occurs.loops occurs.

Smaller loops dominate:Smaller loops dominate: higher reproductive ratehigher reproductive rate structurally robuststructurally robust

Fitness landscape balances size-Fitness landscape balances size-based fitness with genealogical based fitness with genealogical connectivity.connectivity.



Graph-based genealogyGraph-based genealogyL

oop

Si z

e



Mutation insensitive Mutation insensitive regionsregions

Certain gene subsequences are insensitive to Certain gene subsequences are insensitive to mutations:mutations:

GG{{CC}}TT{{CC}}TTGG These subsequences force a minimum loop These subsequences force a minimum loop

size.size. Evolution confined to non-overlapping subsets Evolution confined to non-overlapping subsets

of genealogy state-space.of genealogy state-space.

GGGGGGGGCCGGC C GGCCCCTTCCCCTTG GG G



New discoveriesNew discoveries

Long-term genetic diversity:Long-term genetic diversity: System continues to evolve over millions System continues to evolve over millions

of iterations.of iterations. Selection criteria not exclusively size-Selection criteria not exclusively size-

based for species with long subsequences.based for species with long subsequences. Complex evolutionary dynamics:Complex evolutionary dynamics:

Strong graph-based genealogy.Strong graph-based genealogy. Genealogical connectivity plays more Genealogical connectivity plays more

important role in selection.important role in selection.



Convergence to minimal Convergence to minimal looploop

SizeSize Gene sequenceGene sequence1414 GGGGGGGGCCGGGGGGG GGGGGGGG GTTCCCCCCCCCCCCCCCCCCCCCCTTG GG G1515 GGGGGGGGGGCCGGGGGGG GGGGGGGG GTTCCCCCCCCCCCCCCCCCCCCCCTTG G CCGG1616 GGGGGGGGGGGGCCGGGGGGG GGGGGGGG GTTCCCCCCCCCCCCCCCCCCCCCCTTG G CCCCGG1717 GGGGGGGGGGGGGGCCGGGGGGG GGGGGGGG GTTCCCCCCCCCCCCCCCCCCCCCCTTG G CCCCCCGG1515 GGGGGGGGCCGGGGGGGGGGGGGGGGC C GGTTCCCCCCCCCCCCCCCCCCCCCCTTG GG G1414 GGGGGGGGGGGGGGGGCCGGG GGGG GTTCCCCCCCCCCCCCCCCCCCCCCTTG GG G1515 GGGGGGGGGGGGGGGGCCGGGGGGGGC C GGTTCCCCCCCCCCCCCCCCCCCCCCTTG GG G1313 GGGGGGGGGG GGGGGGGGGGG GTTCCCCCCCCCCCCCCCCCCCCCCTTG GG G

11 22 33 44 55 66



Cyclic genealogyCyclic genealogy

SizeSize Gene sequenceGene sequence1818 GGGGGGGGGGGGGGG GGGGGGGGGGGGGGGG GCCCCCCTTCCCCCCCCCCCCCCCCCCCCCCCCCCTTG GG G1919 GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGCC G GCCCCCCTTCCCCCCCCCCCCCCCCCCCCCCCCCCTTG GG G1919 GGGGGGGGGGGGGGGG GGGGGGGGGGGGGGGGG GCCCCCCTTCCCCCCCCCCCCCCCCCCCCCCCCCCTTG G CCGG2020 GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGCC G GCCCCCCTTCCCCCCCCCCCCCCCCCCCCCCCCCCTTG G CCGG2020 GGGGGGGGGGGGGGGGG GGGGGGGGGGGGGGGGGG GCCCCCCTTCCCCCCCCCCCCCCCCCCCCCCCCCCTTG G CCCCGG2020 GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGCCGGCC G GCCCCCCTTCCCCCCCCCCCCCCCCCCCCCCCCCCTTG GG G2020 GGGGGGGGGGGGGGGGG GGGGGGGGGGGGGGGGGG GCCCCCCTTCCCCCCCCCCCCCCCCCCCCCCCCCCTTG G CCGGCC1919 GGGGGGGGGGGGGGGG GGGGGGGGGGGGGGGGG GCCCCCCTTCCCCCCCCCCCCCCCCCCCCCCCCCCTTG GG GCC2020 GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGCC G GCCCCCCTTCCCCCCCCCCCCCCCCCCCCCCCCCCTTG GG GCC



ObservationsObservations

Fitness landscape:Fitness landscape: fitness fitness reproduction rate reproduction rate genealogical connectivity (cycles) genealogical connectivity (cycles) self-generated environments self-generated environments

(remnants) ?(remnants) ? Stable state is reached with Stable state is reached with

dominant species + nearest relatives.dominant species + nearest relatives. Similar to “quasi-species” model of Similar to “quasi-species” model of

Eigen, McCaskill & Schuster (1988).Eigen, McCaskill & Schuster (1988).



ConclusionsConclusions

Simple models may hide their complexity:Simple models may hide their complexity: graph-based genealogygraph-based genealogy mutation-insensitive regionsmutation-insensitive regions emergent selection (self-generated env.)emergent selection (self-generated env.)

Sophisticated observation and Sophisticated observation and interpretation techniques play critical interpretation techniques play critical role.role.

Complex evolutionary phenomena need Complex evolutionary phenomena need not require a complex model.not require a complex model.

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1 Emergent Evolutionary Dynamics of Self-Reproducing Cellular Automata Chris Salzberg